100 doors

100 doors
You are encouraged to solve this task according to the task description, using any language you may know.

There are 100 doors in a row that are all initially closed.

You make 100 passes by the doors.

The first time through, visit every door and  toggle  the door  (if the door is closed,  open it;   if it is open,  close it).

The second time, only visit every 2^nd door   (door #2, #4, #6, ...),   and toggle it.

The third time, visit every 3^rd door   (door #3, #6, #9, ...), etc,   until you only visit the 100^th door.

Task

Answer the question:   what state are the doors in after the last pass?   Which are open, which are closed?

Alternate: As noted in this page's   discussion page,   the only doors that remain open are those whose numbers are perfect squares.

Opening only those doors is an   optimization   that may also be expressed; however, as should be obvious, this defeats the intent of comparing implementations across programming languages.

11l

Translation of: Python

V doors = [0B] * 100
L(i) 100
   L(j) (i .< 100).step(i + 1)
      doors[j] = !doors[j]
   print(‘Door ’(i + 1)‘: ’(I doors[i] {‘open’} E ‘close’))

360 Assembly

*        100 doors                 13/08/2015
HUNDOOR  CSECT
         USING  HUNDOOR,R12
         LR     R12,R15
         LA     R6,0
         LA     R8,1               step 1
         LA     R9,100
LOOPI    BXH    R6,R8,ELOOPI       do ipass=1 to 100 (R6)
         LR     R7,R6
         SR     R7,R6
         LR     R10,R6             step ipass
         LA     R11,100
LOOPJ    BXH    R7,R10,ELOOPJ      do idoor=ipass to 100 by ipass (R7)
         LA     R5,DOORS-1
         AR     R5,R7
         XI     0(R5),X'01'        doors(idoor)=not(doors(idoor))
NEXTJ    B      LOOPJ
ELOOPJ   B      LOOPI
ELOOPI   LA     R10,BUFFER         R10 address of the buffer
         LA     R5,DOORS           R5 address of doors item
         LA     R6,1               idoor=1 (R6)
         LA     R9,100             loop counter
LOOPN    CLI    0(R5),X'01'        if doors(idoor)=1
         BNE    NEXTN
         XDECO  R6,XDEC            idoor to decimal
         MVC    0(4,R10),XDEC+8    move decimal to buffer
         LA     R10,4(R10)
NEXTN	 LA     R6,1(R6)           idoor=idoor+1
         LA     R5,1(R5)
         BCT    R9,LOOPN           loop
ELOOPN   XPRNT  BUFFER,80
RETURN   XR     R15,R15
         BR     R14
DOORS    DC     100X'00'
BUFFER   DC     CL80' '
XDEC     DS     CL12
         YREGS
         END    HUNDOOR

Output:

   1   4   9  16  25  36  49  64  81 100

4DOS Batch

 
@echo off
set doors=%@repeat[C,100]
do step = 1 to 100
  do door = %step to 100 by %step
    set doors=%@left[%@eval[%door-1],%doors]%@if[%@instr[%@eval[%door-1],1,%doors]==C,O,C]%@right[%@eval[100-%door],%doors]
  enddo
enddo
 

The SET line consists of three functions:

 
%@left[n,string]                      ^: Return n leftmost chars in string
%@right[n,string]                     ^: Return n rightmost chars in string
%@if[condition,true-val,false-val]    ^: Evaluate condition; return true-val if true, false-val if false
 

Here @IF is used to toggle between C and O.

6502 Assembly

Works with: [www.6502asm.com] version beta

unoptimized Based on BASIC QB64 unoptimized version

; 100 DOORS in  6502 assembly language for: http://www.6502asm.com/beta/index.html
; Written for the original MOS Technology, Inc. NMOS version of the 6502, but should work with any version.
; Based on BASIC QB64 unoptimized version: http://rosettacode.org/wiki/100_doors#BASIC
;
; Notes:
;    Doors array[1..100] is at $0201..$0264. On the specified emulator, this is in video memory, so tbe results will 
; be directly shown as pixels in the display.
;    $0200 (door 0) is cleared for display purposes but is not involved in the open/close loops.
;    Y register holds Stride
;    X register holds Index
;    Zero Page address $01 used to add Stride to Index (via A) because there's no add-to-X or add-Y-to-A instruction.
 
  ; First, zero door array
    LDA #00
    LDX #100
Z_LOOP:
    STA 200,X
    DEX
    BNE Z_LOOP
    STA 200,X
 
  ; Now do doors repeated open/close
    LDY #01        ; Initial value of Stride
S_LOOP:
    CPY #101
    BCS S_DONE
    TYA            ; Initial value of Index
I_LOOP:
    CMP #101
    BCS I_DONE
    TAX            ; Use as Door array index
    INC $200,X     ; Toggle bit 0 to reverse state of door
    STY 01         ; Add stride (Y) to index (X, via A)
    ADC 01
    BCC I_LOOP
I_DONE:
    INY
    BNE S_LOOP
S_DONE:
 
  ; Finally, format array values for output: 0 for closed, 1 for open
    LDX #100
C_LOOP:
    LDA $200,X
    AND #$01
    STA $200,X
    DEX
    BNE C_LOOP

48. bytes of code; the specified emulator does not report cycles.

Works with: [6502asm.com] version 1.2

optimized Largely inspired by the optimized C implementation - makes use of the fact that finally only the doors whose numbers are squares of integers are open, as well as the fact that

$n^{2}=1+3+5+\ldots +(2n-1)$.

  ;assumes memory at $02xx is initially set to 0 and stack pointer is initialized
  ;the 1 to 100 door byte array will be at $0200-$0263 (decimal 512 to 611)
  ;Zero-page location $01 will hold delta
  ;At end, closed doors = $00, open doors = $01
 
start:    ldx #0        ;initialize index - first door will be at $200 + $0
          stx $1
          inc $1        ;start out with a delta of 1 (0+1=1)
openloop: inc $200,X    ;open X'th door
          inc $1        ;add 2 to delta
          inc $1
          txa           ;add delta to X by transferring X to A, adding delta to A, then transferring back to X
          clc           ;  clear carry before adding (6502 has no add-without-carry instruction)
          adc $1
          tax
          cpx #$64      ;check to see if we're at or past the 100th door (at $200 + $63)
          bmi openloop  ;jump back to openloop if less than 100

22. bytes of code; the specified emulator does not report cycles.

68000 Assembly

Works with: [EASy68K v5.13.00]

Some of the macro code is derived from the examples included with EASy68K.

*-----------------------------------------------------------
* Title      : 100Doors.X68
* Written by : G. A. Tippery
* Date       : 2014-01-17
* Description: Solves "100 Doors" problem, see: http://rosettacode.org/wiki/100_doors
* Notes      : Translated from C "Unoptimized" version, http://rosettacode.org/wiki/100_doors#unoptimized
*            : No optimizations done relative to C version; "for("-equivalent loops could be optimized.
*-----------------------------------------------------------
 
*
*   System-specific general console I/O macros (Sim68K, in this case)
*
PUTS    MACRO
    ** Print a null-terminated string w/o CRLF **
    ** Usage: PUTS stringaddress
    ** Returns with D0, A1 modified
        MOVEQ   #14,D0      ; task number 14 (display null string)
        LEA     \1,A1       ; address of string
        TRAP    #15         ; display it
        ENDM
*
PRINTN  MACRO
    ** Print decimal integer from number in register
    ** Usage: PRINTN register
    ** Returns with D0,D1 modified
        IFNC '\1','D1'      ;if some register other than D1
          MOVE.L \1,D1      ;put number to display in D1
        ENDC
        MOVE.B  #3,D0
        TRAP    #15         ;display number in D1
*
*   Generic constants
*
CR      EQU     13      ;ASCII Carriage Return
LF      EQU     10      ;ASCII Line Feed
 
*
*   Definitions specific to this program
*
*   Register usage:
*   D3 == pass (index)
*   D4 == door (index)
*   A2 == Doors array pointer
*
SIZE    EQU     100             ;Define a symbolic constant for # of doors
 
        ORG     $1000           ;Specify load address for program -- actual address system-specific
START:                          ; Execution starts here
        LEA     Doors,A2        ; make A2 point to Doors byte array
        MOVEQ   #0,D3
PassLoop:
        CMP     #SIZE,D3
        BCC     ExitPassLoop    ; Branch on Carry Clear - being used as Branch on Higher or Equal
        MOVE    D3,D4
DoorLoop:
        CMP     #SIZE,D4
        BCC     ExitDoorLoop
        NOT.B   0(A2,D4)
        ADD     D3,D4
        ADDQ    #1,D4
        BRA     DoorLoop
ExitDoorLoop:
        ADDQ    #1,D3
        BRA     PassLoop
ExitPassLoop:

* $28 = 40. bytes of code to this point. 32626 cycles so far.
*   At this point, the result exists as the 100 bytes starting at address Doors.
* To get output, we must use methods specific to the particular hardware, OS, or
* emulator system that the code is running on.  I use macros to "hide" some of the
* system-specific details; equivalent macros would be written for another system.
 
        MOVEQ   #0,D4
PrintLoop:
        CMP     #SIZE,D4
        BCC     ExitPrintLoop
        PUTS    DoorMsg1
        MOVE    D4,D1
        ADDQ    #1,D1           ; Convert index to 1-based instead of 0-based
        PRINTN  D1
        PUTS    DoorMsg2
        TST.B   0(A2,D4)        ; Is this door open (!= 0)?
        BNE     ItsOpen
        PUTS    DoorMsgC
        BRA     Next
ItsOpen:
        PUTS    DoorMsgO
Next:
        ADDQ    #1,D4
        BRA     PrintLoop
ExitPrintLoop:

*  What to do at end of program is also system-specific
        SIMHALT             ;Halt simulator
*
* $78 = 120. bytes of code to this point, but this will depend on how the I/O macros are actually written.
* Cycle count is nearly meaningless, as the I/O hardware and routines will dominate the timing.
 
*
*   Data memory usage
*
        ORG     $2000
Doors   DCB.B   SIZE,0      ;Reserve 100 bytes, prefilled with zeros
 
DoorMsg1 DC.B   'Door ',0
DoorMsg2 DC.B   ' is ',0
DoorMsgC DC.B   'closed',CR,LF,0
DoorMsgO DC.B   'open',CR,LF,0
 
        END     START       ;last line of source
 
 

8080 Assembly

page:	equ	2	; Store doors in page 2
doors:	equ	100	; 100 doors
puts:	equ	9	; CP/M string output
	org	100h
	xra	a	; Set all doors to zero
	lxi	h,256*page
	mvi	c,doors
zero:	mov	m,a
	inx	h
	dcr	c
	jnz	zero
	mvi	m,'$'	; CP/M string terminator (for easier output later)
	mov	d,a	; D=0 so that DE=E=pass counter
	mov	e,a	; E=0, first pass
	mvi	a,doors-1	; Last pass and door
pass:	mov	l,e	; L=door counter, start at first door in pass
door:	inr	m	; Incrementing always toggles the low bit
	dad	d	; Go to next door in pass
	inr	l
	cmp	l	; Was this the last door?
	jnc	door	; If not, do the next door
	inr	e	; Next pass
	cmp	e	; Was this the last pass?
	jnc	pass	; If not, do the next pass
	lxi	h,256*page
	mvi	c,doors	; Door counter
	lxi	d,130h	; D=1 (low bit), E=30h (ascii 0)
char:	mov	a,m	; Get door	
	ana	d	; Low bit gives door status
	ora	e	; ASCII 0 or 1
	mov	m,a	; Write character back
	inx	h	; Next door
	dcr	c	; Any doors left?
	jnz	char	; If so, next door
	lxi	d,256*page
	mvi	c,puts	; CP/M system call to print the string
	jmp	5

Output:

1001000010000001000000001000000000010000000000001000000000000001000000000000000010000000000000000001

8086 Assembly

See 100 doors/8086 Assembly

8th

 
\ Array of doors; init to empty; accessing a non-extant member will return
\ 'null', which is treated as 'false', so we don't need to initialize it:
[] var, doors    
 
\ given a door number, get the value and toggle it:
: toggle-door \ n --
	doors @ over a:@
	not rot swap a:! drop ;
 
\ print which doors are open:
: .doors
	( 
		doors @ over a:@ nip
		if . space else drop then
	) 1 100 loop ;
 
\ iterate over the doors, skipping 'n':
: main-pass \ n --
	0
	true
	repeat
		drop
		dup toggle-door
		over n:+
		dup 101 <
	while 2drop drop ;
 
\ calculate the first 100 doors:
' main-pass 1 100 loop
\ print the results:
.doors cr bye
 

Output:

1 4 9 16 25 36 49 64 81 100

AArch64 Assembly

Works with: as version Raspberry Pi 3B version Buster 64 bits

unoptimized

 
/* ARM assembly AARCH64 Raspberry PI 3B */
/*  program 100doors64.s   */
 
/*******************************************/
/* Constantes file                         */
/*******************************************/
/* for this file see task include a file in language AArch64 assembly*/
.include "../includeConstantesARM64.inc"
 
.equ NBDOORS,   100
/*********************************/
/* Initialized data              */
/*********************************/
.data
sMessResult:       .asciz "The door @ is open.\n"
 
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss  
stTableDoors:    .skip   8 * NBDOORS
sZoneConv:       .skip 24
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main 
main:                             // entry of program 
    // display first line
    ldr x3,qAdrstTableDoors       // table address
    mov x5,1             
1:
    mov x4,x5
2:                               // begin loop
    ldr x2,[x3,x4,lsl #3]        // read doors index x4
    cmp x2,#0
    cset x2,eq
    //moveq x2,#1                // if x2 = 0   1 -> x2
    //movne x2,#0                // if x2 = 1   0 -> x2
    str x2,[x3,x4,lsl #3]        // store value of doors
    add x4,x4,x5                 // increment x4 with  x5 value
    cmp x4,NBDOORS               // number of doors ?
    ble 2b                       // no -> loop
    add x5,x5,#1                 // increment the increment !!
    cmp x5,NBDOORS               // number of doors ?
    ble 1b                       // no -> loop
 
                                 // loop display state doors
    mov x4,#0              
3:
    ldr x2,[x3,x4,lsl #3]        // read state doors x4 index
    cmp x2,#0
    beq 4f
    mov x0,x4                    // open -> display message
    ldr x1,qAdrsZoneConv          // display value index
    bl conversion10              // call function
    ldr x0,qAdrsMessResult
    ldr x1,qAdrsZoneConv 
    bl strInsertAtCharInc        // insert result at first @ character
    bl affichageMess             // display message
4:
    add x4,x4,1
    cmp x4,NBDOORS
    ble 3b                       // loop
 
 
100:                             // standard end of the program 
    mov x0,0                     // return code
    mov x8,EXIT                  // request to exit program
    svc 0                        // perform the system call
 
qAdrstTableDoors:        .quad stTableDoors
qAdrsMessResult:         .quad sMessResult
qAdrsZoneConv:           .quad sZoneConv
/***********************************************/
/*        File Include fonctions                        */
/********************************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeARM64.inc"
 

optimized

 
/* ARM assembly AARCH64 Raspberry PI 3B */
/*  program 100doors64_1.s   */
 
/*******************************************/
/* Constantes file                         */
/*******************************************/
/* for this file see task include a file in language AArch64 assembly*/
.include "../includeConstantesARM64.inc"
 
.equ NBDOORS,   100
/*********************************/
/* Initialized data              */
/*********************************/
.data
sMessResult:       .asciz "The door @ is open.\n"
 
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss  
sZoneConv:        .skip 24
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main 
main:                             // entry of program 
 
    mov x5,3
    mov x4,1
1:
    mov x0,x4
    ldr x1,qAdrsZoneConv          // display value index
    bl conversion10              // call function
    ldr x0,qAdrsMessResult
    ldr x1,qAdrsZoneConv 
    bl strInsertAtCharInc        // insert result at first @ character
    bl affichageMess             // display message
    add x4,x4,x5
    add x5,x5,2
    cmp x4,NBDOORS
    ble 1b                       // loop
 
 
100:                             // standard end of the program 
    mov x0,0                     // return code
    mov x8,EXIT                  // request to exit program
    svc 0                        // perform the system call
 
qAdrsMessResult:         .quad sMessResult
qAdrsZoneConv:           .quad sZoneConv
/***********************************************/
/*        File Include fonctions                        */
/********************************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeARM64.inc"
 

ABAP

unoptimized

form open_doors_unopt.
  data: lv_door  type i,
        lv_count type i value 1.
  data: lt_doors type standard table of c initial size 100.
  field-symbols: <wa_door> type c.
  do 100 times.
    append initial line to lt_doors assigning <wa_door>.
    <wa_door> = 'X'.
  enddo.
 
  while lv_count < 100.
    lv_count = lv_count + 1.
    lv_door = lv_count.
    while lv_door < 100.
      read table lt_doors index lv_door assigning <wa_door>.
      if <wa_door> = ' '.
        <wa_door> = 'X'.
      else.
        <wa_door> = ' '.
      endif.
      add lv_count to lv_door.
    endwhile.
  endwhile.
 
  loop at lt_doors assigning <wa_door>.
    if <wa_door> = 'X'.
      write : / 'Door', (4) sy-tabix right-justified, 'is open' no-gap.
    endif.
  endloop.
endform.

unoptimized / functional

 
cl_demo_output=>display( REDUCE stringtab( INIT list TYPE stringtab
                                              aux TYPE i
                                          FOR door = 1 WHILE door <= 100
                                          FOR pass = 1 WHILE pass <= 100
                                         NEXT aux   = COND #( WHEN pass = 1 THEN 1
                                                              WHEN door MOD pass = 0 THEN aux + 1 ELSE aux  )
                                              list  = COND #( WHEN pass = 100
                                                                THEN COND #( WHEN aux MOD 2 <> 0 THEN VALUE #( BASE list ( CONV #( door ) ) )
                                                                              ELSE list ) ELSE list ) ) ).
 
 

optimized

Using $\sum _{i=1}^{n}(2i-1)=n^{2}$

form open_doors_opt.
  data: lv_square type i value 1,
        lv_inc    type i value 3.
  data: lt_doors  type standard table of c initial size 100.
  field-symbols: <wa_door> type c.
  do 100 times.
    append initial line to lt_doors assigning <wa_door>.
    if sy-index = lv_square.
      <wa_door> = 'X'.
      add: lv_inc to lv_square, 2 to lv_inc.
      write : / 'Door', (4) sy-index right-justified, 'is open' no-gap.
    endif.
  enddo.
endform.

ultra-optimized / imperative

 
DO 10 TIMES.
  DATA(val) = sy-index * sy-index.
  WRITE: / val.
ENDDO.
 

ultra-optimized / functional

 
cl_demo_output=>display( REDUCE stringtab( INIT list TYPE stringtab
                                          FOR i = 1 WHILE i <= 10
                                         NEXT list = VALUE #( BASE list ( i * i ) ) ) ).
 

ACL2

(defun rep (n x)
   (if (zp n)
       nil
       (cons x
             (rep (- n 1) x))))
 
(defun toggle-every-r (n i bs)
   (if (endp bs)
       nil
       (cons (if (zp i)
                 (not (first bs))
                 (first bs))
             (toggle-every-r n (mod (1- i) n) (rest bs)))))
 
(defun toggle-every (n bs)
   (toggle-every-r n (1- n) bs))
 
(defun 100-doors (i doors)
   (if (zp i)
       doors
       (100-doors (1- i) (toggle-every i doors))))

Action!

DEFINE COUNT="100"
 
PROC Main()
  BYTE ARRAY doors(COUNT+1)
  BYTE door,pass
 
  FOR door=1 TO COUNT
  DO
    doors(door)=0
  OD
 
  PrintE("Following doors are open:")
  FOR pass=1 TO COUNT
  DO
    FOR door=pass TO COUNT STEP pass
    DO
      doors(door)==!$FF
    OD
    IF doors(pass)=$FF THEN
      PrintB(pass) Put(32)
    FI
  OD
RETURN

Output:

Screenshot from Atari 8-bit computer

Following doors are open:
1 4 9 16 25 36 49 64 81 100

ActionScript

Works with: ActionScript version 3.0

unoptimized

package {                                                                                
    import flash.display.Sprite;                                              
 
    public class Doors extends Sprite {
        public function Doors() {
 
            // Initialize the array
            var doors:Array = new Array(100);
            for (var i:Number = 0; i < 100; i++) {
                doors[i] = false;
 
            // Do the work
            for (var pass:Number = 0; pass < 100; pass++) {
                for (var j:Number = pass; j < 100; j += (pass+1)) {
                    doors[j] = !doors[j];
                }
            }
            trace(doors);
        }
    }
}

Acurity Architect

Using #HASH-OFF, OPTION OICC ="^" , CICC ="^"

 
VAR sStatus: SHORT
VAR sArray: SHORT
VAR sCount: SHORT
VAR sDoor: SHORT
VAR sPass: SHORT
VAR zIndex: STRING
VAR zState: STRING
//
SET sStatus = GET_UNUSED_ARRAY_HANDLE(sArray)
SET sStatus = INIT_SORTED_ARRAY(sArray, 0, 0, 1)
//
DO sCount = 1 TO 100
  DO sPass = 1 TO 100
    SET sDoor = sCount * sPass
    IF sDoor <= 100
      SET zIndex = REPEAT("0", 3 - LENGTH(STR(sDoor))) + STR(sDoor)
      SET sStatus = READ_ARRAY_REC("=", sArray, zIndex)
      SET zState = "OPEN"
      IF GET_STRING_SAY(sArray, 1) = "OPEN"
        SET zState = "CLOSE"
      ENDIF
      //
      SET sStatus = ADD_ARRAY_REC(sArray, zIndex)
      SET sStatus = PUT_STRING_SAY(sArray, 1, zState)
    ELSE
      BREAK
    ENDIF
  ENDDO
ENDDO
//
SET zIndex = ""
SET sStatus = READ_ARRAY_REC(">=", sArray, zIndex)
DO WHILE sStatus = 0
  >>Door:  ^zIndex^  State: ^GET_STRING_SAY(sArray, 1)^
  SET sStatus = READ_ARRAY_REC("+", sArray, zIndex)
ENDDO
 

Output:

Door:  001  State: OPEN
Door:  002  State: CLOSE
Door:  003  State: CLOSE
Door:  004  State: OPEN
Door:  005  State: CLOSE
Door:  006  State: CLOSE
Door:  007  State: CLOSE
Door:  008  State: CLOSE
Door:  009  State: OPEN
Door:  010  State: CLOSE
Door:  011  State: CLOSE
Door:  012  State: CLOSE
Door:  013  State: CLOSE
Door:  014  State: CLOSE
Door:  015  State: CLOSE
Door:  016  State: OPEN
Door:  017  State: CLOSE
Door:  018  State: CLOSE
Door:  019  State: CLOSE
Door:  020  State: CLOSE
Door:  021  State: CLOSE
Door:  022  State: CLOSE
Door:  023  State: CLOSE
Door:  024  State: CLOSE
Door:  025  State: OPEN
Door:  026  State: CLOSE
Door:  027  State: CLOSE
Door:  028  State: CLOSE
Door:  029  State: CLOSE
Door:  030  State: CLOSE
Door:  031  State: CLOSE
Door:  032  State: CLOSE
Door:  033  State: CLOSE
Door:  034  State: CLOSE
Door:  035  State: CLOSE
Door:  036  State: OPEN
Door:  037  State: CLOSE
Door:  038  State: CLOSE
Door:  039  State: CLOSE
Door:  040  State: CLOSE
Door:  041  State: CLOSE
Door:  042  State: CLOSE
Door:  043  State: CLOSE
Door:  044  State: CLOSE
Door:  045  State: CLOSE
Door:  046  State: CLOSE
Door:  047  State: CLOSE
Door:  048  State: CLOSE
Door:  049  State: OPEN
Door:  050  State: CLOSE
Door:  051  State: CLOSE
Door:  052  State: CLOSE
Door:  053  State: CLOSE
Door:  054  State: CLOSE
Door:  055  State: CLOSE
Door:  056  State: CLOSE
Door:  057  State: CLOSE
Door:  058  State: CLOSE
Door:  059  State: CLOSE
Door:  060  State: CLOSE
Door:  061  State: CLOSE
Door:  062  State: CLOSE
Door:  063  State: CLOSE
Door:  064  State: OPEN
Door:  065  State: CLOSE
Door:  066  State: CLOSE
Door:  067  State: CLOSE
Door:  068  State: CLOSE
Door:  069  State: CLOSE
Door:  070  State: CLOSE
Door:  071  State: CLOSE
Door:  072  State: CLOSE
Door:  073  State: CLOSE
Door:  074  State: CLOSE
Door:  075  State: CLOSE
Door:  076  State: CLOSE
Door:  077  State: CLOSE
Door:  078  State: CLOSE
Door:  079  State: CLOSE
Door:  080  State: CLOSE
Door:  081  State: OPEN
Door:  082  State: CLOSE
Door:  083  State: CLOSE
Door:  084  State: CLOSE
Door:  085  State: CLOSE
Door:  086  State: CLOSE
Door:  087  State: CLOSE
Door:  088  State: CLOSE
Door:  089  State: CLOSE
Door:  090  State: CLOSE
Door:  091  State: CLOSE
Door:  092  State: CLOSE
Door:  093  State: CLOSE
Door:  094  State: CLOSE
Door:  095  State: CLOSE
Door:  096  State: CLOSE
Door:  097  State: CLOSE
Door:  098  State: CLOSE
Door:  099  State: CLOSE
Door:  100  State: OPEN

Ada

unoptimized

with Ada.Text_Io; use Ada.Text_Io;
 
 procedure Doors is
    type Door_State is (Closed, Open);
    type Door_List is array(Positive range 1..100) of Door_State;
    The_Doors : Door_List := (others => Closed);
 begin
    for I in 1..100 loop
       for J in The_Doors'range loop
          if J mod I = 0 then
             if The_Doors(J) = Closed then
                 The_Doors(J) := Open;
             else
                The_Doors(J) := Closed;
             end if;
          end if;
       end loop;
    end loop;
    for I in The_Doors'range loop
       Put_Line(Integer'Image(I) & " is " & Door_State'Image(The_Doors(I)));
    end loop;
 end Doors;

optimized

with Ada.Text_Io; use Ada.Text_Io;
 with Ada.Numerics.Elementary_Functions; use Ada.Numerics.Elementary_Functions;
 
 procedure Doors_Optimized is
    Num : Float;
 begin
    for I in 1..100 loop
       Num := Sqrt(Float(I));
       Put(Integer'Image(I) & " is ");
       if Float'Floor(Num) = Num then
          Put_Line("Opened");
       else
          Put_Line("Closed");
       end if;
    end loop;
 end Doors_Optimized;

Agena

Translation of Algol W. Tested with Agena 2.9.5 Win32

# find the first few squares via the unoptimised door flipping method
scope
 
    local doorMax := 100;
    local door;
    create register door( doorMax );
 
    # set all doors to closed
    for i to doorMax do door[ i ] := false od;
 
    # repeatedly flip the doors
    for i to doorMax do
        for j from i to doorMax by i do door[ j ] := not door[ j ] od
    od;
 
    # display the results
    for i to doorMax do if door[ i ] then write( " ", i ) fi od; print()
 
epocs

Aikido

 
var doors = new int [100]
 
foreach pass 100 {
    for (var door = pass ; door < 100 ; door += pass+1) {
        doors[door] = !doors[door]
    }
}
 
var d = 1
foreach door doors {
    println ("door " + d++ + " is " + (door ? "open" : "closed"))
 
}
 
 

ALGOL 60

Works with: A60

 
begin
 
comment - 100 doors problem in ALGOL-60;
 
boolean array doors[1:100];
integer i, j;
boolean open, closed;
 
open := true;
closed := not true;
 
outstring(1,"100 Doors Problem\n");
 
comment - all doors are initially closed;
for i := 1 step 1 until 100 do
  doors[i] := closed;
 
comment
  cycle through at increasing intervals
  and flip each door encountered;
for i := 1 step 1 until 100 do
  for j := i step i until 100 do
    doors[j] := not doors[j];
 
comment - show which doors are open; 
outstring(1,"The open doors are:");
for i := 1 step 1 until 100 do
  if doors[i] then
     outinteger(1,i);
 
end
 

Output:

100 Doors Problem
The open doors are: 1  4  9  16  25  36  49  64  81  100

ALGOL 68

unoptimized

# declare some constants #
INT limit = 100;
 
PROC doors = VOID:
(
  MODE DOORSTATE = BOOL;
  BOOL closed = FALSE;
  BOOL open = NOT closed;
  MODE DOORLIST = [limit]DOORSTATE;
 
  DOORLIST the doors;
  FOR i FROM LWB the doors TO UPB the doors DO the doors[i]:=closed OD;
 
  FOR i FROM LWB the doors TO UPB the doors DO
    FOR j FROM LWB the doors TO UPB the doors DO
      IF j MOD i = 0 THEN
        the doors[j] :=  NOT the doors[j]
      FI
    OD
  OD;
  FOR i FROM LWB the doors TO UPB the doors DO
    printf(($g" is "gl$,i,(the doors[i]|"opened"|"closed")))
  OD
);
doors;

optimized

PROC doors optimised = ( INT limit )VOID:
  FOR i TO limit DO
    REAL num := sqrt(i);
    printf(($g" is "gl$,i,(ENTIER num = num |"opened"|"closed") ))
  OD
;
doors optimised(limit)

ALGOL W

begin
    % find the first few squares via the unoptimised door flipping method   %
 
    integer doorMax;
    doorMax := 100;
 
    begin
        % need to start a new block so the array can have variable bounds   %
 
        % array of doors - door( i ) is true if open, false if closed       %
        logical array door( 1 :: doorMax );
 
        % set all doors to closed                                           %
        for i := 1 until doorMax do door( i ) := false;
 
        % repeatedly flip the doors                                         %
        for i := 1 until doorMax
        do begin
            for j := i step i until doorMax
            do begin
                door( j ) := not door( j )
            end
        end;
 
        % display the results                                               %
        i_w := 1; % set integer field width                                 %
        s_w := 1; % and separator width                                     %
        for i := 1 until doorMax do if door( i ) then writeon( i )
 
    end
 
end.

Output:

 1 4 9 16 25 36 49 64 81 100 

ALGOL-M

 
BEGIN
 
INTEGER ARRAY DOORS[1:100];
INTEGER I, J, OPEN, CLOSED;
 
OPEN := 1;
CLOSED := 0;
 
% ALL DOORS ARE INITIALLY CLOSED %
FOR I := 1 STEP 1 UNTIL 100 DO
  BEGIN
    DOORS[I] := CLOSED;
  END;
 
% PASS THROUGH AT INCREASING INTERVALS AND FLIP %
FOR I := 1 STEP 1 UNTIL 100 DO
  BEGIN
     FOR J := I STEP I UNTIL 100 DO
       BEGIN
         DOORS[J] := 1 - DOORS[J];
       END;
  END;
 
% SHOW RESULTS %
WRITE("THE OPEN DOORS ARE:");
WRITE("");
FOR I := 1 STEP 1 UNTIL 100 DO
  BEGIN
    IF DOORS[I] = OPEN THEN
      WRITEON(I);
  END;
 
END 

Output:

THE OPEN DOORS ARE:
     1     4     9    16    25    36    49    64    81   100

AmigaE

PROC main()
  DEF t[100]: ARRAY,
      pass, door
  FOR door := 0 TO 99 DO t[door] := FALSE
  FOR pass := 0 TO 99
    door := pass
    WHILE door <= 99
      t[door] := Not(t[door])
      door := door + pass + 1
    ENDWHILE
  ENDFOR
  FOR door := 0 TO 99 DO WriteF('\d is \s\n', door+1,
                                IF t[door] THEN 'open' ELSE 'closed')
ENDPROC

APL

Works with: GNU APL

doors←{100⍴((⍵-1)⍴0),1}
≠⌿⊃doors¨ ⍳100

Output:

1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 
      0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
      0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

optimized Note that ⎕IO = 1

2|+/[1]0=D∘.|D←⍳100

The idea is that the n:th door will be flipped the same number of times as there are divisors for n. So first we make D all ints 1..100 (D←⍳100).
The next step is to find the remainders of every such int when divided by every other (D∘.|D).
This results in a 100×100 matrix which we turn into a binary one by testing if the values are equal to zero i.e. divisors.
Next: sum along axis 1, i.e. the columns. This tells us the number of divisors. Finally calculate the remainder of these when divided by 2, i.e. find which n have an odd number of divisors, i.e. will be flipped an odd number of times and thus end up open.

Works with: Dyalog APL

 
⍝⍝ Also works with GNU APL after introduction of
⍝⍝ the ⍸ function with SVN r1368, Dec 03 2020
⍸≠⌿0=(⍳100)∘.|⍳100

Output:

1 4 9 16 25 36 49 64 81 100

AppleScript

Iteration

set is_open to {}
repeat 100 times
   set end of is_open to false
end
repeat with pass from 1 to 100
  repeat with door from pass to 100 by pass
    set item door of is_open to not item door of is_open
  end
end
set open_doors to {}
repeat with door from 1 to 100
   if item door of is_open then
     set end of open_doors to door
   end
end
set text item delimiters to ", "
display dialog "Open doors: " & open_doors

Functional composition

-- FINAL DOOR STATES ---------------------------------------------------------
 
-- finalDoors :: Int -> [(Int, Bool)]
on finalDoors(n)
 
    -- toggledCorridor :: [(Int, Bool)] -> (Int, Bool) -> Int -> [(Int, Bool)]
    script toggledCorridor
        on |λ|(a, _, k)
 
            -- perhapsToggled :: Bool -> Int -> Bool
            script perhapsToggled
                on |λ|(x, i)
                    if i mod k = 0 then
                        {i, not item 2 of x}
                    else
                        {i, item 2 of x}
                    end if
                end |λ|
            end script
 
            map(perhapsToggled, a)
        end |λ|
    end script
 
    set xs to enumFromTo(1, n)
 
    foldl(toggledCorridor, ¬
        zip(xs, replicate(n, {false})), xs)
end finalDoors
 
-- TEST ----------------------------------------------------------------------
on run
    -- isOpenAtEnd :: (Int, Bool) -> Bool
    script isOpenAtEnd
        on |λ|(door)
            (item 2 of door)
        end |λ|
    end script
 
    -- doorNumber :: (Int, Bool) -> Int
    script doorNumber
        on |λ|(door)
            (item 1 of door)
        end |λ|
    end script
 
    map(doorNumber, filter(isOpenAtEnd, finalDoors(100)))
 
    --> {1, 4, 9, 16, 25, 36, 49, 64, 81, 100}
end run
 
 
-- GENERIC FUNCTIONS ---------------------------------------------------------
 
-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
    if n < m then
        set d to -1
    else
        set d to 1
    end if
    set lst to {}
    repeat with i from m to n by d
        set end of lst to i
    end repeat
    return lst
end enumFromTo
 
-- filter :: (a -> Bool) -> [a] -> [a]
on filter(f, xs)
    tell mReturn(f)
        set lst to {}
        set lng to length of xs
        repeat with i from 1 to lng
            set v to item i of xs
            if |λ|(v, i, xs) then set end of lst to v
        end repeat
        return lst
    end tell
end filter
 
-- foldl :: (a -> b -> a) -> a -> [b] -> a
on foldl(f, startValue, xs)
    tell mReturn(f)
        set v to startValue
        set lng to length of xs
        repeat with i from 1 to lng
            set v to |λ|(v, item i of xs, i, xs)
        end repeat
        return v
    end tell
end foldl
 
-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
    tell mReturn(f)
        set lng to length of xs
        set lst to {}
        repeat with i from 1 to lng
            set end of lst to |λ|(item i of xs, i, xs)
        end repeat
        return lst
    end tell
end map
 
-- min :: Ord a => a -> a -> a
on min(x, y)
    if y < x then
        y
    else
        x
    end if
end min
 
-- Lift 2nd class handler function into 1st class script wrapper 
-- mReturn :: Handler -> Script
on mReturn(f)
    if class of f is script then
        f
    else
        script
            property |λ| : f
        end script
    end if
end mReturn
 
-- replicate :: Int -> a -> [a]
on replicate(n, a)
    set out to {}
    if n < 1 then return out
    set dbl to {a}
 
    repeat while (n > 1)
        if (n mod 2) > 0 then set out to out & dbl
        set n to (n div 2)
        set dbl to (dbl & dbl)
    end repeat
    return out & dbl
end replicate
 
-- zip :: [a] -> [b] -> [(a, b)]
on zip(xs, ys)
    set lng to min(length of xs, length of ys)
    set lst to {}
    repeat with i from 1 to lng
        set end of lst to {item i of xs, item i of ys}
    end repeat
    return lst
end zip

Output:

{1, 4, 9, 16, 25, 36, 49, 64, 81, 100}

Odd numbers of integer factors

The question of which doors are flipped an odd number of times reduces to the question of which numbers in the range have an odd number of integer factors (for an AppleScript implementation of integerFactors(n) see Factors of An Integer). Using map from the functional composition example above:

map(factorCountMod2, enumFromTo(1, 100))
 
on factorCountMod2(n)
    {n, (length of integerFactors(n)) mod 2 = 1}
end factorCountMod2

This, on inspection, and further reflection, then collapses to the even simpler question of which numbers are perfect squares, since all other numbers have an even number of integer factors (n factors below the square root, plus n paired cofactors above the square root). Using map and enumFromTo from the functional composition example above:

-- perfectSquaresUpTo :: Int -> [Int]
on perfectSquaresUpTo(n)
    script squared
        -- (Int -> Int)
        on |λ|(x)
            x * x
        end |λ|
    end script
 
    set realRoot to n ^ (1 / 2)
    set intRoot to realRoot as integer
    set blnNotPerfectSquare to not (intRoot = realRoot)
 
    map(squared, enumFromTo(1, intRoot - (blnNotPerfectSquare as integer)))
end perfectSquaresUpTo
 
on run
 
    perfectSquaresUpTo(100)
 
end run

Output:

{1, 4, 9, 16, 25, 36, 49, 64, 81, 100}

Arbre

 
openshut(n):
  for x in [1..n]
    x%n==0
 
pass(n):
  if n==100
    openshut(n)
  else
    openshut(n) xor pass(n+1)
 
100doors():
  pass(1) -> io
 

Argile

use std, array
 
close all doors
for each pass from 1 to 100
  for (door = pass) (door <= 100) (door += pass)
    toggle door
 
let int pass, door.
 
.: close all doors :. {memset doors 0 size of doors}
.:toggle <int door>:. {    !!(doors[door - 1])     }
 
let doors be an array of 100 bool
 
for each door from 1 to 100
  printf "#%.3d %s\n" door (doors[door - 1]) ? "[ ]", "[X]"

ARM Assembly

Works with: as version Raspberry Pi

unoptimized

 
 
/* ARM assembly Raspberry PI  */
/*  program 100doors.s   */
 
/************************************/
/* Constantes                       */
/************************************/
.equ STDOUT, 1                                 @ Linux output console
.equ EXIT,   1                                 @ Linux syscall
.equ WRITE,  4                                 @ Linux syscall
.equ NBDOORS,   100
/*********************************/
/* Initialized data              */
/*********************************/
.data
sMessResult:       .ascii "The door "
sMessValeur:       .fill 11, 1, ' '            @ size => 11
                      .asciz "is open.\n"
 
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss  
stTableDoors:	.skip   4 * NBDOORS
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main 
main:                                         @ entry of program 
    push {fp,lr}                              @ saves 2 registers 
    @ display first line
    ldr r3,iAdrstTableDoors                   @ table address
    mov r5,#1            
1:
    mov r4,r5
2:                                            @ begin loop
    ldr r2,[r3,r4,lsl #2]                     @ read doors index r4
    cmp r2,#0
    moveq r2,#1                               @ if r2 = 0   1 -> r2
    movne r2,#0                               @ if r2 = 1   0 -> r2
    str r2,[r3,r4,lsl #2]                     @ store value of doors
    add r4,r5                                 @ increment r4 with  r5 value
    cmp r4,#NBDOORS                           @ number of doors ?
    ble 2b                                    @ no -> loop
    add r5,#1                                 @ increment the increment !!
    cmp r5,#NBDOORS                           @ number of doors ?
    ble 1b                                    @ no -> loop
 
                                              @ loop display state doors
    mov r4,#0              
3:
    ldr r2,[r3,r4,lsl #2]                     @ read state doors r4 index
    cmp r2,#0
    beq 4f
    mov r0,r4                                 @ open -> display message
    ldr r1,iAdrsMessValeur                    @ display value index
    bl conversion10                           @ call function
    ldr r0,iAdrsMessResult
    bl affichageMess                          @ display message
4:
    add r4,#1
    cmp r4,#NBDOORS
    ble 3b                                    @ loop
 
 
100:                                          @ standard end of the program 
    mov r0, #0                                @ return code
    pop {fp,lr}                               @restaur 2 registers
    mov r7, #EXIT                             @ request to exit program
    svc #0                                    @ perform the system call
 
iAdrsMessValeur:                .int sMessValeur
iAdrstTableDoors:		.int stTableDoors
iAdrsMessResult:		.int sMessResult
 
/******************************************************************/
/*     display text with size calculation                         */ 
/******************************************************************/
/* r0 contains the address of the message */
affichageMess:
    push {r0,r1,r2,r7,lr}                     @ save  registres
    mov r2,#0                                 @ counter length 
1:                                            @ loop length calculation 
    ldrb r1,[r0,r2]                           @ read octet start position + index 
    cmp r1,#0                                 @ if 0 its over 
    addne r2,r2,#1                            @ else add 1 in the length 
    bne 1b                                    @ and loop 
                                              @ so here r2 contains the length of the message 
    mov r1,r0        			      @ address message in r1 
    mov r0,#STDOUT      		      @ code to write to the standard output Linux 
    mov r7, #WRITE                            @ code call system "write" 
    svc #0                                    @ call systeme 
    pop {r0,r1,r2,r7,lr}                      @ restaur des  2 registres */ 
    bx lr                                     @ return  
/******************************************************************/
/*     Converting a register to a decimal unsigned                */ 
/******************************************************************/
/* r0 contains value and r1 address area   */
/* r0 return size of result (no zero final in area) */
/* area size => 11 bytes          */
.equ LGZONECAL,   10
conversion10:
    push {r1-r4,lr}                            @ save registers 
    mov r3,r1
    mov r2,#LGZONECAL
 
1:	                                       @ start loop
    bl divisionpar10U                          @unsigned  r0 <- dividende. quotient ->r0 reste -> r1
    add r1,#48                                 @ digit	
    strb r1,[r3,r2]                            @ store digit on area
    cmp r0,#0                                  @ stop if quotient = 0 
    subne r2,#1                                @ else previous position
    bne 1b	                               @ and loop
    // and move digit from left of area
    mov r4,#0
2:
    ldrb r1,[r3,r2]
    strb r1,[r3,r4]
    add r2,#1
    add r4,#1
    cmp r2,#LGZONECAL
    ble 2b
    // and move spaces in end on area
    mov r0,r4                                 @ result length 
    mov r1,#' '                               @ space	
3:
    strb r1,[r3,r4]                           @ store space in area
    add r4,#1                                 @ next position
    cmp r4,#LGZONECAL
    ble 3b                                    @ loop if r4 <= area size
 
100:
    pop {r1-r4,lr}                            @ restaur registres 
    bx lr                                     @return
 
/***************************************************/
/*   division par 10   unsigned                    */
/***************************************************/
/* r0 dividende   */
/* r0 quotient */	
/* r1 remainder  */
divisionpar10U:
    push {r2,r3,r4, lr}
    mov r4,r0                                        @ save value
    //mov r3,#0xCCCD                                 @ r3 <- magic_number  lower   @ for Raspberry pi 3
    //movt r3,#0xCCCC                                @ r3 <- magic_number  upper   @ for Raspberry pi 3
    ldr r3,iMagicNumber                              @ for Raspberry pi 1 2
    umull r1, r2, r3, r0                             @ r1<- Lower32Bits(r1*r0) r2<- Upper32Bits(r1*r0) 
    mov r0, r2, LSR #3                               @ r2 <- r2 >> shift 3
    add r2,r0,r0, lsl #2                             @ r2 <- r0 * 5 
    sub r1,r4,r2, lsl #1                             @ r1 <- r4 - (r2 * 2)  = r4 - (r0 * 10)
    pop {r2,r3,r4,lr}
    bx lr                                            @ leave function 
iMagicNumber:            .int 0xCCCCCCCD
 

optimized

 
/*********************************************/
/* optimized version                         */
/*********************************************/
/* ARM assembly Raspberry PI  */
/*  program 100doors.s   */
 
/************************************/
/* Constantes                       */
/************************************/
.equ STDOUT, 1     @ Linux output console
.equ EXIT,   1     @ Linux syscall
.equ WRITE,  4     @ Linux syscall
.equ NBDOORS,   100
/*********************************/
/* Initialized data              */
/*********************************/
.data
sMessResult:       .ascii "The door "
sMessValeur:       .fill 11, 1, ' '                 @ size => 11
                   .asciz "is open.\n"
 
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss  
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main 
main:                                               @ entry of program 
    push {fp,lr}                                    @ saves 2 registers 
                                                    @ display first line
    mov r5,#3                                       @ start value of increment
    mov r4,#1                                       @ start doors
                                                    @ loop display state doors
1:
    mov r0,r4                                       @ open -> display message
    ldr r1,iAdrsMessValeur                          @ display value index
    bl conversion10                                 @ call function
    ldr r0,iAdrsMessResult
    bl affichageMess                                @ display message
    add r4,r5                                       @ add increment
    add r5,#2                                       @ new increment
    cmp r4,#NBDOORS
    ble 1b                                          @ loop
 
 
100:   @ standard end of the program 
    mov r0, #0                                      @ return code
    pop {fp,lr}                                     @ restaur 2 registers
    mov r7, #EXIT                                   @ request to exit program
    svc #0                                          @ perform the system call
 
iAdrsMessValeur:                .int sMessValeur
iAdrsMessResult:		.int sMessResult
 
/******************************************************************/
/*     display text with size calculation                         */ 
/******************************************************************/
/* r0 contains the address of the message */
affichageMess:
    push {r0,r1,r2,r7,lr}                           @ save  registres
    mov r2,#0                                       @ counter length 
1:                                                  @ loop length calculation 
    ldrb r1,[r0,r2]                                 @ read octet start position + index 
    cmp r1,#0                                       @ if 0 its over 
    addne r2,r2,#1                                  @ else add 1 in the length 
    bne 1b                                          @ and loop 
                                                    @ so here r2 contains the length of the message 
    mov r1,r0        			            @ address message in r1 
    mov r0,#STDOUT      		            @ code to write to the standard output Linux 
    mov r7, #WRITE                                  @ code call system "write" 
    svc #0                                          @ call systeme 
    pop {r0,r1,r2,r7,lr}                            @ restaur des  2 registres */ 
    bx lr                                           @ return  
/******************************************************************/
/*     Converting a register to a decimal unsigned                */ 
/******************************************************************/
/* r0 contains value and r1 address area   */
/* r0 return size of result (no zero final in area) */
/* area size => 11 bytes          */
.equ LGZONECAL,   10
conversion10:
    push {r1-r4,lr}                                 @ save registers 
    mov r3,r1
    mov r2,#LGZONECAL
 
1:	                                            @ start loop
    bl divisionpar10U                               @ unsigned  r0 <- dividende. quotient ->r0 reste -> r1
    add r1,#48                                      @ digit	
    strb r1,[r3,r2]                                 @ store digit on area
    cmp r0,#0                                       @ stop if quotient = 0 
    subne r2,#1                                     @ else previous position
    bne 1b	                                    @ and loop
                                                    @ and move digit from left of area
    mov r4,#0
2:
    ldrb r1,[r3,r2]
    strb r1,[r3,r4]
    add r2,#1
    add r4,#1
    cmp r2,#LGZONECAL
    ble 2b
                                                    @ and move spaces in end on area
    mov r0,r4                                       @ result length 
    mov r1,#' '                                     @ space	
3:
    strb r1,[r3,r4]                                 @ store space in area
    add r4,#1                                       @ next position
    cmp r4,#LGZONECAL
    ble 3b                                          @ loop if r4 <= area size
 
100:
    pop {r1-r4,lr}                                  @ restaur registres 
    bx lr                                           @return
 
/***************************************************/
/*   division par 10   unsigned                    */
/***************************************************/
/* r0 dividende   */
/* r0 quotient */	
/* r1 remainder  */
divisionpar10U:
    push {r2,r3,r4, lr}
    mov r4,r0                                       @ save value
    //mov r3,#0xCCCD                                @ r3 <- magic_number  lower   @ for raspberry 3
    //movt r3,#0xCCCC                               @ r3 <- magic_number  upper   @ for raspberry 3
    ldr r3,iMagicNumber                             @ for raspberry 1 2
    umull r1, r2, r3, r0                            @ r1<- Lower32Bits(r1*r0) r2<- Upper32Bits(r1*r0) 
    mov r0, r2, LSR #3                              @ r2 <- r2 >> shift 3
    add r2,r0,r0, lsl #2                            @ r2 <- r0 * 5 
    sub r1,r4,r2, lsl #1                            @ r1 <- r4 - (r2 * 2)  = r4 - (r0 * 10)
    pop {r2,r3,r4,lr}
    bx lr                                           @ leave function 
iMagicNumber:            .int 0xCCCCCCCD
 

Arturo

isOpen: map 1..101 => false
 
loop 1..100 'pass ->
	loop (range.step:pass pass 100) 'door [
		isOpen\[door]: not? isOpen\[door]
	]
 
loop 1..100 'x ->
	if isOpen\[x] [
		print ["Door" x "is open."]
	]

Output:

Door 1 is open. 
Door 4 is open. 
Door 9 is open. 
Door 16 is open. 
Door 25 is open. 
Door 36 is open. 
Door 49 is open. 
Door 64 is open. 
Door 81 is open. 
Door 100 is open.

Astro

var doors = falses(100)
 
for a in 1..100: for b in a..a..100:
    doors[b] = not doors[b]
 
for a in 1..100:
    print "Door $a is ${(doors[a]) ? 'open.': 'closed.'}"
 

Asymptote

for(int i = 1; i < 100; ++i) {
    if (i % i^2 < 11)  {
      write("Door ", i^2, suffix=none);
      write(" is open");
    }
  }

ATS

 
#include "share/atspre_staload.hats"
 
implement
main0((*void*)) = let
//
var A = @[bool][100](false)
val A = $UNSAFE.cast{arrayref(bool,100)}([email protected])
//
fnx
loop
(
  pass: intGte(0)
) : void =
  if pass < 100
    then loop2 (pass, pass)
  // end of [if]
and
loop2
(
  pass: natLt(100), door: intGte(0)
) : void =
  if door < 100
    then (A[door] := ~A[door]; loop2(pass, door+pass+1))
    else loop(pass+1)
  // end of [if]
//
fun
loop3
(
  door: intGte(0)
) : void =
  if door < 100
    then (
      println!("door #", door+1, " is ", (if A[door] then "open" else "closed"): string, ".");
      loop3(door+1)
    ) (* end of [then] *)
  // end of [if]
//
in
  loop(0); loop3 (0)
end // end of [main0]
 

AutoHotkey

Standard Approach

Loop, 100
  Door%A_Index% := "closed"
 
Loop, 100 {
  x := A_Index, y := A_Index
  While (x <= 100)
  {
    CurrentDoor := Door%x%
    If CurrentDoor contains closed
    {
      Door%x% := "open"
      x += y
    }
    else if CurrentDoor contains open
    {
      Door%x% := "closed"
      x += y
    }
  }
}
 
Loop, 100 {
   CurrentDoor := Door%A_Index%
   If CurrentDoor contains open
      Res .= "Door " A_Index " is open`n"
}
MsgBox % Res

Alternative Approach

Making use of the identity:

$\sum _{i=1}^{n}(2i-1)=n^{2}$

increment := 3, square := 1 
Loop, 100 
    If (A_Index = square) 
        outstring .= "`nDoor " A_Index " is open" 
        ,square += increment, increment += 2 
MsgBox,, Succesfull, % SubStr(outstring, 2)

Optimized

While (Door := A_Index ** 2) <= 100
   Result .= "Door " Door " is open`n"
MsgBox, %Result%

AutoIt

 
#include <array.au3>
$doors = 100
 
;door array, 0 = closed, 1 = open
Local $door[$doors +1]
 
For $ii = 1 To $doors
	For $i = $ii To $doors Step $ii
		$door[$i] = Not $door[$i]
	next
Next
 
;display to screen
For $i = 1 To $doors
	ConsoleWrite (Number($door[$i])& " ")
	If Mod($i,10) = 0 Then ConsoleWrite(@CRLF)
Next
 

AWK

unoptimized

BEGIN {
  for(i=1; i <= 100; i++)
  {
    doors[i] = 0 # close the doors
  }
  for(i=1; i <= 100; i++)
  {
    for(j=i; j <= 100; j += i)
    {
      doors[j] = (doors[j]+1) % 2
    }
  }
  for(i=1; i <= 100; i++)
  {
    print i, doors[i] ? "open" : "close"
  }
}

optimized

BEGIN {
  for(i=1; i <= 100; i++) {
    doors[i] = 0 # close the doors
  }
  for(i=1; i <= 100; i++) {
    if ( int(sqrt(i)) == sqrt(i) ) {
      doors[i] = 1
    }
  }
  for(i=1; i <= 100; i++)
  {
    print i, doors[i] ? "open" : "close"
  }
}

Axiom

Unoptimized:

(open,closed,change,open?) := (true,false,not,test);
doors := bits(100,closed);
for i in 1..#doors repeat
  for j in i..#doors by i repeat
    doors.j := change doors.j
[i for i in 1..#doors | open? doors.i]
 

Optimized:

[i for i in 1..100 | perfectSquare? i] -- or
[i^2 for i in 1..sqrt(100)::Integer]

B

Works with: The Amsterdam Compiler Kit - B version V6.1pre1

main()
{
  auto doors[100]; /* != 0 means open */
  auto pass, door;
 
  door = 0;
  while( door<100 ) doors[door++] = 0;
 
  pass = 0;
  while( pass<100 )
  {
    door = pass;
    while( door<100 )
    {
      doors[door] = !doors[door];
      door =+ pass+1;
    }
    ++pass;
  }
 
  door = 0;
  while( door<100 )
  {
    printf("door #%d is %s.*n", door+1, doors[door] ? "open" : "closed");
    ++door;
  }
 
  return(0);
}

BaCon

 
OPTION BASE 1
 
DECLARE doors[100]
 
FOR size = 1 TO 100
    FOR pass = 0 TO 100 STEP size
	doors[pass] = NOT(doors[pass])
    NEXT
NEXT
 
FOR which = 1 TO 100
    IF doors[which] THEN PRINT which
NEXT
 

Output:

1
4
9
16
25
36
49
64
81
100

BASIC

Applesoft BASIC

Based on the Sinclair ZX81 BASIC implementation.

 
 100 :
 110  REM  100 DOORS PROBLEM
 120 :
 130  DIM D(100)
 140  FOR P = 1 TO 100
 150  FOR T = P TO 100 STEP P
 160  D(T) =  NOT D(T): NEXT T
 170  NEXT P
 180  FOR I = 1 TO 100
 190  IF D(I) THEN  PRINT I;" ";
 200  NEXT I
 

Output:

                                        
]RUN
1 4 9 16 25 36 49 64 81 100

BASIC256

# 100 doors problem
dim d(100)
 
# simple solution
print "simple solution"
gosub initialize
for t = 1 to 100
   for j = t to 100 step t
      d[j-1] = not d[j-1]
   next j
next t
gosub showopen
 
# more optimized solution
print "more optimized solution"
gosub initialize
for t = 1 to 10
      d[t^2-1] = true
next t
gosub showopen
end
 
initialize:
for t = 1 to d[?]
   d[t-1] = false	 # closed
next t
return
 
showopen:
for t = 1 to d[?]
   print d[t-1]+ " ";
   if t%10 = 0 then print
next t
return

ultra optimizado: portado desde la versión Julia

 
for i = 1 to 10 : if i % i^2 < 11 then print "La puerta "; int(i^2); " esta abierta" : end if : next i : end
 

Commodore BASIC

Based on the Sinclair ZX81 BASIC implementation.

10 DIM D(100)
20 FOR I=1 TO 100
30 FOR J=I TO 100 STEP I
40 D(J) = NOT D(J)
50 NEXT J
60 NEXT I
70 FOR I=1 TO 100
80 IF D(I) THEN PRINT I,
90 NEXT I

IS-BASIC

100 PROGRAM "100doors.bas"
110 NUMERIC D(1 TO 100)
120 FOR I=1 TO 100
130   LET D(I)=0
140 NEXT
150 FOR I=1 TO 100
160   FOR J=I TO 100 STEP I
170     LET D(J)=NOT D(J)
180   NEXT 
190 NEXT
200 FOR I=1 TO 100
210   IF D(I) THEN PRINT I
220 NEXT

Optimized:

100 PROGRAM "100doors.bas"
110 LET NR=1:LET D=3
120 DO
130   PRINT NR
140   LET NR=NR+D:LET D=D+2
150 LOOP WHILE NR<=100

QBasic

Works with: QBASIC, QB64

unoptimized

REM "100 Doors" program FOR QB64 BASIC (http://www.qb64.net/), a QuickBASIC-like compiler.
REM Author: G. A. Tippery
REM Date: 12-Feb-2014
REM
REM   Unoptimized (naive) version, per specifications at http://rosettacode.org/wiki/100_doors
 
DEFINT A-Z
CONST N = 100
DIM door(N)
 
FOR stride = 1 TO N
    FOR index = stride TO N STEP stride
        LET door(index) = NOT (door(index))
    NEXT index
NEXT stride
 
PRINT "Open doors:"
FOR index = 1 TO N
    IF door(index) THEN PRINT index
NEXT index
 
END

Works with: QuickBasic version 4.5

unoptimized

DIM doors(0 TO 99)
FOR pass = 0 TO 99
	FOR door = pass TO 99 STEP pass + 1
		PRINT doors(door)
		PRINT NOT doors(door)
		doors(door) = NOT doors(door)
	NEXT door
NEXT pass
FOR i = 0 TO 99
	PRINT "Door #"; i + 1; " is ";
	IF NOT doors(i) THEN
		PRINT "closed"
	ELSE
		PRINT "open"
	END IF
NEXT i

optimized

DIM doors(0 TO 99)
FOR door = 0 TO 99
	IF INT(SQR(door)) = SQR(door) THEN doors(door) = -1
NEXT door
FOR i = 0 TO 99
	PRINT "Door #"; i + 1; " is ";
	IF NOT doors(i) THEN
		PRINT "closed"
	ELSE
		PRINT "open"
	END IF
NEXT i

Sinclair ZX81 BASIC

Works with only 1k of RAM, although it doesn't leave too much to play with.

10 DIM D(100)
20 FOR I=1 TO 100
30 FOR J=I TO 100 STEP I
40 LET D(J)=NOT D(J)
50 NEXT J
60 NEXT I
70 FOR I=1 TO 100
80 IF D(I) THEN PRINT I,
90 NEXT I

MSX Basic

Based on the Sinclair ZX81 BASIC implementation.

 
10 DIM D(100)
20 FOR I=1 TO 100
30 FOR J=i TO 100 STEP I
40 D(J)=NOT D(J)
50 NEXT J
60 NEXT I
70 FOR I=1 TO 100
80 IF D(I) THEN PRINT I;
90 NEXT I
100 END
 

Output:

                                        
]RUN
1 4 9 16 25 36 49 64 81 100

Batch File

unoptimized

 
@echo off
setlocal enableDelayedExpansion
:: 0 = closed
:: 1 = open
:: SET /A treats undefined variable as 0
:: Negation operator ! must be escaped because delayed expansion is enabled
for /l %%p in (1 1 100) do for /l %%d in (%%p %%p 100) do set /a "door%%d=^!door%%d"
for /l %%d in (1 1 100) do if !door%%d!==1 (
  echo door %%d is open
) else echo door %%d is closed
 

optimized

 
@echo off
setlocal enableDelayedExpansion
set /a square=1, incr=3
for /l %%d in (1 1 100) do (
  if %%d neq !square! (echo door %%d is closed) else (
    echo door %%d is open
    set /a square+=incr, incr+=2
  )
)
 

BBC BASIC

DIM doors%(100)
FOR pass% = 1 TO 100
    FOR door% = pass% TO 100 STEP pass%
        doors%(door%) = NOT doors%(door%)
    NEXT door%
NEXT pass%      
FOR door% = 1 TO 100
    IF doors%(door%) PRINT "Door " ; door% " is open"
NEXT door%

bc

/* 0 means door is closed, 1 means door is open */
for (i = 0; i < 100; i++) {
    for (j = i; j < 100; j += (i + 1)) {
        d[j] = 1 - d[j]     /* Toggle door */
    }
}
 
"Open doors:
"
for (i = 0; i < 100; i++) {
    if (d[i] == 1) (i + 1)
}

BCPL

get "libhdr"
 
let start() be 
$(  let doors = vec 100
 
    // close all doors
    for n = 1 to 100 do doors!n := 0
 
    // make 100 passes
    for pass = 1 to 100 do
    $(  let n = pass
        while n <= 100 do
        $(  doors!n := ~doors!n
            n := n + pass
        $)
    $)
 
    // report which doors are open
    for n = 1 to 100 do
        if doors!n then
            writef("Door %N is open.*N", n)
$)

Output:

Door 1 is open.
Door 4 is open.
Door 9 is open.
Door 16 is open.
Door 25 is open.
Door 36 is open.
Door 49 is open.
Door 64 is open.
Door 81 is open.
Door 100 is open.

Befunge

Befunge-93

Unoptimized

Requires an interpreter with working read-write memory support. Padding the code page with extra blank lines can sometimes help.

>"d">:00p1-:>:::9%\9/9+g2%!\:9v
$.v_^#!$::$_^#`"c":+g00p+9/9\%<
::<[email protected]#`$:\*:+55:+1p27g1g+9/9\%9
 

Optimized

Just calculates the first 10 perfect squares.

1+:::*.9`#@_
 

Befunge-98

Works with: CCBI version 2.1

108p0>:18p;;>:9g!18g9p08g]
*`!0\|+relet|-1`*aap81::+]
;::+1<r]!g9;>$08g1+:08paa[
*`#@_^._aa

Blade

Unoptimized version

var doors = [false] * 100
for i in 0..100 {
  iter var j = i; j < 100; j += i + 1 {
    doors[j] = !doors[j]
  }
  var state = doors[i] ? 'open' : 'closed'
  echo 'Door ${i + 1} is ${state}'
}

Optimized version

for i in 1..101 {
  echo 'Door ${i} is ${i ** 0.5 % 1 > 0 ? "closed" : "open"}'
}

Ultra-optimized version

for i in 1..11 echo 'Door ${i**2} is open'

BlitzMax

Works with: BlitzMax version 1.37

optimized

Graphics 640,480
i=1
While ((i*i)<=100)
	a$=i*i
	DrawText a$,10,20*i
	Print i*i
	i=i+1 
Wend
Flip 
WaitKey 

BlooP

The currently available BlooP interpreters don't really allow iterating over cells with any level of ease, so instead I loop over each door in turn, running it through all 100 cycles and toggling it when it is a multiple of the step number.

 
DEFINE PROCEDURE ''DIVIDE'' [A,B]:
BLOCK 0: BEGIN
  IF A < B, THEN:
    QUIT BLOCK 0;
  CELL(0) <= 1;
  OUTPUT <= 1;
  LOOP AT MOST A TIMES:
  BLOCK 2: BEGIN
    IF OUTPUT * B = A, THEN:
    QUIT BLOCK 0;
    OUTPUT <= OUTPUT + 1;
    IF OUTPUT * B > A, THEN:
    BLOCK 3: BEGIN
      OUTPUT <= CELL(0);
      QUIT BLOCK 0;
    BLOCK 3: END;
    CELL(0) <= OUTPUT;
  BLOCK 2: END;
BLOCK 0: END.
 
DEFINE PROCEDURE ''MINUS'' [A,B]:
BLOCK 0: BEGIN
  IF A < B, THEN:
    QUIT BLOCK 0;
  LOOP AT MOST A TIMES:
  BLOCK 1: BEGIN
    IF OUTPUT + B = A, THEN:
      QUIT BLOCK 0;
    OUTPUT <= OUTPUT + 1;
  BLOCK 1: END;
BLOCK 0: END.
 
DEFINE PROCEDURE ''MODULUS'' [A,B]:
BLOCK 0: BEGIN
  CELL(0) <= DIVIDE[A,B];
  OUTPUT <= MINUS[A,CELL(0) * B];
BLOCK 0: END.
 
 
 
DEFINE PROCEDURE ''TOGGLE'' [DOOR]:
BLOCK 0: BEGIN
  IF DOOR = 1, THEN:
    QUIT BLOCK 0;
  OUTPUT <= 1;
BLOCK 0: END.
 
DEFINE PROCEDURE ''NUMBERS'' [DOOR, COUNT]:
BLOCK 0: BEGIN
  CELL(0) <= 1; /*each number*/
  OUTPUT <= 0; /*current door state*/
 
  LOOP COUNT TIMES:
  BLOCK 1: BEGIN
 
    IF MODULUS[DOOR, CELL(0)] = 0, THEN:
      OUTPUT <= TOGGLE[OUTPUT];
 
    CELL(0) <= CELL(0) + 1;
 
  BLOCK 1: END;
 
BLOCK 0: END.
 
DEFINE PROCEDURE ''DOORS'' [COUNT]:
BLOCK 0: BEGIN
 
  CELL(0) <= 1; /*each door*/
  LOOP COUNT TIMES:
  BLOCK 1: BEGIN
 
    CELL(1) <= NUMBERS[CELL(0), COUNT];  /*iterate over the states of this door to get its final state*/
    IF CELL(1) = 1, THEN: /*door state = open*/
      PRINT[CELL(0), '   '];
 
    CELL(0) <= CELL(0) + 1;
 
  BLOCK 1: END;
BLOCK 0: END.
 
DOORS[100];
 

Output:

 > 1   
 > 4   
 > 9   
 > 16   
 > 25   
 > 36   
 > 49   
 > 64   
 > 81   
 > 100   

Bracmat

Bracmat is not really at home in tasks that involve addressing things by index number. Here are four solutions that each do the task, but none should win a price for cleanliness.

Solution 1. Use an indexable array. Local variables are stored in stacks. Each stack corresponds to one variable name and vice versa. Stacks can also be used as arrays, but because of how local variables are implemented, arrays cannot be declared as local variables.

( 100doors-tbl
=   door step
  .   tbl$(doors.101) { Create an array. Indexing is 0-based. Add one extra for addressing element nr. 100 }
    & 0:?step
    &   whl
      ' ( 1+!step:~>100:?step   { ~> means 'not greater than', i.e. 'less than or equal' }
        & 0:?door
        &   whl
          ' ( !step+!door:~>100:?door
            & 1+-1*!(!door$doors):?doors  { <number>$<variable> sets the current index, which stays the same until explicitly changed. }
            )
        )
    & 0:?door
    &   whl
      ' ( 1+!door:~>100:?door
        &   out
          $ ( door
              !door
              is
              ( !(!door$doors):1&open
              | closed
              )
            )
        )
    & tbl$(doors.0)  { clean up the array }
)

Solution 2. Use one variable for each door. In Bracmat, a variable name can be any non-empty string, even a number, so we use the numbers 1 .. 100 as variable names, but also as door numbers. When used as variable an extra level of indirection is needed. See the occurrences of ?! and !! in the following code.

( 100doors-var
=   step door
  .   0:?door
    &   whl
      ' ( 1+!door:~>100:?door
        & closed:?!door { this creates a variable and assigns a value 'closed' to it }
        )
    & 0:?step
    &   whl
      ' ( 1+!step:~>100:?step
        & 0:?door
        &   whl
          ' ( !step+!door:~>100:?door
            &   ( !!door:closed&open
                | closed
                )
              : ?!door   
            )
        )
    & 0:?door
    &   whl
      ' ( 1+!door:~>100:?door
        & out$(door !door is !!door)
        )
    & 0:?door
    &   whl
      ' ( 1+!door:~>100:?door
        & tbl$(!door.0)         { cleanup the variable }
        )
)

Solution 3. Use a list and a dedicated positioning pattern to address the right door in the list. Create a new list by concatenating the skipped elements with the toggled elements. This solution is computationally unfavourable because of the many concatenations.

( 100doors-list
=   doors door doorIndex step
  .   :?doors
    & 0:?door
    &   whl
      ' ( 1+!door:~>100:?door
        & closed !doors:?doors
        )
    & 0:?skip
    &   whl
      ' ( :?ndoors
        &   whl
          ' ( !doors:?skipped [!skip %?door ?doors  { the [<number> pattern only succeeds when the scanning cursor is at position <number> }
            &     !ndoors
                  !skipped
                  ( !door:open&closed
                  | open
                  )
              : ?ndoors
            )
        & !ndoors !doors:?doors
        & 1+!skip:<100:?skip
        )
    & out$!doors
)

Solution 4. Use a list of objects. Each object can be changed without the need to re-create the whole list.

( 100doors-obj
=   doors door doorIndex step
  .   :?doors
    & 0:?door
    &   whl
      ' ( 1+!door:~>100:?door
        & new$(=closed) !doors:?doors
        )
    & 0:?skip
    &   whl
      ' ( !doors:?tododoors
        &   whl
          ' ( !tododoors:? [!skip %?door ?tododoors
            &   ( !(door.):open&closed
                | open
                )
              : ?(door.)
            )
        & 1+!skip:<100:?skip
        )
    & out$!doors
)

These four functions are called in the following way:

100doors-tbl$
& 100doors-var$
& 100doors-list$
& 100doors-obj$;

Burlesque

Version using square numbers:

 
blsq ) 10ro2?^
{1 4 9 16 25 36 49 64 81 100}
 

BQN

swch ← ≠´{100⥊1«𝕩⥊0}¨1+↕100
¯1↓∾{𝕩∾@+10}¨•Fmt¨⟨swch,/swch⟩

"⟨ 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⟩
⟨ 0 3 8 15 24 35 48 63 80 99 ⟩"

swch uses an idea similar to the GNU APL solution to generate a boolean array of the correct switches.

The second line then formats the boolean array and the truthy indices into a string for display.

Try it here!

C

unoptimized

Uses: C Runtime (Components:printf,)

#include <stdio.h>
 
int main()
{
  char is_open[100] = { 0 };
  int pass, door;
 
  /* do the 100 passes */
  for (pass = 0; pass < 100; ++pass)
    for (door = pass; door < 100; door += pass+1)
      is_open[door] = !is_open[door];
 
  /* output the result */
  for (door = 0; door < 100; ++door)
    printf("door #%d is %s.\n", door+1, (is_open[door]? "open" : "closed"));
 
  return 0;
}

Using defensive programming, pointers, sentinel values and some other standard programming practices,

Uses: C Runtime (Components:printf,)

#include <stdio.h>
 
#define NUM_DOORS 100
 
int main(int argc, char *argv[])
{
  int is_open[NUM_DOORS] = { 0 } ;
  int * doorptr, * doorlimit = is_open + NUM_DOORS ;
  int pass ;
 
  /* do the N passes, go backwards because the order is not important */
  for ( pass= NUM_DOORS ; ( pass ) ; -- pass ) {
    for ( doorptr= is_open + ( pass-1 ); ( doorptr < doorlimit ) ; doorptr += pass ) {
      ( * doorptr ) ^= 1 ;
    }
  }
 
  /* output results */
  for ( doorptr= is_open ; ( doorptr != doorlimit ) ; ++ doorptr ) {
    printf("door #%lld is %s\n", ( doorptr - is_open ) + 1, ( * doorptr ) ? "open" : "closed" ) ;
  }
}

optimized

This optimized version makes use of the fact that finally only the doors with square index are open, as well as the fact that $n^{2}=1+3+5+\ldots +(2n-1)$.

Uses: C Runtime (Components:printf,)

#include <stdio.h>
 
int main()
{
  int square = 1, increment = 3, door;
  for (door = 1; door <= 100; ++door)
  {
    printf("door #%d", door);
    if (door == square)
    {
      printf(" is open.\n");
      square += increment;
      increment += 2;
    }
    else
      printf(" is closed.\n");
  }
  return 0;
}

The following ultra-short optimized version demonstrates the flexibility of C loops, but isn't really considered good C style:

#include <stdio.h>
 
int main()
{
  int door, square, increment;
  for (door = 1, square = 1, increment = 1; door <= 100; door++ == square && (square += increment += 2))
    printf("door #%d is %s.\n", door, (door == square? "open" : "closed"));
  return 0;
}

Or really optimize it -- square of an integer is, well, computable:

#include <stdio.h>
 
int main()
{
	int i;
	for (i = 1; i * i <= 100; i++)
		printf("door %d open\n", i * i);
 
	return 0;
}

C#

Unoptimized with Modulus % Operator

namespace ConsoleApplication1
{
    using System;
    class Program
    {
        static void Main(string[] args)
        {
            bool[] doors = new bool[100];
 
            //Close all doors to start.
            for (int d = 0; d < 100; d++) doors[d] = false;
 
            //For each pass...
            for (int p = 0; p < 100; p++)//number of passes
            {
                //For each door to toggle...
                for (int d = 0; d < 100; d++)//door number
                {
                    if ((d + 1) % (p + 1) == 0)
                    {
                        doors[d] = !doors[d];
                    }
                }
            }
 
            //Output the results.
            Console.WriteLine("Passes Completed!!!  Here are the results: \r\n");
            for (int d = 0; d < 100; d++)
            {
                if (doors[d])
                {
                    Console.WriteLine(String.Format("Door #{0}: Open", d + 1));
                }
                else
                {
                    Console.WriteLine(String.Format("Door #{0}: Closed", d + 1));
                }
            }
            Console.ReadKey(true);
        }
    }
}

Optimized for Orthogonality

(This version demonstrates a different thought pattern during development, where operation and presentation are separated. It could easily be refactored so that the operations to determine which doors are opened and to display the list of doors would be in separate methods, at which point it would become simple to extract them to separate classes and employ a DI pattern to switch the algorithm or display mechanism being used. It also keeps the calculation clear and concise.)

namespace ConsoleApplication1
{
    using System;
    class Program
    {
        static void Main(string[] args)
        {
            //Perform the operation.
            bool[] doors = new bool[100];
            int n = 0;
            int d;
            while ((d = (++n * n)) <= 100)
                doors[d - 1] = true;
 
            //Perform the presentation.
            for (d = 0; d < doors.Length; d++)
                Console.WriteLine("Door #{0}: {1}", d + 1, doors[d] ? "Open" : "Closed");
            Console.ReadKey(true);
        }
    }
}

Unoptimized but Concise

namespace ConsoleApplication1
{
    using System;
    class Program
    {
        static void Main()
        {
            bool[] doors = new bool[100];
 
            //The number of passes can be 1-based, but the number of doors must be 0-based.
            for (int p = 1; p <= 100; p++)
                for (int d = p - 1; d < 100; d += p)
                    doors[d] = !doors[d];
            for (int d = 0; d < 100; d++)
                Console.WriteLine("Door #{0}: {1}", d + 1, doors[d] ? "Open" : "Closed");
            Console.ReadKey(true);
        }
    }
}

Optimized for brevity

namespace ConsoleApplication1
{
    using System;
    class Program
    {
        static void Main()
        {
            double n;
 
            //If the current door number is the perfect square of an integer, say it is open, else say it is closed.
            for (int d = 1; d <= 100; d++)
                Console.WriteLine("Door #{0}: {1}", d, (n = Math.Sqrt(d)) == (int)n ? "Open" : "Closed");
            Console.ReadKey(true);
        }
    }
}

Optimized for Flexibility

This version supports altering the number of doors through console commands. Its main intent is to be flexible and easy to use.

 
using System;
using System.IO;
using System.Collections.Generic;
 
class Program
{
    static void Main()
    {
        Console.Clear();
        Console.WriteLine("Input a number of doors to calculate, then press enter");
        StartCalculator();
    }
 
    static void StartCalculator()
    {
        //The number to calculate is input here
        string input = Console.ReadLine();
        Console.Clear();
 
        try
        {
            //The program attempts to convert the string to an int
            //Exceptions will be caught on this line
            int numberOfDoors = Convert.ToInt32(input);
 
            //Will call method recursively if input number is less than 1
            if (numberOfDoors <= 0)
            {
                Console.WriteLine("Please use a number greater than 0");
                StartCalculator();
            }
 
            //The program then starts the calculation process
            Calculate(numberOfDoors);
 
            //After calculation process is finished, restart method is called
            RestartCalculator();
        }
        catch(FormatException)
        {
            //Code will be executed if the number has a decimal or has an unrecognizable symbol
            Console.WriteLine("Unable to read. Please use a real number without a decimal");
            StartCalculator();
        }
        catch (OverflowException)
        {
            //Code will be executed if number is too long
            Console.WriteLine("You number is too long");
            StartCalculator();
        }
    }
 
    static void Calculate(int numberOfDoors)
    {
        //Increases numberOfDoors by 1 since array starts at 0
        numberOfDoors++;
 
        //Dictionary key represents door number, value represents if the door is open
        //if value == true, the door is open
        Dictionary<int, bool> doors = new Dictionary<int, bool>();
 
        //Creates Dictionary size of numberOfDoors, all initialized at false
        for(int i = 0; i < numberOfDoors; i++)
        {
            doors.Add(i, false);
        }
 
        //Creates interval between doors, starting at 0, while less than numberOfDoors
        for (int doorInterval = 0; doorInterval < numberOfDoors; doorInterval++)
        {
            //Will alter every cubby at doorInterval
            //1 needs to be added since doorInterval will start at 0 and end when equal to numberOfDoors
            for(int i = 0; i < numberOfDoors; i += doorInterval + 1)
            {
                //Changes a false value to true and vice versa
                doors[i] = doors[i] ? false: true;
            }
        }
 
        //Writes each door and whether it is open or closed
        for(int i = 0; i < numberOfDoors; i++)
        {
            //Skips over door 0
            if (i == 0) continue;
            //Writes open if door value is true, writes closed if door value is false
            Console.WriteLine("Door " + (i) + " is " + (doors[i] ? "open" : "closed"));
        }
    }
 
    static void RestartCalculator()
    {   
        Console.WriteLine("Press any key to restart");
        Console.ReadKey(true);
        Main();
    }
}
 

C++

Works with: GCC version 4.1.2 20061115 (prerelease) (SUSE Linux)

unoptimized

#include <iostream>
 
int main()
{
  bool is_open[100] = { false };
 
  // do the 100 passes
  for (int pass = 0; pass < 100; ++pass)
    for (int door = pass; door < 100; door += pass+1)
      is_open[door] = !is_open[door];
 
  // output the result
  for (int door = 0; door < 100; ++door)
    std::cout << "door #" << door+1 << (is_open[door]? " is open." : " is closed.") << std::endl;
  return 0;
}

optimized This optimized version makes use of the fact that finally only the doors with square index are open, as well as the fact that $(n+1)^{2}=1+3+5+\ldots +(2n+1)$.

#include <iostream>
 
int main()
{
  int square = 1, increment = 3;
  for (int door = 1; door <= 100; ++door)
  {
    std::cout << "door #" << door;
    if (door == square)
    {
      std::cout << " is open." << std::endl;
      square += increment;
      increment += 2;
    }
    else
      std::cout << " is closed." << std::endl;
  }
  return 0;
}

The only calculation that's really needed:

#include <iostream> //compiled with "Dev-C++" , from RaptorOne
 
int main()
{
    for(int i=1; i*i<=100; i++)
            std::cout<<"Door "<<i*i<<" is open!"<<std::endl;
}

Compile time computation using C++17 to produce fastest runtime.

#include <iostream>    // compiled with clang (tags/RELEASE_600/final)
#include <type_traits> // or g++ (GCC) 7.3.1 20180406 -- from hare1039
namespace functional_list // basic building block for template meta programming
{
struct NIL
{
	using head = NIL;
	using tail = NIL;
	friend std::ostream& operator << (std::ostream& os, NIL const) { return os; }
};
 
template <typename H, typename T = NIL>
struct list
{
	using head = H;
	using tail = T;
};
 
template <int i>
struct integer
{
	static constexpr int value = i;
	friend std::ostream& operator << (std::ostream& os, integer<i> const) { os << integer<i>::value; return os;}
};
 
template <typename L, int nTH> constexpr
auto at()
{
	if constexpr (nTH == 0)
		return (typename L::head){};
	else if constexpr (not std::is_same_v<typename L::tail, NIL>) 
		return at<typename L::tail, nTH - 1>();
	else
		return NIL{};
}
template <typename L, int nTH>
using at_t = decltype(at<L, nTH>());
 
template <typename L, typename elem> constexpr
auto prepend() { return list<elem, L>{}; }
 
template <typename L, typename elem>
using prepend_t = decltype(prepend<L, elem>());
 
template <int Size, typename Dat = integer<0>> constexpr
auto gen_list()
{
	if constexpr (Size == 0)
		return NIL{};
	else
	{
		using next = decltype(gen_list<Size - 1, Dat>());
		return prepend<next, Dat>();
	}
}
template <int Size, typename Dat = integer<0>>
using gen_list_t = decltype(gen_list<Size, Dat>());
 
} namespace fl = functional_list;
 
constexpr int door_amount = 101; // index from 1 to 100
 
template <typename L, int current, int moder> constexpr
auto construct_loop()
{
	using val_t = fl::at_t<L, current>;
	if constexpr (std::is_same_v<val_t, fl::NIL>)
		return fl::NIL{};
	else
	{
		constexpr int val = val_t::value;
		using val_add_t = fl::integer<val + 1>;
		using val_old_t = fl::integer<val>;
 
		if constexpr (current == door_amount)
		{
			if constexpr(current % moder == 0)
				return fl::list<val_add_t>{};
			else
				return fl::list<val_old_t>{};
		}
		else
		{
			using sub_list = decltype(construct_loop<L, current + 1, moder>());
			if constexpr(current % moder == 0)
				return fl::prepend<sub_list, val_add_t>();
			else
				return fl::prepend<sub_list, val_old_t>();
		}
	}
}
 
template <int iteration> constexpr
auto construct()
{
	if constexpr (iteration == 1) // door index = 1
	{
		using l = fl::gen_list_t<door_amount>;
		return construct_loop<l, 0, iteration>();
	}
	else
	{
		using prev_iter_list = decltype(construct<iteration - 1>());
		return construct_loop<prev_iter_list, 0, iteration>();
	}
}
 
template <typename L, int pos> constexpr
void show_ans()
{
	if constexpr (std::is_same_v<typename L::head, fl::NIL>)
		return;
	else
	{
		if constexpr (L::head::value % 2 == 1)
			std::cout << "Door " << pos << " is opened.\n";
		show_ans<typename L::tail, pos + 1>();
	}
}
 
int main()
{
	using result = decltype(construct<100>());
	show_ans<result, 0>();
}

C1R

100_doors

Caché ObjectScript

 
 for i=1:1:100 {
	 set doors(i) = 0
 }
 for i=1:1:100 {
	 for door=i:i:100 {
		  Set doors(door)='doors(door)
	 }
 }
 for i = 1:1:100
 {
	if doors(i)=1 write i_": open",!
 }
 

Output:

 
1: open
4: open
9: open
16: open
25: open
36: open
49: open
64: open
81: open
100: open
 

Ceylon

shared void run() {
    print("Open doors (naive):     ``naive()``
           Open doors (optimized): ``optimized()``");
 
}
 
shared {Integer*} naive(Integer count = 100) {
    variable value doors = [ for (_ in 1..count) closed ];
    for (step in 1..count) {
        doors = [for (i->door in doors.indexed) let (index = i+1) if (step == 1 || step.divides(index)) then door.toggle() else door ];
    }
    return doors.indexesWhere((door) => door == opened).map(1.plusInteger);
}
 
shared {Integer*} optimized(Integer count = 100) =>
        { for (i in 1..count) i*i }.takeWhile(count.notSmallerThan);
 
 
shared abstract class Door(shared actual String string) of opened | closed {
    shared formal Door toggle();
}
object opened extends Door("opened") { toggle() => closed; }
object closed extends Door("closed") { toggle() => opened; }

Output:

Open doors (naive):     { 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 }
Open doors (optimized): { 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 }

Clarion

 
    program
 
    map
    end
 
MAX_DOOR_NUMBER         equate(100)
CRLF                    equate('<13,10>')
 
Doors                   byte,dim(MAX_DOOR_NUMBER)
Pass                    byte
DoorNumber              byte
DisplayString           cstring(2000)
 
ResultWindow            window('Result'),at(,,133,291),center,double,auto
                            prompt('Door states:'),at(8,4),use(?PromptTitle)
                            text,at(8,16,116,266),use(DisplayString),boxed,vscroll,font('Courier New',,,,CHARSET:ANSI),readonly
                        end
 
    code
 
    Doors :=: false
    loop Pass = 1 to MAX_DOOR_NUMBER
        loop DoorNumber = Pass to MAX_DOOR_NUMBER by Pass
            Doors[DoorNumber] = choose(Doors[DoorNumber], false, true)
        end
    end
 
    clear(DisplayString)
    loop DoorNumber = 1 to MAX_DOOR_NUMBER
        DisplayString = DisplayString & format(DoorNumber, @n3) & ' is ' & choose(Doors[DoorNumber], 'opened', 'closed') & CRLF
    end
    open(ResultWindow)
    accept
    end
    close(ResultWindow)
 
    return
 

Clio

Unoptimized

fn visit-doors doors step:
  if step > 100: doors
  else:
    [1:100]
      -> * fn index:
            if index % step: doors[(index - 1)]
            else: not doors[(index - 1)]
      -> visit-doors (step + 1)
 
[1:100] -> * n: false -> visit-doors 1 => doors
[1:100] -> * (@eager) fn i:
  doors[(i - 1)]
    -> if = true: #open
            else: #closed
    -> print #Door i #is @

Optimized

[1:100] -> * (@eager) fn i:
  i ^ 0.5
    -> eq @ (transform i: floor)
    -> if = true: #open
            else: #closed
    -> print #Door i #is @

CLIPS

Unoptimized

(deffacts initial-state
  (door-count 100)
)
 
(deffunction toggle
  (?state)
  (switch ?state
    (case "open" then "closed")
    (case "closed" then "open")
  )
)
 
(defrule create-doors-and-visits
  (door-count ?count)
  =>
  (loop-for-count (?num 1 ?count) do
    (assert (door ?num "closed"))
    (assert (visit-from ?num ?num))
  )
  (assert (doors initialized))
)
 
(defrule visit
  (door-count ?max)
  ?visit <- (visit-from ?num ?step)
  ?door <- (door ?num ?state)
  =>
  (retract ?visit)
  (retract ?door)
  (assert (door ?num (toggle ?state)))
  (if
    (<= (+ ?num ?step) ?max)
    then
    (assert (visit-from (+ ?num ?step) ?step))
  )
)
 
(defrule start-printing
  (doors initialized)
  (not (visit-from ? ?))
  =>
  (printout t "These doors are open:" crlf)
  (assert (print-from 1))
)
 
(defrule print-door
  (door-count ?max)
  ?pf <- (print-from ?num)
  (door ?num ?state)
  =>
  (retract ?pf)
  (if
    (= 0 (str-compare "open" ?state))
    then
    (printout t ?num " ")
  )
  (if
    (< ?num ?max)
    then
    (assert (print-from (+ ?num 1)))
    else
    (printout t crlf "All other doors are closed." crlf)
  )
)

Optimized

(deffacts initial-state
  (door-count 100)
)
 
(deffunction is-square
  (?num)
  (= (sqrt ?num) (integer (sqrt ?num)))
)
 
(defrule check-doors
  (door-count ?count)
  =>
  (printout t "These doors are open:" crlf)
  (loop-for-count (?num 1 ?count) do
    (if (is-square ?num) then
      (printout t ?num " ")
    )
  )
  (printout t crlf "All other doors are closed." crlf)
)

Clojure

Unoptimized / mutable array

(defn doors []
  (let [doors (into-array (repeat 100 false))]
    (doseq [pass   (range 1 101) 
            i      (range (dec pass) 100 pass) ]
      (aset doors i (not (aget doors i))))
    doors))   
 
(defn open-doors [] (for [[d n] (map vector (doors) (iterate inc 1)) :when d] n))
 
(defn print-open-doors []
  (println 
    "Open doors after 100 passes:"
    (apply str (interpose ", " (open-doors)))))

Unoptimized / functional

(defn doors []
  (reduce (fn [doors toggle-idx] (update-in doors [toggle-idx] not))
          (into [] (repeat 100 false))
          (for [pass   (range 1 101)
                i      (range (dec pass) 100 pass) ]
            i)))
 
(defn open-doors [] (for [[d n] (map vector (doors) (iterate inc 1)) :when d] n))
 
(defn print-open-doors []
  (println 
    "Open doors after 100 passes:"
    (apply str (interpose ", " (open-doors)))))

Alternative Unoptimized / functional

(defn open-doors []
  (->> (for [step (range 1 101), occ (range step 101 step)] occ)
       frequencies
       (filter (comp odd? val))
       keys
       sort))
 
(defn print-open-doors []
  (println 
    "Open doors after 100 passes:"
    (apply str (interpose ", " (open-doors)))))

Optimized / functional

(defn doors []
	(reduce (fn [doors idx] (assoc doors idx true)) 
	        (into [] (repeat 100 false))
	        (map #(dec (* % %)) (range 1 11))))
 
(defn open-doors [] (for [[d n] (map vector (doors) (iterate inc 1)) :when d] n))
 
(defn print-open-doors []
  (println 
    "Open doors after 100 passes:"
    (apply str (interpose ", " (open-doors)))))

Alternative Optimized / functional

(defn open-doors [] (->> (iterate inc 1) (map #(* % %)) (take-while #(<= % 100))))
 
(defn print-open-doors []
  (println 
    "Open doors after 100 passes:"
    (apply str (interpose ", " (open-doors)))))

CLU

start_up = proc ()
    max = 100
    po: stream := stream$primary_output()
    open: array[bool] := array[bool]$fill(1, max, false)
 
    for pass: int in int$from_to(1, max) do
        for door: int in int$from_to_by(pass, max, pass) do
            open[door] := ~open[door]
        end
    end
 
    for door: int in array[bool]$indexes(open) do
        if open[door] then
            stream$putl(po, "Door " || int$unparse(door) || " is open.")
        end
    end
end start_up

Output:

Door 1 is open.
Door 4 is open.
Door 9 is open.
Door 16 is open.
Door 25 is open.
Door 36 is open.
Door 49 is open.
Door 64 is open.
Door 81 is open.
Door 100 is open.

COBOL

       IDENTIFICATION DIVISION.
       PROGRAM-ID. 100Doors.
 
       DATA DIVISION.
       WORKING-STORAGE SECTION.
       01 Current-n      PIC 9(3).
       01 StepSize       PIC 9(3).
       01 DoorTable.
          02 Doors       PIC 9(1)   OCCURS 100 TIMES.
             88 ClosedDoor          VALUE ZERO.
       01 Idx            PIC 9(3).
 
       PROCEDURE DIVISION.
       Begin.
           INITIALIZE DoorTable
           PERFORM VARYING StepSize FROM 1 BY 1 UNTIL StepSize > 100
             PERFORM VARYING Current-n FROM StepSize BY StepSize
                     UNTIL Current-n > 100
               SUBTRACT Doors (Current-n) FROM 1 GIVING Doors (Current-n)
             END-PERFORM
           END-PERFORM
 
           PERFORM VARYING Idx FROM 1 BY 1
                   UNTIL Idx > 100
             IF ClosedDoor (Idx)
               DISPLAY Idx " is closed."
             ELSE
               DISPLAY Idx " is open."
             END-IF
           END-PERFORM
 
           STOP RUN
           .

Coco

We use the naive algorithm.

doors = [false] * 100
 
for pass til doors.length
    for i from pass til doors.length by pass + 1
        ! = doors[i]
 
for i til doors.length
    console.log 'Door %d is %s.', i + 1, if doors[i] then 'open' else 'closed'

CoffeeScript

unoptimized:

doors = []
 
for pass in [1..100]
  for i in [pass..100] by pass
    doors[i] = !doors[i]
 
console.log "Doors #{index for index, open of doors when open} are open"
 
# matrix output
console.log doors.map (open) -> +open
 

optimized:

isInteger = (i) -> Math.floor(i) == i
 
console.log door for door in [1..100] when isInteger Math.sqrt door

ultra-optimized:

console.log Math.pow(i,2) for i in [1..10]

ColdFusion

Basic Solution: Returns List of 100 values: 1=open 0=closed

 
	doorCount = 1;
	doorList = "";
	// create all doors and set all doors to open
	while (doorCount LTE 100) {
		doorList = ListAppend(doorList,"1");
		doorCount = doorCount + 1;
	}
	loopCount = 2;
	doorListLen = ListLen(doorList);
	while (loopCount LTE 100) {
		loopDoorListCount = 1;
		while (loopDoorListCount LTE 100) {
			testDoor = loopDoorListCount / loopCount;
			if (testDoor EQ Int(testDoor)) {
				checkOpen = ListGetAt(doorList,loopDoorListCount);
				if (checkOpen EQ 1) {
					doorList = ListSetAt(doorList,loopDoorListCount,"0");
				} else {
					doorList = ListSetAt(doorList,loopDoorListCount,"1");
				}
			}
			loopDoorListCount = loopDoorListCount + 1;
		}
		loopCount = loopCount + 1;
	}
 

Squares of Integers Solution: Returns List of 100 values: 1=open 0=closed

 
	doorCount = 1;
	doorList = "";
	loopCount = 1;
	while (loopCount LTE 100) {
		if (Sqr(loopCount) NEQ Int(Sqr(loopCount))) {
			doorList = ListAppend(doorList,0);
		} else {
			doorList = ListAppend(doorList,1);
		}
		loopCount = loopCount + 1;
	}
 

Display only

// Display all doors
<cfloop from="1" to="100" index="x">
    Door #x# Open: #YesNoFormat(ListGetAt(doorList,x))#<br />
</cfloop>
 
// Output only open doors
<cfloop from="1" to="100" index="x">
    <cfif ListGetAt(doorList,x) EQ 1>
        #x#<br />
    </cfif>
</cfloop>

Another Route

<Cfparam name="doorlist" default="">
<cfloop from="1" to="100" index="i">
    <Cfset doorlist = doorlist & 'c,'>
</cfloop>
<cfloop from="1" to="100" index="i">
    <Cfloop from="1" to="100" index="door" step="#i#">
    <Cfif listgetat(doorlist, door) eq 'c'>
        <Cfset doorlist = listsetat(doorlist, door, 'O')>
    <Cfelse>
        <Cfset doorlist = listsetat(doorlist, door, 'c')>
    </Cfif>
    </Cfloop>
</cfloop>
<Cfoutput>#doorlist#</Cfoutput>

Comal

0010 DIM doors#(100)
0020 FOR pass#:=1 TO 100 DO
0030   FOR door#:=pass# TO 100 STEP pass# DO doors#(door#):=NOT doors#(door#)
0040 ENDFOR pass#
0050 FOR door#:=1 TO 100 DO
0060   IF doors#(door#) THEN PRINT "Door ",door#," is open."
0070 ENDFOR door#
0080 END

Output:

Door 1 is open.
Door 4 is open.
Door 9 is open.
Door 16 is open.
Door 25 is open.
Door 36 is open.
Door 49 is open.
Door 64 is open.
Door 81 is open.
Door 100 is open.

Commodore BASIC

 
10 D=100: DIMD(D): P=1
20 PRINT CHR$(147);"PASS: ";P
22 FOR I=P TO D STEP P: D(I)=NOTD(I): NEXT
30 IF P=100 THEN 40
32 P=P+1: GOTO20
40 PRINT: PRINT"THE FOLLOWING DOORS ARE OPEN: "
42 FOR I=1 TO D: IF D(I)=-1 THEN PRINTI;
44 NEXT
 

Common Lisp

Unoptimized / functional This is a very unoptimized version of the problem, using recursion and quite considerable list-copying. It emphasizes the functional way of solving this problem.

(defun visit-door (doors doornum value1 value2)
  "visits a door, swapping the value1 to value2 or vice-versa"
  (let ((d (copy-list doors))
        (n (- doornum 1)))
    (if (eql  (nth n d) value1)
        (setf (nth n d) value2)
      (setf (nth n d) value1))
    d))
 
(defun visit-every (doors num iter value1 value2)
  "visits every 'num' door in the list"
  (if (> (* iter num) (length doors))
      doors
    (visit-every (visit-door doors (* num iter) value1 value2)
                 num
                 (+ 1 iter)
                 value1
                 value2)))
 
(defun do-all-visits (doors cnt value1 value2)
  "Visits all doors changing the values accordingly"
  (if (< cnt 1)
      doors
    (do-all-visits (visit-every doors cnt 1 value1 value2)
                   (- cnt 1)
                   value1
                   value2)))
 
(defun print-doors (doors)
  "Pretty prints the doors list"
  (format T "~{~A ~A ~A ~A ~A ~A ~A ~A ~A ~A~%~}~%" doors))
 
(defun start (&optional (size 100))
  "Start the program"
  (let* ((open "_")
         (shut "#")
         (doors (make-list size :initial-element shut)))
    (print-doors (do-all-visits doors size open shut))))

Unoptimized, imperative This is a version that closely follows the problem description and is still quite short. Of all the presented solutions it might be closest to "idiomatic Common Lisp".

(define-modify-macro toggle () not)
 
(defun 100-doors ()
  (let ((doors (make-array 100)))
    (dotimes (i 100)
      (loop for j from i below 100 by (1+ i)
	 do (toggle (svref doors j))))
    (dotimes (i 100)
      (format t "door ~a: ~:[closed~;open~]~%" (1+ i) (svref doors i)))))

Unoptimized, n-doors.

(defun doors (z &optional (w (make-list z)) (n 1))
  (if (> n z) w (doors z (toggle w n z) (1+ n))))
 
(defun toggle (w m z)
  (loop for a in w for n from 1 to z
        collect (if (zerop (mod n m)) (not a) a)))
 
> (doors 100)
(T NIL NIL T NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL
 NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL
 NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL
 NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T
 NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T)

Optimized, n-doors.

(defun doors (n)
  (loop for a from 1 to n collect
        (zerop (mod (sqrt a) 1))))
 
> (doors 100)
(T NIL NIL T NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL
 NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL
 NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL
 NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T
 NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T)

Optimized This is an optimized version, using the perfect square algorithm.

(defun 100-doors ()
  (let ((doors (make-array 100)))
    (dotimes (i 10)
      (setf (svref doors (* i i)) t))
    (dotimes (i 100)
      (format t "door ~a: ~:[closed~;open~]~%" (1+ i) (svref doors i)))))

Optimized 2 Another optimized version, with finer granular separation of functionality (might be a bit excessive).

(defun perfect-square-list (n)                       
  "Generates a list of perfect squares from 0 up to n"
  (loop for i from 1 to (isqrt n) collect (expt i 2))) 
 
(defun print-doors (doors)
  "Pretty prints the doors list"
  (format T "~{~A ~A ~A ~A ~A ~A ~A ~A ~A ~A~%~}~%" doors))
 
(defun open-door (doors num open)
  "Sets door at num to open"
  (setf (nth (- num 1) doors) open)) 
 
(defun visit-all (doors vlist open)
  "Visits and opens all the doors indicated in vlist"
  (dolist (dn vlist doors)
    (open-door doors dn open)))
 
(defun start2 (&optional (size 100))                        
  "Start the program"
  (print-doors
   (visit-all (make-list size :initial-element '\#)
              (perfect-square-list size)
              '_)))

Optimized (2) This version displays a much more functional solution through the use of MAPCAR.

(let  ((i 0))
    (mapcar (lambda (x)
                (if (zerop (mod (sqrt (incf i)) 1))
                    "_" "#"))
            (make-list 100)))

Component Pascal

BlackBox Component Builder

 
MODULE Doors100;
IMPORT StdLog;
 
PROCEDURE Do*;
VAR
	i,j: INTEGER;
	closed: ARRAY 101 OF BOOLEAN;
BEGIN
	(* initialization of closed to true *)
	FOR i := 0 TO LEN(closed) - 1 DO closed[i] := TRUE END;
	(* process *)
	FOR i := 1 TO LEN(closed)  DO;
		j := 1;
		WHILE j < LEN(closed) DO
			IF j MOD i = 0 THEN closed[j] := ~closed[j] END;INC(j)
		END
	END;
	(* print results *)
	i := 1;
	WHILE  i < LEN(closed)  DO
		IF (i - 1) MOD 10 = 0 THEN StdLog.Ln END;
		IF closed[i] THEN StdLog.String("C ") ELSE StdLog.String("O ") END;
		INC(i) 
	END;
END Do;
END Doors100.
 
 

Execute: ^Q Doors100.Do

Output:

O C C O C C C C O C 
C C C C C O C C C C 
C C C C O C C C C C 
C C C C C O C C C C 
C C C C C C C C O C 
C C C C C C C C C C 
C C C O C C C C C C 
C C C C C C C C C C 
O C C C C C C C C C 
C C C C C C C C C O 

Coq

Basic solution:

Require Import List.
 
Fixpoint rep {A} (a : A) n :=
  match n with
    | O => nil
    | S n' => a::(rep a n')
  end.
 
Fixpoint flip (l : list bool) (n k : nat) : list bool :=
  match l with
    | nil => nil
    | cons h t => match k with
                | O => (negb h) :: (flip t n n)
                | S k' => h :: (flip t n k')
              end
  end.
 
Definition flipeach l n := flip l n n.
 
Fixpoint flipwhile l n :=
  match n with
    | O => flipeach l 0
    | S n' => flipwhile (flipeach l (S n')) n'
  end.
 
Definition prison cells := flipwhile (rep false cells) cells.

Optimized version ((n+1)^2 = n^2 + 2n + 1):

Require Import List.
 
Fixpoint prisoo' nd n k accu :=
  match nd with
    | O => rev accu
    | S nd' => let ra := match k with
                 | O => (true, S n, (n + n))
                 | S k' => (false, n, k')
               end in
               prisoo' nd' (snd (fst ra)) (snd ra) ((fst (fst ra))::accu)
  end.
 
Definition prisoo cells := prisoo' cells 1 0 nil.

Unit test:

Goal prison 100 = prisoo 100. compute. reflexivity. Qed.

Full proof at github:

Goal forall n, prison n = prisoo n. Abort.

Cowgol

include "cowgol.coh";
 
var doors: uint8[101];  # one extra so we can start at 1
var pass: @indexof doors;
var door: @indexof doors;
 
MemZero(&doors as [uint8], @bytesof doors);
 
pass := 1;
while pass <= 100 loop
    door := pass;
    while door <= 100 loop
        doors[door] := 1-doors[door];
        door := door + pass;
    end loop;
    pass := pass + 1;
end loop;
 
door := 1;
while door <= 100 loop
    if doors[door] == 1 then
        print_i8(door);
        print(" is open\n");
    end if;
    door := door + 1;
end loop;

Output:

1 is open
4 is open
9 is open
16 is open
25 is open
36 is open
49 is open
64 is open
81 is open
100 is open

Crystal

doors = Array.new(100, false)
 
1.upto(100) do |i|
  i.step(by: i, to: 100) do |j|
    doors[j - 1] = !doors[j - 1]
  end
end
 
doors.each_with_index do |open, i|
  puts "Door #{i + 1} is #{open ? "open" : "closed"}"
end

D

Unoptimized

import std.stdio;
const N = 101; // #doors + 1
void main() {
  bool[N] doors = false;
  for(auto door=1; door<N; door++ ) {
    for(auto i=door; i<N; i+=door ) doors[i] = !doors[i];
    if (doors[door]) write(door, " ");
  }
}

Output:

1 4 9 16 25 36 49 64 81 100 

Optimized

The problem of the 100 doors is an algorithm to find the squares between 1 and 100.

This optimized version prints these squares using an alternative algorithm based on $\sum _{i=1}^{n}(2i-1)=n^{2}$

import std.stdio;
const N = 101; // #doors + 1
void main() {
  for( auto door=1,s=3; door<N; door+=s, s+=2 )
    write(door, " ");
}

Output:

1 4 9 16 25 36 49 64 81 100 

Other proposals

import std.stdio, std.algorithm, std.range;
 
enum DoorState : bool { closed, open }
alias Doors = DoorState[];
 
Doors flipUnoptimized(Doors doors) pure nothrow {
    doors[] = DoorState.closed;
 
    foreach (immutable i; 0 .. doors.length)
        for (ulong j = i; j < doors.length; j += i + 1)
            if (doors[j] == DoorState.open)
                doors[j] = DoorState.closed;
            else
                doors[j] = DoorState.open;
    return doors;
}
 
Doors flipOptimized(Doors doors) pure nothrow {
    doors[] = DoorState.closed;
    for (int i = 1; i ^^ 2 <= doors.length; i++)
        doors[i ^^ 2 - 1] = DoorState.open;
    return doors;
}
 
void main() {
    auto doors = new Doors(100);
 
    foreach (const open; [doors.dup.flipUnoptimized,
                          doors.dup.flipOptimized])
        iota(1, open.length + 1).filter!(i => open[i - 1]).writeln;
}

Output:

[1, 4, 9, 16, 25, 36, 49, 64, 81, 100]
[1, 4, 9, 16, 25, 36, 49, 64, 81, 100]

Unoptimized. Demonstrates very basic language syntax/features. Program output allows to see what the code is doing:

 
import std.stdio;
 
void printAllDoors(bool[] doors)
{
   // Prints the state of all the doors
   foreach(i, door; doors)
   {
      writeln("#: ", i + 1, (door) ? " open" : " closed");
      }
}
void main()
{
   bool[100] doors = false;   //Create 100 closed doors
   for(int a = 0; a < 100; ++a) {
      writefln("Pass #%s; visiting every %s door.", a + 1, a + 1);  // Optional
	 for(int i = a; i < 100; i += (a + 1)) {
	 writefln("Visited door %s", i + 1);  //Optional
	 doors[i] = !doors[i];
	 }
      writeln();  // Optional
      }
   printAllDoors(doors);   // Prints the state of each door
}
 

Dafny

The InitializeDoors function demonstrates some of Dafny's advanced features.

 
datatype Door = Closed | Open
 
method InitializeDoors(n:int) returns (doors:array<Door>)
  // Precondition: n must be a valid array size.
  requires n >= 0
  // Postcondition: doors is an array, which is not an alias for any other
  // object, with a length of n, all of whose elements are Closed. The "fresh"
  // (non-alias) condition is needed to allow doors to be modified by the
  // remaining code.
  ensures doors != null && fresh(doors) && doors.Length == n
  ensures forall j :: 0 <= j < doors.Length ==> doors[j] == Closed;
{
  doors := new Door[n];
  var i := 0;
  // Invariant: i is always a valid index inside the loop, and all doors less
  // than i are Closed. These invariants are needed to ensure the second
  // postcondition.
  while i < doors.Length
    invariant i <= doors.Length
    invariant forall j :: 0 <= j < i ==> doors[j] == Closed;
  {
    doors[i] := Closed;
    i := i + 1;
  }
}
 
method Main ()
{
  var doors := InitializeDoors(100);
 
  var pass := 1;
  while pass <= doors.Length
  {
    var door := pass;
    while door < doors.Length
    {
      doors[door] := if doors[door] == Closed then Open else Closed;
      door := door + pass;
    }
    pass := pass + 1;
  }
  var i := 0;
  while i < doors.Length
  {
    print i, " is ", if doors[i] == Closed then "closed\n" else "open\n";
    i := i + 1;
  }
}
 

Dart

unoptimized

main() {
    for (var k = 1, x = new List(101); k <= 100; k++) {
        for (int i = k; i <= 100; i += k)
            x[i] = !x[i];
        if (x[k]) print("$k open");
    }
}

optimized version (including generating squares without multiplication)

main() {
  for(int i=1,s=3;i<=100;i+=s,s+=2)
    print("door $i is open");
}

comprehensible (not "code golf") version for a pedestrian language

import 'dart:io';
 
final numDoors = 100;
final List<bool> doorClosed = List(numDoors);
 
String stateToString(String message) {
  var res = '';
  for (var i = 0; i < numDoors; i++) {
    res += (doorClosed[i] ? 'X' : '\u2610');
  }
  return res + " " + message;
}
 
main() {
  for (var i = 0; i < numDoors; i++) {
    doorClosed[i] = true;
  }
  stdout.writeln(stateToString("after initialization"));
  for (var step = 1; step <= numDoors; step++) {
    final start = step - 1;
    for (var i = start; i < numDoors; i += step) {
      doorClosed[i] = !doorClosed[i];
    }
    stdout.writeln(stateToString("after toggling with step = $step"));
  }
}

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX after initialization
☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐ after toggling with step = 1
☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X after toggling with step = 2
☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX after toggling with step = 3
☐XX☐☐☐☐☐XX☐X☐XX☐☐☐☐☐XX☐X☐XX☐☐☐☐☐XX☐X☐XX☐☐☐☐☐XX☐X☐XX☐☐☐☐☐XX☐X☐XX☐☐☐☐☐XX☐X☐XX☐☐☐☐☐XX☐X☐XX☐☐☐☐☐XX☐X☐XX☐ after toggling with step = 4
☐XX☐X☐☐☐X☐☐X☐X☐☐☐☐☐XXX☐XXXX☐☐X☐☐XXXX☐XXX☐☐☐☐☐X☐X☐☐X☐☐☐X☐XX☐☐☐XX☐X☐☐☐X☐☐X☐X☐☐☐☐☐XXX☐XXXX☐☐X☐☐XXXX☐XXX after toggling with step = 5
☐XX☐XX☐☐X☐☐☐☐X☐☐☐X☐XXX☐☐XXX☐☐☐☐☐XXX☐☐XXX☐X☐☐☐X☐☐☐☐X☐☐XX☐XX☐X☐XX☐XX☐☐X☐☐☐☐X☐☐☐X☐XXX☐☐XXX☐☐☐☐☐XXX☐☐XXX after toggling with step = 6
☐XX☐XXX☐X☐☐☐☐☐☐☐☐X☐X☐X☐☐XXXX☐☐☐☐XX☐☐☐XXX☐☐☐☐☐X☐☐X☐X☐☐XXXXX☐X☐X☐☐XX☐☐XX☐☐☐X☐☐XX☐XXX☐XXXX☐☐☐X☐XXX☐☐☐XX after toggling with step = 7
☐XX☐XXXXX☐☐☐☐☐☐X☐X☐X☐X☐XXXXX☐☐☐XXX☐☐☐XX☐☐☐☐☐☐X☐XX☐X☐☐XX☐XX☐X☐X☐XXX☐☐XX☐X☐X☐☐XX☐☐XX☐XXXXX☐☐X☐XXXX☐☐XX after toggling with step = 8
☐XX☐XXXX☐☐☐☐☐☐☐X☐☐☐X☐X☐XXX☐X☐☐☐XXX☐X☐XX☐☐☐☐☐XX☐XX☐X☐☐☐X☐XX☐X☐XXXXX☐☐XX☐☐☐X☐☐XX☐☐☐X☐XXXXX☐XX☐XXXX☐☐☐X after toggling with step = 9
☐XX☐XXXX☐X☐☐☐☐☐X☐☐☐☐☐X☐XXX☐X☐X☐XXX☐X☐XXX☐☐☐☐XX☐XXXX☐☐☐X☐XX☐☐☐XXXXX☐☐X☐☐☐☐X☐☐XX☐X☐X☐XXXXX☐☐X☐XXXX☐☐☐☐ after toggling with step = 10
☐XX☐XXXX☐XX☐☐☐☐X☐☐☐☐☐☐☐XXX☐X☐X☐X☐X☐X☐XXX☐☐☐XXX☐XXXX☐☐☐☐☐XX☐☐☐XXXX☐☐☐X☐☐☐☐X☐☐☐X☐X☐X☐XXXX☐☐☐X☐XXXX☐☐X☐ after toggling with step = 11
☐XX☐XXXX☐XXX☐☐☐X☐☐☐☐☐☐☐☐XX☐X☐X☐X☐X☐☐☐XXX☐☐☐XXX☐☐XXX☐☐☐☐☐XX☐X☐XXXX☐☐☐X☐☐X☐X☐☐☐X☐X☐X☐☐XXX☐☐☐X☐XXX☐☐☐X☐ after toggling with step = 12
☐XX☐XXXX☐XXXX☐☐X☐☐☐☐☐☐☐☐X☐☐X☐X☐X☐X☐☐☐X☐X☐☐☐XXX☐☐XXXX☐☐☐☐XX☐X☐XXX☐☐☐☐X☐☐X☐X☐☐☐☐☐X☐X☐☐XXX☐☐☐☐☐XXX☐☐☐X☐ after toggling with step = 13
☐XX☐XXXX☐XXXXX☐X☐☐☐☐☐☐☐☐X☐☐☐☐X☐X☐X☐☐☐X☐X☐X☐XXX☐☐XXXX☐☐☐XXX☐X☐XXX☐☐☐☐XX☐X☐X☐☐☐☐☐X☐X☐XXXX☐☐☐☐☐XXX☐☐XX☐ after toggling with step = 14
☐XX☐XXXX☐XXXXXXX☐☐☐☐☐☐☐☐X☐☐☐☐☐☐X☐X☐☐☐X☐X☐X☐X☐X☐☐XXXX☐☐☐XXX☐☐☐XXX☐☐☐☐XX☐X☐XX☐☐☐☐X☐X☐XXXX☐☐X☐☐XXX☐☐XX☐ after toggling with step = 15
☐XX☐XXXX☐XXXXXX☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐X☐☐☐X☐X☐X☐X☐X☐XXXXX☐☐☐XXX☐☐☐XX☐☐☐☐☐XX☐X☐XX☐☐☐☐☐☐X☐XXXX☐☐X☐☐XXXX☐XX☐ after toggling with step = 16
☐XX☐XXXX☐XXXXXX☐X☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐X☐X☐X☐X☐XXX☐X☐☐☐XXX☐☐☐XX☐☐☐☐XXX☐X☐XX☐☐☐☐☐☐X☐X☐XX☐☐X☐☐XXXX☐XX☐ after toggling with step = 17
☐XX☐XXXX☐XXXXXX☐XX☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐X☐X☐X☐X☐X☐X☐XXX☐X☐X☐XXX☐☐☐XX☐☐☐☐XXX☐☐☐XX☐☐☐☐☐☐X☐X☐XX☐☐☐☐☐XXXX☐XX☐ after toggling with step = 18
☐XX☐XXXX☐XXXXXX☐XXX☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐X☐☐☐X☐X☐X☐X☐XXX☐X☐X☐X☐X☐☐☐XX☐☐☐☐XXX☐☐☐XXX☐☐☐☐☐X☐X☐XX☐☐☐☐☐XX☐X☐XX☐ after toggling with step = 19
☐XX☐XXXX☐XXXXXX☐XXXX☐☐☐☐X☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐X☐X☐X☐XXX☐X☐X☐X☐X☐X☐XX☐☐☐☐XXX☐☐☐XXX☐☐☐X☐X☐X☐XX☐☐☐☐☐XX☐X☐XXX after toggling with step = 20
☐XX☐XXXX☐XXXXXX☐XXXXX☐☐☐X☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐X☐X☐XXX☐X☐X☐X☐X☐X☐X☐☐☐☐☐XXX☐☐☐XXX☐☐☐X☐X☐☐☐XX☐☐☐☐☐XX☐X☐XXX after toggling with step = 21
☐XX☐XXXX☐XXXXXX☐XXXXXX☐☐X☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐X☐XXX☐X☐X☐X☐X☐X☐X☐☐☐X☐XXX☐☐☐XXX☐☐☐X☐X☐☐☐XXX☐☐☐☐XX☐X☐XXX after toggling with step = 22
☐XX☐XXXX☐XXXXXX☐XXXXXXX☐X☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐XXX☐X☐X☐X☐X☐X☐X☐☐☐X☐X☐X☐☐☐XXX☐☐☐X☐X☐☐☐XXX☐☐☐XXX☐X☐XXX after toggling with step = 23
☐XX☐XXXX☐XXXXXX☐XXXXXXXXX☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐XX☐X☐X☐X☐X☐X☐X☐☐☐X☐X☐X☐X☐XXX☐☐☐X☐X☐☐☐XXX☐☐☐XXX☐☐☐XXX after toggling with step = 24
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐X☐X☐X☐X☐X☐X☐☐☐X☐X☐X☐X☐X☐X☐☐☐X☐X☐☐☐XXX☐☐☐XXX☐☐☐XX☐ after toggling with step = 25
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐X☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐X☐X☐X☐X☐X☐☐☐X☐X☐X☐X☐X☐X☐X☐X☐X☐☐☐XXX☐☐☐XXX☐☐☐XX☐ after toggling with step = 26
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XX☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐X☐X☐X☐X☐☐☐X☐X☐X☐X☐X☐X☐X☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XX☐ after toggling with step = 27
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXX☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐X☐X☐X☐☐☐X☐X☐X☐X☐X☐X☐X☐XXX☐X☐XXX☐☐☐XXX☐☐☐XX☐ after toggling with step = 28
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXX☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐X☐X☐☐☐X☐X☐X☐X☐X☐X☐X☐XXX☐X☐X☐X☐☐☐XXX☐☐☐XX☐ after toggling with step = 29
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXX☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐X☐X☐X☐X☐X☐X☐X☐XXX☐X☐X☐X☐X☐XXX☐☐☐XX☐ after toggling with step = 30
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXX☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐X☐X☐X☐X☐X☐X☐XXX☐X☐X☐X☐X☐X☐X☐☐☐XX☐ after toggling with step = 31
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXX☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐X☐X☐X☐X☐X☐X☐X☐XXX☐X☐X☐X☐X☐X☐X☐X☐XX☐ after toggling with step = 32
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXX☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐X☐X☐X☐X☐X☐X☐XXX☐X☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 33
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXX☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐X☐X☐X☐X☐X☐XXX☐X☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 34
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXXX☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐X☐X☐X☐X☐XXX☐X☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 35
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐X☐X☐X☐XXX☐X☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 36
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐X☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐X☐X☐XXX☐X☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 37
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XX☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐X☐XXX☐X☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 38
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXX☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐XXX☐X☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 39
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXX☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐XX☐X☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 40
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXX☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐X☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 41
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXX☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 42
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXX☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 43
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXX☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐X☐X☐X☐X☐X☐☐ after toggling with step = 44
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXX☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐X☐X☐X☐X☐☐ after toggling with step = 45
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXX☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐X☐X☐☐ after toggling with step = 46
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXX☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐X☐☐ after toggling with step = 47
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXXX☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐ after toggling with step = 48
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐ after toggling with step = 49
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐X☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 50
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XX☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 51
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXX☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 52
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXX☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 53
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXX☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 54
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXX☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 55
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXX☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 56
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXX☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 57
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXX☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 58
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXX☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 59
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXX☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 60
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXX☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 61
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXX☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 62
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXXX☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 63
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 64
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 65
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XX☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 66
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXX☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 67
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXX☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 68
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXX☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 69
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXX☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 70
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXX☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 71
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXX☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 72
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXX☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 73
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXX☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 74
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXX☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 75
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXX☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 76
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXX☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 77
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXX☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 78
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXX☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 79
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXXX☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 80
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 81
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 82
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XX☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 83
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXX☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 84
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXX☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 85
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXX☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 86
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXX☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 87
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXX☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 88
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXX☐☐☐☐☐☐☐☐☐☐X after toggling with step = 89
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXX☐☐☐☐☐☐☐☐☐X after toggling with step = 90
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXX☐☐☐☐☐☐☐☐X after toggling with step = 91
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXXX☐☐☐☐☐☐☐X after toggling with step = 92
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXXXX☐☐☐☐☐☐X after toggling with step = 93
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXXXXX☐☐☐☐☐X after toggling with step = 94
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXXXXXX☐☐☐☐X after toggling with step = 95
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXXXXXXX☐☐☐X after toggling with step = 96
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐☐X after toggling with step = 97
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXXX☐X after toggling with step = 98
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXXXXX after toggling with step = 99
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXXXX☐ after toggling with step = 100

Dc

Unoptimized:

Works with: GNU dc version 1.3.95

 
## NB: This code uses the dc command "r" via register "r".
##     You may comment out the unwanted version.
[SxSyLxLy]sr    # this should work with every "dc"
[r]sr           # GNU dc can exchange top 2 stack values by "r"
## Now use "lrx" instead of "r" ...
 
0k              # we work without decimal places
[q]sq           # useful e.g. as loop termination
 
## (x)(y)>R  ==  if (y)>(x) eval R
## isle         x y --> (x <= y)
[
    [1q]S. [ !<. 0 ]x s.L.
]sl
## l: isle
 
[
    100 llx
]sL
## L: isle100
 
## for  initcode condcode incrcode body
##       [1]      [2]      [3]      [4]
[
    [q]S. 4:. 3:. 2:. 1:.  1;.x [2;.x 0=. 4;.x 3;.x 0;.x]d0:.x Os.L.o
]sf
## f: for
##----------------------------------------------------------------------------
 
##      for( i=1 ; i<=100 ; ++i ) {
##          door[i] = 0;
##      }
#[init ...]P []ps-
[1si] [li lLx] [li1+si] [
    li 0:d
]lfx
 
##      for( s=1 ; s<=100 ; ++s ) {
##          for( i=s ; i<=100 ; i+=s ) {
##              door[i] = 1 - door[i]
##          }
##      }
[1ss] [ls lLx] [ls1+ss] [
    #[step ]P lsn [ ...]ps-
    [lssi] [li lLx] [lils+si] [
        1 li;d - li:d
    ]lfx
]lfx
 
##      long output:
##          for( i=1 ; i<=100 ; ++i ) {
##              print "door #", i, " is ", (door[i] ? "open" : "closed")), NL
##          }
[
    [1si] [li lLx] [li1+si] [
        [door #]P
        li n
        [ is ]P
            [closed]
            [open]
        li;d 0=r lrx s- n
        [.]ps-
    ]lfx
]
 
##      terse output:
##          for( i=1 ; i<=100 ; ++i ) {
##              if( door[i] ) {
##                  print i
##              }
##              print NL
##          }
[
    [1si] [li lLx] [li1+si] [
        [] [ [ ]n lin ]
        li;d 0=r lrx s- x
    ]lfx
    []ps-
]
 
lrx             # comment out for the long output version
s- x
#[stack rest...]P []ps- f
 

Output:

 1 4 9 16 25 36 49 64 81 100

DCL

Adapted from optimized Batch example

 
$! doors.com
$! Excecute by running @doors at prompt.
$ square = 1
$ incr = 3
$ count2 = 0
$ d = 1
$ LOOP2:
$       count2 = count2 + 1
$       IF (d .NE. square)
$               THEN WRITE SYS$OUTPUT "door ''d' is closed"
$       ELSE WRITE SYS$OUTPUT "door ''d' is open"
$               square = incr + square
$               incr = incr + 2
$       ENDIF
$       d = d + 1
$       IF (count2 .LT. 100) THEN GOTO LOOP2
 

Delphi

See Pascal

Draco

proc nonrec main() void:
    byte DOORS = 100;
    [DOORS+1] bool door_open;
    unsigned DOORS i, j;
 
    /* make sure all doors are closed */
    for i from 1 upto DOORS do door_open[i] := false od;
 
    /* pass through the doors */
    for i from 1 upto DOORS do
        for j from i by i upto DOORS do
            door_open[j] := not door_open[j]
        od
    od;
 
    /* show the open doors */
    for i from 1 upto DOORS do
        if door_open[i] then
            writeln("Door ", i, " is open.")
        fi
    od
corp

Output:

Door 1 is open.
Door 4 is open.
Door 9 is open.
Door 16 is open.
Door 25 is open.
Door 36 is open.
Door 49 is open.
Door 64 is open.
Door 81 is open.
Door 100 is open.

DUP

100[$][0^:1-]#                                                  {initialize doors}
%
[s;[$101<][$$;~\:s;+]#%]d:                                     {function d, switch door state function}
1s:[s;101<][d;!s;1+s:]#                                        {increment step width from 1 to 100, execute function d each time}
1[$101<][$$.' ,;['o,'p,'e,'n,10,]['c,'l,'o,'s,'e,'d,10,]?1+]#  {loop through doors, print door number and state}

Result:

1 open
2 closed
3 closed
4 open
5 closed
6 closed
7 closed
8 closed
9 open
10 closed
11 closed
12 closed
...
94 closed
95 closed
96 closed
97 closed
98 closed
99 closed
100 open

Compare this solution to the FALSE solution of this problem.

DWScript

Unoptimized

var doors : array [1..100] of Boolean;
var i, j : Integer;
 
for i := 1 to 100 do
   for j := i to 100 do
      if (j mod i) = 0 then
         doors[j] := not doors[j];F
 
for i := 1 to 100 do
   if doors[i] then
      PrintLn('Door '+IntToStr(i)+' is open');

Dyalect

Outputs only open doors to save up space:

var doors = Array.Empty(100, false)
 
for p in 0..99 {
    for d in 0..99 {
        if (d + 1) % (p + 1) == 0 {
            doors[d] = !doors[d];
        }
    }
}
 
for d in doors.Indices() when doors[d] {
    print("Door \(d+1): Open")
}

Output:

Door 1: Open
Door 4: Open
Door 9: Open
Door 16: Open
Door 25: Open
Door 36: Open
Door 49: Open
Door 64: Open
Door 81: Open
Door 100: Open

Dylan

Unoptimized

define method doors()
  let doors = make(<array>, fill: #f, size: 100);
  for (x from 0 below 100)
    for (y from x below 100 by x + 1)
      doors[y] := ~doors[y]
    end
  end;
  for (x from 1 to 100) 
    if (doors[x - 1]) 
      format-out("door %d open\n", x)
    end
  end
end

Déjà Vu

local :open-doors [ rep 101 false ]
 
for i range 1 100:
	local :j i
	while <= j 100:
		set-to open-doors j not open-doors! j
		set :j + j i
 
!print\ "Open doors: "
for i range 1 100:
	if open-doors! i:
		!print\( to-str i " " )

Output:

Open doors: 1 4 9 16 25 36 49 64 81 100 

E

Graphical

Works with: E-on-Java

This version animates the changes of the doors (as checkboxes).

#!/usr/bin/env rune
 
var toggles := []
var gets := []
 
# Set up GUI (and data model)
def frame := <swing:makeJFrame>("100 doors")
frame.getContentPane().setLayout(<awt:makeGridLayout>(10, 10))
for i in 1..100 {
  def component := <import:javax.swing.makeJCheckBox>(E.toString(i))
  toggles with= fn { component.setSelected(!component.isSelected()) }
  gets with= fn { component.isSelected() }
  frame.getContentPane().add(component)
}
 
# Set up termination condition
def done
frame.addWindowListener(def _ {
  to windowClosing(event) {
    bind done := true
  }
  match _ {}
})
 
# Open and close doors
def loop(step, i) {
  toggles[i] <- ()
  def next := i + step
  timer.whenPast(timer.now() + 10, fn {
    if (next >= 100) {
      if (step >= 100) {
        # Done.
      } else {
        loop <- (step + 1, step)
      }
    } else {
      loop <- (step, i + step)
    }    
  })
}
loop(1, 0)
 
frame.pack()
frame.show()
interp.waitAtTop(done)

EasyLang

len d[] 101
for p = 1 to 100
  i = p
  while i <= 100
    d[i] = 1 - d[i]
    i += p
  .
.
for i = 1 to 100
  if d[i] = 1
    print i
  .
.

EchoLisp

The result is obviously the same in we run the process backwards. So, we check the state of each door during the 100-th step (opening/closing every door)

 
; initial state = closed = #f
(define doors (make-vector 101 #f))
; run pass 100 to 1
(for* 
   ((pass (in-range 100 0 -1)) 
   (door (in-range 0 101 pass))) 
    (when (and 
        (vector-set! doors door (not (vector-ref doors door))) 
        (= pass 1)) 
        (writeln door "is open"))) 
 
1     "is open"    
4     "is open"    
9     "is open"    
16     "is open"    
25     "is open"    
36     "is open"    
49     "is open"    
64     "is open"    
81     "is open"    
100     "is open"    
 

ECL

optimized version

 
Doors := RECORD
 UNSIGNED1 DoorNumber;
 STRING6   State;
END;
 
AllDoors := DATASET([{0,0}],Doors);
 
Doors  OpenThem(AllDoors L,INTEGER Cnt) := TRANSFORM
 SELF.DoorNumber := Cnt;
 SELF.State      := IF((CNT * 10) % (SQRT(CNT)*10)<>0,'Closed','Opened');
END;
 
OpenDoors := NORMALIZE(AllDoors,100,OpenThem(LEFT,COUNTER));
 
OpenDoors;
 

unoptimized version - demonstrating LOOP

 
Doors := RECORD
  UNSIGNED1 DoorNumber;
  STRING6   State;
END;
 
AllDoors := DATASET([{0,'0'}],Doors);
 
//first build the 100 doors
 
Doors  OpenThem(AllDoors L,INTEGER Cnt) := TRANSFORM
  SELF.DoorNumber := Cnt;
  SELF.State      := 'Closed';
END;
 
ClosedDoors := NORMALIZE(AllDoors,100,OpenThem(LEFT,COUNTER));
 
//now iterate through them and use door logic
 
loopBody(DATASET(Doors) ds, UNSIGNED4 c) :=
            PROJECT(ds,    //ds=original input
              TRANSFORM(Doors,
                      	SELF.State := CASE((COUNTER % c) * 100,
		                            0 => IF(LEFT.STATE = 'Opened','Closed','Opened')
					    ,LEFT.STATE);
			SELF.DoorNumber := COUNTER;     //PROJECT COUNTER
                    ));
 
g1 := LOOP(ClosedDoors,100,loopBody(ROWS(LEFT),COUNTER));
 
OUTPUT(g1);
 
 

unoptimized version - using ITERATE This is a bit more efficient than the LOOP version

 
DoorSet := DATASET(100,TRANSFORM({UNSIGNED1 DoorState},SELF.DoorState := 1));
SetDoors := SET(DoorSet,DoorState);
 
Doors := RECORD
  UNSIGNED1 Pass;
  SET OF UNSIGNED1 DoorSet;
END;
 
StartDoors := DATASET(100,TRANSFORM(Doors,SELF.Pass := COUNTER,SELF.DoorSet := SetDoors));
 
Doors XF(Doors L, Doors R) := TRANSFORM
  ds := DATASET(L.DoorSet,{UNSIGNED1 DoorState});
  NextDoorSet := PROJECT(ds,  
                         TRANSFORM({UNSIGNED1 DoorState},
                      	           SELF.DoorState := CASE((COUNTER % R.Pass) * 100,
                                                          0 => IF(LEFT.DoorState = 1,0,1),
                                                          LEFT.DoorState)));
  SELF.DoorSet := IF(L.Pass=0,R.DoorSet,SET(NextDoorSet,DoorState));									
  SELF.Pass := R.Pass										
END;										
 
Res := DATASET(ITERATE(StartDoors,XF(LEFT,RIGHT))[100].DoorSet,{UNSIGNED1 DoorState});
PROJECT(Res,TRANSFORM({STRING20 txt},SELF.Txt := 'Door ' + COUNTER + ' is ' + IF(LEFT.DoorState=1,'Open','Closed')));
 

EDSAC order code

Since there are only 100 doors, we'll keep things simple and use a whole EDSAC location for each door. A single bit would be enough, but that would make the code much longer.

The program works through the array of doors by modifying its own orders (instructions). This would be considered bad practice today, but was quite usual on the EDSAC.

 
[Hundred doors problem from Rosetta Code website]
[EDSAC program, Initial Orders 2]
 
[Library subroutine M3. Prints header and is then overwritten.
Here, the last character sets the teleprinter to figures.]
       [email protected]@E8FEZPF
       @&*[email protected]&#
       ..PZ   [blank tape, needed to mark end of header text]
 
[Library subroutine P6. Prints strictly positive integer.
32 locations; working locations 1, 4, 5]
        T56K  [define load address for subroutine]
        [email protected]@[email protected]@[email protected]
        [email protected]
        [email protected]@[email protected]@J995FJF!F
 
        T88K   [define load address for main program]
        GK     [set @ (theta) for relative addresses]
 
[The 100 doors are at locations 200..299.
Doors are numbered 0..99 internally, and 1..100 for output.
The base address and the number of doors can be varied.
The value of a door is 0 if open, negative if closed.]
 
                   [Constants. Program also uses order 'P 1 F'
                    which is permanently at absolute address 2.]
    [0] P200F  [address of door #0]
    [1] P100F  [number of doors, as an address]
    [2] UF     [makes S order from T, since 'S' = 'T' + 'U']
    [3] MF     [makes A order from T, since 'A' = 'T' + 'M']
    [4] V2047D [all 1's for "closed" (any negative value will do)]
    [5] &F     [line feed]
    [6] @F     [carriage return]
    [7] K4096F [teleprinter null[
 
                   [Variables]
    [8] PF   [pass number; step when toggling doors]
    [9] PF   [door number, as address, 0-based]
   [10] PF   [order referring to door 0]
 
                   [Enter with acc = 0]
                   [Part 1 : close all the doors]
   [11] [email protected]  [pass := 0 (used in part 2)]
        [email protected]  [door number := 0]
        [email protected] [load 'T F' order]
        [email protected]   [add base address]
        [email protected] [store T order for door #0]
   [16] TF   [clear acc; also serves as constant]
        [email protected]  [load door number]
        [email protected] [make T order]
        [email protected] [plant in code]
        [email protected]  [load value for "closed"]
   [21] TF   [store in current door]
        [email protected]  [load door number]
        A2F  [add 1]
        [email protected]  [update door number]
        [email protected]  [done all doors yet?]
        [email protected] [if not, loop back]
 
                   [Part 2 : 100 passes, toggling the doors]
   [27] TF   [clear acc]
        [email protected]  [load pass number]
        A2F  [add 1]
        [email protected]  [save updated pass number]
        S2F  [make -1]
        [email protected]  [door number := -1]
        [email protected]  [add pass number to get first door toggled on this pass]
        [email protected]  [gone beyond end?]
        [email protected] [if so, move on to part 3]
   [36] [email protected]  [restore acc after test]
        [email protected]  [store current door number]
        [email protected] [make T order to load status]
        [email protected] [plant T order for first door in pass]
        [email protected]  [convert to S order]
        [email protected] [plant S order]
        [email protected]  [load value for "closed"]
   [43] SF   [subtract status; toggles status]
   [44] TF   [update status]
        [email protected]  [load door number just toggled]
        [email protected]  [add pass number to get next door in pass]
        [email protected]  [gone beyond end?]
        [email protected] [no, loop to do next door]
        [email protected] [yes, loop to do next pass]
 
                   [Part 3 : Print list of open doors.
                    Header has set teleprinter to figures.]
   [50] TF   [clear acc]
        [email protected]  [door nr := 0]
        [email protected] [T order for door 0]
        [email protected]  [convert to A order]
        [email protected]
   [55] TF
        [email protected]  [load door number]
        [email protected] [make A order to load value]
        [email protected] [plant in next order]
   [59] AF   [acc := 0 if open, < 0 if closed]
        [email protected] [skip if closed]
        [email protected]  [door number as address]
        A2F  [add 1 for 1-based output]
        RD   [shift 1 right, address --> integer]
        TF   [store integer at 0 for printing]
   [65] [email protected] [for return from subroutine]
        G56F [call subroutine to print door number]
        [email protected]  [followed by CRLF]
        [email protected]
   [69] TF   [clear acc]
        [email protected]  [load door number]
        A2F  [add 1]
        [email protected]  [update door number]
        [email protected]  [done all doors yet?]
        [email protected]  [if not, loop back]
   [75] [email protected]  [output null to flush teleprinter buffer]
        ZF   [stop]
        E11Z [define relative start address]
        PF
 

Output:

THE OPEN DOORS ARE
    1
    4
    9
   16
   25
   36
   49
   64
   81
  100

Eero

 
#import <Foundation/Foundation.h>
 
int main()
  square := 1, increment = 3
 
  for int door in 1 .. 100
    printf("door #%d", door)
 
    if door == square
      puts(" is open.")
      square += increment
      increment += 2
    else
      puts(" is closed.")
 
  return 0
 

Egel

 
import "prelude.eg"
 
using System
using List
 
data open, closed
 
def toggle =
    [ open N -> closed N | closed N -> open N ]
 
def doors =
    [ N -> map [ N -> closed N ] (fromto 1 N) ]
 
def toggleK =
    [ K nil              -> nil
    | K (cons (D N) DD)  -> 
         let DOOR = if (N%K) == 0 then toggle (D N) else D N in
             cons DOOR (toggleK K DD) ]
 
def toggleEvery =
    [ nil DOORS -> DOORS
    | (cons K KK) DOORS -> toggleEvery KK (toggleK K DOORS) ]
 
def run =
    [ N -> toggleEvery (fromto 1 N) (doors N) ]
 
def main = run 100
 

EGL

 
program OneHundredDoors
 
   function main()
 
      doors boolean[] = new boolean[100];
      n int = 100;
 
      for (i int from 1 to n)
         for (j int from i to n by i)
            doors[j] = !doors[j];
         end
      end
 
      for (i int from 1 to n)
         if (doors[i])
            SysLib.writeStdout( "Door " + i + " is open" );
         end
      end
 
   end
 
end
 

Eiffel

This is my first RosettaCode submission, as well as a foray into Eiffel for myself. I've tried to adhere to the description of the problem statement, as well as showcase a few Eiffelisms shown in the documentation.

The replacement code below took the original code and has made improvements in some ways, such as:

1. Removal of "magic" many magic numbers and strings.
2. Refactor of various code blocks to routines (commands and queries with good CQS).
3. Utilization/Demonstration of full, secret, and selective feature exporting.
4. Utilization/Demonstration of constants as expanded type constants and once-functions.
5. Utilization/Demonstration of static-references (e.g. {APPLICATION}.min_door_count).
6. Utilization/Demonstration of "like" keyword type anchoring (e.g. a_index_address: like {DOOR}.address).
7. Utilization/Demonstration of semi-strict logical implication (e.g. consistency: is_open implies not Is_closed).
8. Utilization/Demonstration of contracts, including require, ensure, and class invariant.
9. Utilization/Demonstration of agent and `do_all' call on ITERABLE type.
10. Utilization/Demonstration of various forms of across including "loop" and "all".

... as well as other Eiffel-ism's and some coding standards/best-practices.

file: application.e

note
	description: "100 Doors problem"
	date: "08-JUL-2015"
	revision: "1.1"
 
class
	APPLICATION
 
create
	make
 
feature {NONE} -- Initialization
 
	make
			-- Main application routine.
		do
			initialize_closed_doors
			toggle_doors
			output_door_states
		end
 
feature -- Access
 
	doors: ARRAYED_LIST [DOOR]
			-- A set of doors (self-initialized to capacity of `max_door_count').
		attribute
			create Result.make (max_door_count)
		end
 
feature -- Basic Operations
 
	initialize_closed_doors
			-- Initialize all `doors'.
		do
			across min_door_count |..| max_door_count as ic_address_list loop
				doors.extend (create {DOOR}.make_closed (ic_address_list.item))
			end
		ensure
			has_all_closed_doors: across doors as ic_doors_list all not ic_doors_list.item.is_open end
		end
 
	toggle_doors
			-- Toggle all `doors'.
		do
			across min_door_count |..| max_door_count as ic_addresses_list loop
				across doors as ic_doors_list loop
					if is_door_to_toggle (ic_doors_list.item.address, ic_addresses_list.item) then
						ic_doors_list.item.toggle_door
					end
				end
			end
		end
 
	output_door_states
			-- Output the state of all `doors'.
		do
			doors.do_all (agent door_state_out)
		end
 
feature -- Status Report
 
	is_door_to_toggle (a_door_address, a_index_address: like {DOOR}.address): BOOLEAN
			-- Is the door at `a_door_address' needing to be toggled, when compared to `a_index_address'?
		do
			Result := a_door_address \\ a_index_address = 0
		ensure
			only_modulus_zero: Result = (a_door_address \\ a_index_address = 0)
		end
 
feature -- Outputs
 
	door_state_out (a_door: DOOR)
			-- Output the state of `a_door'.
		do
			print ("Door " + a_door.address.out + " is ")
			if a_door.is_open then
				print ("open.")
			else
				print ("closed.")
			end
			io.new_line
		end
 
feature {DOOR} -- Constants
 
	min_door_count: INTEGER = 1
			-- Minimum number of doors.
 
	max_door_count: INTEGER = 100
			-- Maximum number of doors.
 
end

file: door.e

note
	description: "A door with an address and an open or closed state."
	date: "08-JUL-2015"
	revision: "1.1"
 
class
	DOOR
 
create
	make_closed,
	make
 
feature {NONE} -- initialization
 
	make_closed (a_address: INTEGER)
			-- Initialize Current {DOOR} at `a_address' and state of `Is_closed'.
		require
			positive: a_address >= {APPLICATION}.min_door_count and a_address >= Min_door_count
		do
			make (a_address, Is_closed)
		ensure
			closed: is_open = Is_closed
		end
 
	make (a_address: INTEGER; a_status: BOOLEAN)
			-- Initialize Current {DOOR} with `a_address' and `a_status', denoting position and `is_open' or `Is_closed'.
		require
			positive: a_address >= {APPLICATION}.min_door_count and a_address >= Min_door_count
		do
			address := a_address
			is_open := a_status
		ensure
			address_set: address = a_address
			status_set: is_open = a_status
		end
 
feature -- access
 
	address: INTEGER
			-- `address' of Current {DOOR}.
 
	is_open: BOOLEAN assign set_open
			-- `is_open' (or not) status of Current {DOOR}.
 
feature -- Setters
 
	set_open (a_status: BOOLEAN)
			-- Set `status' with `a_status'
		do
			is_open := a_status
		ensure
			open_updated: is_open = a_status
		end
 
feature {APPLICATION} -- Basic Operations
 
	toggle_door
			-- Toggle Current {DOOR} from `is_open' to not `is_open'.
		do
			is_open := not is_open
		ensure
			toggled: is_open /= old is_open
		end
 
feature {NONE} -- Implementation: Constants
 
	Is_closed: BOOLEAN = False
			-- State of being not `is_open'.
 
	Min_door_count: INTEGER = 1
			-- Minimum door count.
 
invariant
	one_or_more: address >= 1
	consistency: is_open implies not Is_closed
 
end

Ela

Standard Approach

open generic
 
type Door = Open | Closed
  deriving Show
 
gate [] _ = []
gate (x::xs) (y::ys) 
  | x == y = Open :: gate xs ys
  | else = Closed :: gate xs ys
 
run n = gate [1..n] [& k*k \\ k <- [1..]]

Alternate Approach

open list
run n = takeWhile (<n) [& k*k \\ k <- [1..]]

Elena

ELENA 4.0 :

import system'routines;
import extensions;
 
public program()
{ 
    var Doors := Array.allocate(100).populate:(n=>false);
    for(int i := 0, i < 100, i := i + 1)
    {
        for(int j := i, j < 100, j := j + i + 1)
        {
            Doors[j] := Doors[j].Inverted
        }
    };
 
    for(int i := 0, i < 100, i := i + 1)
    {
        console.printLine("Door #",i + 1," :",Doors[i].iif("Open","Closed"))
    };
 
    console.readChar()
}

Elixir

defmodule HundredDoors do
  def doors(n \\ 100) do
    List.duplicate(false, n)
  end
 
  def toggle(doors, n) do
    List.update_at(doors, n, &(!&1))
  end
 
  def toggle_every(doors, n) do
    Enum.reduce( Enum.take_every((n-1)..99, n), doors, fn(n, acc) -> toggle(acc, n) end )
  end
end
 
# unoptimized
final_state = Enum.reduce(1..100, HundredDoors.doors, fn(n, acc) -> HundredDoors.toggle_every(acc, n) end)
 
open_doors = Enum.with_index(final_state)
             |> Enum.filter_map(fn {door,_} -> door end, fn {_,index} -> index+1 end)
 
IO.puts "All doors are closed except these: #{inspect open_doors}"
 
 
# optimized 
final_state = Enum.reduce(1..10, HundredDoors.doors, fn(n, acc) -> HundredDoors.toggle(acc, n*n-1) end)
 
open_doors = Enum.with_index(final_state)
             |> Enum.filter_map(fn {door,_} -> door end, fn {_,index} -> index+1 end)
 
IO.puts "All doors are closed except these: #{inspect open_doors}"

Output:

All doors are closed except these: [1, 4, 9, 16, 25, 36, 49, 64, 81, 100]

Elm

-- Unoptimized
import List exposing (indexedMap, foldl, repeat, range)
import Html exposing (text)
import Debug exposing (toString)
 
type Door = Open | Closed
 
toggle d = if d == Open then Closed else Open
 
toggleEvery : Int -> List Door -> List Door
toggleEvery k doors = indexedMap 
  (\i door -> if modBy k (i+1) == 0 then toggle door else door)
  doors
 
n = 100
 
main = 
  text (toString (foldl toggleEvery (repeat n Closed) (range 1 n)))
 

Emacs Lisp

Unoptimized

(defun create-doors ()
  "Returns a list of closed doors
 
Each door only has two status: open or closed.
If a door is closed it has the value 0, if it's open it has the value 1."
  (let ((return_value '(0))
         ;; There is already a door in the return_value, so k starts at 1
         ;; otherwise we would need to compare k against 99 and not 100 in
         ;; the while loop
         (k 1))
    (while (< k 100)
      (setq return_value (cons 0 return_value))
      (setq k (+ 1 k)))
    return_value))
 
(defun toggle-single-door (doors)
  "Toggle the stat of the door at the `car' position of the DOORS list
 
DOORS is a list of integers with either the value 0 or 1 and it represents
a row of doors.
 
Returns a list where the `car' of the list has it's value toggled (if open
it becomes closed, if closed it becomes open)."
  (if (= (car doors) 1)
    (cons 0 (cdr doors))
    (cons 1 (cdr doors))))
 
(defun toggle-doors (doors step original-step)
  "Step through all elements of the doors' list and toggle a door when step is 1
 
DOORS is a list of integers with either the value 0 or 1 and it represents
a row of doors.
STEP is the number of doors we still need to transverse before we arrive
at a door that has to be toggled.
ORIGINAL-STEP is the value of the argument step when this function is
called for the first time.
 
Returns a list of doors"
  (cond ((null doors)
          '())
    ((= step 1)
      (cons (car (toggle-single-door doors))
        (toggle-doors (cdr doors) original-step original-step)))
    (t
      (cons (car doors)
        (toggle-doors (cdr doors) (- step 1) original-step)))))
 
(defun main-program ()
  "The main loop for the program"
  (let ((doors_list (create-doors))
         (k 1)
         ;; We need to define max-specpdl-size and max-specpdl-size to big
         ;; numbers otherwise the loop reaches the max recursion depth and
         ;; throws an error.
         ;; If you want more information about these variables, press Ctrl
         ;; and h at the same time and then press v and then type the name
         ;; of the variable that you want to read the documentation.
         (max-specpdl-size 5000)
         (max-lisp-eval-depth 2000))
    (while (< k 101)
      (setq doors_list (toggle-doors doors_list k k))
      (setq k (+ 1 k)))
    doors_list))
 
(defun print-doors (doors)
  "This function prints the values of the doors into the current buffer.
 
DOORS is a list of integers with either the value 0 or 1 and it represents
a row of doors.
"
  ;; As in the main-program function, we need to set the variable
  ;; max-lisp-eval-depth to a big number so it doesn't reach max recursion
  ;; depth.
  (let ((max-lisp-eval-depth 5000))
    (unless (null doors)
      (insert (int-to-string (car doors)))
      (print-doors (cdr doors)))))
 
;; Returns a list with the final solution
(main-program)
 
;; Print the final solution on the buffer
(print-doors (main-program))

Erlang

non-optimized

 
-module(hundoors).
 
-export([go/0]).
 
toggle(closed) -> open;
toggle(open) -> closed.
 
go() -> go([closed || _ <- lists:seq(1, 100)],[], 1, 1).
go([], L, N, _I) when N =:= 101 -> lists:reverse(L);
go([], L, N, _I) -> go(lists:reverse(L), [], N + 1, 1);
go([H|T], L, N, I) ->
  H2 = case I rem N of
    0 -> toggle(H);
    _ -> H
  end,
  go(T, [H2|L], N, I + 1).
 

optimized

doors() ->
     F = fun(X) -> Root = math:pow(X,0.5), Root == trunc(Root) end,
     Out = fun(X, true) -> io:format("Door ~p: open~n",[X]);
              (X, false)-> io:format("Door ~p: close~n",[X]) end,
     [Out(X,F(X)) || X <- lists:seq(1,100)].

ERRE

 
! "100 Doors" program for ERRE LANGUAGE
! Author: Claudio Larini
! Date: 21-Nov-2014
!
! PC Unoptimized version translated from a QB version
 
PROGRAM 100DOORS
 
!$INTEGER
 
CONST N=100
 
DIM DOOR[N]
 
BEGIN
 
FOR STRIDE=1 TO N DO
    FOR INDEX=STRIDE TO N STEP STRIDE DO
        DOOR[INDEX]=NOT(DOOR[INDEX])
    END FOR
END FOR
 
PRINT("Open doors:";)
FOR INDEX=1 TO N DO
    IF DOOR[INDEX] THEN PRINT(INDEX;) END IF
END FOR
PRINT
 
END PROGRAM
 

Euler Math Toolbox

 
>function Doors () ...
$  doors:=zeros(1,100);
$  for i=1 to 100
$    for j=i to 100 step i
$      doors[j]=!doors[j];
$    end;
$  end;
$  return doors
$endfunction
>nonzeros(Doors())
 [ 1  4  9  16  25  36  49  64  81  100 ]
 

Euphoria

unoptimised

-- doors.ex
include std/console.e
sequence doors
doors = repeat( 0, 100 ) -- 1 to 100, initialised to false 
 
for pass = 1 to 100 do
	for door = pass to 100 by pass do
		--printf( 1, "%d", doors[door] )
		--printf( 1, "%d", not doors[door] )
		doors[door] = not doors[door]
	end for
end for
 
sequence oc
 
for i = 1 to 100 do
	if doors[i] then
		oc = "open"
	else
		oc = "closed"
	end if
 	printf( 1, "door %d is %s\n", { i, oc } )
end for
 

Excel

Note: The use of Auto Fill saves a lot of time when entering this code. One can refer to Excel help pages to learn about Auto Fill features.
Create a labelling column (A) and row (1) labelling the number of the door (column A, labelling starts in row 2 with a "1" and continues counting up to "100" in row 101) and the number of the pass (row 1, labelling starts in column B with a "0" and continues counting up to "100" in column CX). Additonally, you can label cell A1 as "Door/Pass" or so.
Closed doors are represented by zeroes ("0"), open doors are represented by ones ("1"). To represent the initial condition fill rows 2 to 101 in column B (pass "0") with zeroes.
Starting in column C, row 2, you enter code as shown in the examples below. The examples show the code to be entered in cells C2, C3, and D2. Continue to write code for the rest of the 4245 data cells, accordingly. Excel Auto Fill feature is best used for this.

Cell C2:

 
=IF($A2/C$1=INT($A2/C$1),IF(B2=0,1,IF(B2=1,0)),B2)
 

Cell C3:

 
=IF($A3/C$1=INT($A3/C$1),IF(B3=0,1,IF(B3=1,0)),B3)
 

Cell D2:

 
=IF($A2/D$1=INT($A2/D$1),IF(C2=0,1,IF(C2=1,0)),C2)
 

The last column (column CX, labelled "100") shows a "1" for each door (labelled by the rows in column A) that is open after the 100th pass. It shows a "1" for the following doors: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

F#

Requires #light in versions of F# prior to 2010 beta.

let answerDoors =
    let ToggleNth n (lst:bool array) =                  // Toggle every n'th door
        [(n-1) .. n .. 99]                              // For each appropriate door
        |> Seq.iter (fun i -> lst.[i] <- not lst.[i])   // toggle it
    let doors = Array.create 100 false                  // Initialize all doors to closed
    Seq.iter (fun n -> ToggleNth n doors) [1..100]      // toggle the appropriate doors for each pass
    doors                                               // Initialize all doors to closed
 

Unoptimized / functional

 
let modifier doors skip =
    let rec modifierInner doors skip counter =
        match doors with
        | [] -> []                                                  //base case: end of hall
        | first::rest when counter >= skip ->                       //case: reached door marked for change
            not first::(modifierInner rest skip 0)                  //  open or close that door
        | first::rest ->                                            //case: reached door to skip
            first::(modifierInner rest skip (counter+1))            //  skip it                         
    modifierInner doors skip 0                                      //Initial state for walkthrough
 
let answerDoors doors =
    let rec modifyDoors skipRange doors modifier =                  //fold each door result to the next with
        List.fold modifier doors skipRange                          //with an increasing skip
    modifyDoors [0..99] doors modifier                              //Initial starting state
 
let initDoors = Array.create 100 false |> Array.toList              //Initialize all doors to closed (false)
 
answerDoors initDoors |> printfn "%A"                               //print answer (false is closed door)
 

Tail-Recursive Optimized/Functional

 
let modifier doors skip =
    let rec modifier' doors skip counter result =
        match doors with
        | [] -> result |> List.rev                                  //base case: end of hall
        | first::rest when counter >= skip ->                       //case: reached door marked for change
            modifier' rest skip 0 ((not first)::result)             //  open or close that door
        | first::rest ->                                            //case: reached door to skip
            modifier' rest skip (counter+1) (first::result)         //  skip it                         
    modifier' doors skip 0 []                                       //Initial state for walkthrough
 

Following is the solution using perfect squares. The coercions in PerfectSquare are, I believe, slightly different in versions prior to 2010 beta and, again, #light is required in those versions.

open System
let answer2 =
    let PerfectSquare n =
        let sqrt = int(Math.Sqrt(float n))
        n = sqrt * sqrt
    [| for i in 1..100 do yield PerfectSquare i |]

Simple single line solution using nothing but List

 
[1..100] |> List.fold (fun doors pass->List.mapi (fun i x->if ((i + 1) % pass)=0 then not x else x) doors) (List.init 100 (fun _->false))
 

Factor

Unoptimized

USING: bit-arrays formatting fry kernel math math.ranges
sequences ;
IN: rosetta.doors
 
CONSTANT: number-of-doors 100
 
: multiples ( n -- range )
    0 number-of-doors rot <range> ;
 
: toggle-multiples ( n doors -- )
    [ multiples ] dip '[ _ [ not ] change-nth ] each ;
 
: toggle-all-multiples ( doors -- )
    [ number-of-doors [1,b] ] dip '[ _ toggle-multiples ] each ;
 
: print-doors ( doors -- )
    [
        swap "open" "closed" ? "Door %d is %s\n" printf
    ] each-index ;
 
: main ( -- )
    number-of-doors 1 + <bit-array>
    [ toggle-all-multiples ] [ print-doors ] bi ;
 
main

Optimized

 
USING:
    formatting
    math math.primes.factors math.ranges
    sequences ;
IN: rosetta-doors2
 
: main ( -- )
    100 [1,b] [ divisors length odd? ] filter "Open %[%d, %]\n" printf ;
 

Falcon

Unoptimized code

doors = arrayBuffer( 101, false )
 
for pass in [ 0 : doors.len() ]
  for door in [ 0 : doors.len() : pass+1 ]
    doors[ door ] = not doors[ door ]
  end
end
 
for door in [ 1 : doors.len() ]  // Show Output
  >  "Door ", $door, " is: ", ( doors[ door ] ) ? "open" : "closed"
end
 

Optimized code

 
for door in [ 1 : 101 ]: > "Door ", $door, " is: ", fract( door ** 0.5 ) ? "closed" : "open"

FALSE

100[$][0 1ø:1-]#              {initialize doors}
%
[s;[$101\>][$$;~\:s;+]#%]d:   {function d, switch door state function}
1s:[s;101\>][d;!s;1+s:]#      {increment step width from 1 to 100, execute function d each time}
1[$101\>][$$." ";$["open
"]?~["closed
"]?1+]#                       {loop through doors, print door number and state}

Result:

1 open
2 closed
3 closed
4 open
5 closed
6 closed
7 closed
8 closed
9 open
10 closed
...
98 closed
99 closed
100 open

Compare this solution to the DUP solution of this problem.

Fantom

Unoptimized

 
    states := (1..100).toList
    100.times |i| {
      states = states.map |state| { state % (i+1) == 0 ? -state : +state }
    }
    echo("Open doors are " + states.findAll { it < 0 }.map { -it })
 

Optimized

 
    echo("Open doors are " + (1..100).toList.findAll { it.toFloat.pow(0.5f).toInt.pow(2) == it})
 

FBSL

Unoptimised

#AppType Console
 
DIM doors[], n AS INTEGER = 100
 
FOR DIM i = 1 TO n
	FOR DIM j = i TO n STEP i
		doors[j] = NOT doors[j]
	NEXT
NEXT
 
FOR i = 1 TO n
	IF doors[i] THEN PRINT "Door ", i, " is open"
NEXT
 
Pause

Optimised (by ML)

#APPTYPE CONSOLE
 
DIM i = 0, j = 0, door = 1
 
WHILE INCR(i) < 101
 IF i = door THEN
   PRINT "Door ", door, " open"
   INCR(door, INCR((INCR(j) << 1)))
 END IF
WEND
 
PAUSE

Fhidwfe

unoptomized

 
doors = malloc$ 100u
for uint [0u, sizeof$ doors) with l1 {
  put_byte$ + doors l1 as false byte
}
function void pass(step:uint) {
  location = step
  while <= location sizeof$ doors {
    ac = - + doors location 1u
    put_byte$ ac ~ deref_byte$ ac// true is represented as 255 (0xff)
    location = + location step
  }
}
for uint (0u, sizeof$ doors] with l2 {//range exclusive of 0, inclusive of 100
  pass$ l2
}
count = 1u
for ubyte as doors listubyte with isopen {// list for-each
  if as isopen bool {// cast byte to bool
    puts$ "door "
    putui$ count
    puts$ " is open\n"
  } ;
  count = + count 1u
}
free$ doors
 

Fish

Unoptimized

1001-p01.
>0101-p02.
>101-g001-g+:::aa*)?v101-p03.
>02-g?v1}02-p02.    >05.
      >0}02-p02.
>~~~0101-p001-g:1+001-paa*)?v02.
                            >07.
>0101-p08.
>101-g::02-g?v     >1+:101-paa*=?;
             >n" "o^

FOCAL

1.1 F N=1,100;S D(N)=0
1.2 F M=1,100;F N=M,M,100;S D(N)=1-D(N)
1.3 F N=1,100;D 2.0
1.4 Q
2.1 I (D(N)),,2.2;R
2.2 T "OPEN DOOR ",%3.0,N,!

Output:

OPEN DOOR =   1
OPEN DOOR =   4
OPEN DOOR =   9
OPEN DOOR =  16
OPEN DOOR =  25
OPEN DOOR =  36
OPEN DOOR =  49
OPEN DOOR =  64
OPEN DOOR =  81
OPEN DOOR = 100

Forth

Unoptimized

: toggle ( c-addr -- )  \ toggle the byte at c-addr
    dup [email protected] 1 xor swap c! ;
 
100  1+ ( 1-based indexing ) constant ndoors
create doors  ndoors allot
 
: init ( -- )  doors ndoors erase ;  \ close all doors
 
: pass ( n -- )  \ toggle every nth door
    ndoors over do
        doors i + toggle
    dup ( n ) +loop drop ;
 
: run ( -- )  ndoors 1 do  i pass  loop ;
: display ( -- )  \ display open doors
    ndoors 1 do  doors i + [email protected] if  i .  then loop cr ;
 
init run display

Optimized

: squared ( n -- n' )  dup * ;
: doors ( n -- )
    1 begin 2dup squared >= while
        dup squared .
    1+ repeat 2drop ;
100 doors

Fortran

Works with: Fortran 90

unoptimized

program doors
    implicit none
    integer, allocatable :: door(:)
    character(6), parameter :: s(0:1) = [character(6) :: "closed", "open"]
    integer :: i, n
 
    print "(A)", "Number of doors?"
    read *, n
    allocate (door(n))
    door = 1
    do i = 1, n
        door(i:n:i) = 1 - door(i:n:i)
        print "(A,G0,2A)", "door ", i, " is ", s(door(i))
    end do
end program

optimized

PROGRAM DOORS
 
  INTEGER, PARAMETER :: n = 100    ! Number of doors
  INTEGER :: i
  LOGICAL :: door(n) = .TRUE.      ! Initially closed
 
  DO i = 1, SQRT(REAL(n))
    door(i*i) = .FALSE.
  END DO  
 
  DO i = 1, n
    WRITE(*,"(A,I3,A)", ADVANCE="NO") "Door ", i, " is "
    IF (door(i)) THEN
      WRITE(*,"(A)") "closed"
    ELSE
      WRITE(*,"(A)") "open"
    END IF
  END DO
 
END PROGRAM DOORS

Free Pascal

 
program OneHundredIsOpen;
 
const
  DoorCount = 100;
 
var
  IsOpen: array[1..DoorCount] of boolean;
  Door, Jump: integer;
 
begin
  // Close all doors
  for Door := 1 to DoorCount do
    IsOpen[Door] := False;
  // Iterations
  for Jump := 1 to DoorCount do
  begin
    Door := Jump;
    repeat
      IsOpen[Door] := not IsOpen[Door];
      Door := Door + Jump;
    until Door > DoorCount;
  end;
  // Show final status
  for Door := 1 to DoorCount do
  begin
    Write(Door, ' ');
    if IsOpen[Door] then
      WriteLn('open')
    else
      WriteLn('closed');
  end;
  // Wait for <enter>
  Readln;
end.      
 

FreeBASIC

Toggle

' version 27-10-2016
' compile with: fbc -s console
 
#Define max_doors 100
 
Dim As ULong c, n, n1, door(1 To max_doors)
 
' toggle, at start all doors are closed (0)
' 0 = door closed, 1 = door open
For n = 1 To max_doors
    For n1 = n To max_doors Step n
        door(n1) = 1 - door(n1)
    Next
Next
 
' count the doors that are open (1)
Print "doors that are open nr: ";
For n = 1 To max_doors
    If door(n) = 1 Then
        Print n; " ";
        c = c + 1
    End If
Next
 
Print : Print
Print "There are " + Str(c) + " doors open"
 
' empty keyboard buffer
While InKey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End

Output:

doors that are open nr: 1 4 9 16 25 36 49 64 81 100 

There are 10 doors open

Count

' version 27-10-2016
' compile with: fbc -s console
 
#Define max_doors 100
 
Dim As ULong c, n, n1, door(1 To max_doors)
 
' at start all doors are closed
' simple add 1 each time we open or close a door
' doors with odd numbers are open
' doors with even numbers are closed
For n = 1 To max_doors
    For n1 = n To max_doors Step n
        door(n1) += 1
    Next
Next
 
Print "doors that are open nr: ";
For n = 1 To max_doors
    If door(n) And 1 Then
        Print n; " ";
        c = c + 1
    End If
Next
 
Print : Print
Print "There are " + Str(c) + " doors open"
 
' empty keyboard buffer
While InKey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End

Output is the same as the first version.

Optimized

' version 27-10-2016
' compile with: fbc -s console
 
#Define max_doors 100
 
Dim As ULong c, n
 
Print "doors that are open nr: ";
For n = 1 To 10
    Print n * n; " ";
    c = c + 1
Next
 
Print : Print
Print "There are " + Str(c) + " doors open"
 
' empty keyboard buffer
While InKey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End

Output is the same as the first version.

Ultra optimizado

' version 16-06-2021
' portado desde Julia
 
For i As Integer = 1 To 10
    If (i Mod i^2) < 11  Then Print "La puerta"; i^2; " esta abierta"   
Next i
Sleep
 

friendly interactive shell

Unoptimized

# Set doors to empty list
set doors
 
# Initialize doors arrays
for i in (seq 100)
    set doors[$i] 0
end
 
for i in (seq 100)
    set j $i
    while test $j -le 100
        # Logical not on doors
        set doors[$j] (math !$doors[$j])
        set j (math $j + $i)
    end
end
 
# Print every door
for i in (seq (count $doors))
    echo -n "$i "
    if test $doors[$i] -eq 0
        echo closed
    else
        echo open
    end
end
 

Optimized

# Set doors to empty list
set doors
 
for i in (seq 100)
    set doors[(math "$i * $i")] 1
    echo -n "$i "
    if test $doors[$i] -eq 1
        echo open
    else
        echo closed
    end
end

Frink

 
doors = new array[[101], false]
for pass=1 to 100
   for door=pass to 100 step pass
      [email protected] = ! [email protected]
 
print["Open doors:  "]
for door=1 to 100
   if [email protected]
      print["$door "]
 

FunL

Unoptimized

for i <- 1..100
  r = foldl1( \a, b -> a xor b, [(a|i) | a <- 1..100] )
  println( i + ' ' + (if r then 'open' else 'closed') )

Optimized

import math.sqrt
 
for i <- 1..100
  println( i + ' ' + (if sqrt(i) is Integer then 'open' else 'closed') )

Futhark

 
let main(n: i32): [n]bool =
  loop is_open = replicate n false for i < n do
    let js = map (*i+1) (iota n)
    let flips = map (\j ->
                       if j < n
                       then unsafe !is_open[j]
                       else true -- Doesn't matter.
                    ) js
    in scatter is_open js flips
 

FutureBasic

 
include "NSLog.incl"
 
NSInteger door, square = 1, increment = 3
 
for door = 1 to 100
  if ( door == square )
    NSLog( @"Door %ld is open.", door )
    square += increment : increment += 2
  else
    NSLog( @"Door %ld is closed.", door )
  end if
next
 
HandleEvents
 

Output:

Door 1 is open.
Door 2 is closed.
Door 3 is closed.
Door 4 is open.
Door 5 is closed.
Door 6 is closed.
Door 7 is closed.
Door 8 is closed.
Door 9 is open.
Door 10 is closed.
Door 11 is closed.
Door 12 is closed.
Door 13 is closed.
Door 14 is closed.
Door 15 is closed.
Door 16 is open.
Door 17 is closed.
Door 18 is closed.
Door 19 is closed.
Door 20 is closed.
Door 21 is closed.
Door 22 is closed.
Door 23 is closed.
Door 24 is closed.
Door 25 is open.
Door 26 is closed.
Door 27 is closed.
Door 28 is closed.
Door 29 is closed.
Door 30 is closed.
Door 31 is closed.
Door 32 is closed.
Door 33 is closed.
Door 34 is closed.
Door 35 is closed.
Door 36 is open.
Door 37 is closed.
Door 38 is closed.
Door 39 is closed.
Door 40 is closed.
Door 41 is closed.
Door 42 is closed.
Door 43 is closed.
Door 44 is closed.
Door 45 is closed.
Door 46 is closed.
Door 47 is closed.
Door 48 is closed.
Door 49 is open.
Door 50 is closed.
Door 51 is closed.
Door 52 is closed.
Door 53 is closed.
Door 54 is closed.
Door 55 is closed.
Door 56 is closed.
Door 57 is closed.
Door 58 is closed.
Door 59 is closed.
Door 60 is closed.
Door 61 is closed.
Door 62 is closed.
Door 63 is closed.
Door 64 is open.
Door 65 is closed.
Door 66 is closed.
Door 67 is closed.
Door 68 is closed.
Door 69 is closed.
Door 70 is closed.
Door 71 is closed.
Door 72 is closed.
Door 73 is closed.
Door 74 is closed.
Door 75 is closed.
Door 76 is closed.
Door 77 is closed.
Door 78 is closed.
Door 79 is closed.
Door 80 is closed.
Door 81 is open.
Door 82 is closed.
Door 83 is closed.
Door 84 is closed.
Door 85 is closed.
Door 86 is closed.
Door 87 is closed.
Door 88 is closed.
Door 89 is closed.
Door 90 is closed.
Door 91 is closed.
Door 92 is closed.
Door 93 is closed.
Door 94 is closed.
Door 95 is closed.
Door 96 is closed.
Door 97 is closed.
Door 98 is closed.
Door 99 is closed.
Door 100 is open.

FUZE BASIC

READ x,y,z
PRINT "Open doors: ";x;" ";
CYCLE
    z=x+y
    PRINT z;" ";
    x=z
    y=y+2
REPEAT UNTIL z>=100
DATA 1,3,0
END

Fōrmulæ

Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.

Programs in Fōrmulæ are created/edited online in its website, However they run on execution servers. By default remote servers are used, but they are limited in memory and processing power, since they are intended for demonstration and casual use. A local server can be downloaded and installed, it has no limitations (it runs in your own computer). Because of that, example programs can be fully visualized and edited, but some of them will not run if they require a moderate or heavy computation/memory resources, and no local server is being used.

In this page you can see the program(s) related to this task and their results.

Gambas

Click this link to run this code

Public Sub Main()
Dim bDoor As New Boolean[101]
Dim siCount1, siCount2, siStart As Short
 
For siCount1 = 1 To 100
  Inc siStart
  For siCount2 = siStart To 100 Step siCount1
    bDoor[siCount2] = Not bDoor[siCount2]
  Next
Next
 
For siCount1 = 1 To 100
  If bDoor[siCount1] Then Print siCount1;;
Next
 
End

Output:

1 4 9 16 25 36 49 64 81 100

GAP

doors := function(n)
  local a,j,s;
  a := [ ];
  for j in [1 .. n] do
    a[j] := 0;
  od;
  for s in [1 .. n] do
    j := s;
    while j <= n do
      a[j] := 1 - a[j];
      j := j + s;
    od;
  od;
  return Filtered([1 .. n], j -> a[j] = 1);
end;
 
doors(100);
# [ 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 ]

GDScript

func Doors(door_count:int) -> void :
  var doors : Array
  doors.resize(door_count)
 
  # Note : Initialization is not necessarily mandatory (by default values are false)
  # Intentionally left here
  for i in door_count :
    doors[i] = false
 
  # do visits
  for i in door_count :
    for j in range(i,door_count,i+1) :
      doors[j] = not doors[j]
 
  # print results
  var results : String = ""
  for i in door_count :
    results += str(i+1) + " " if doors[i] else ""
  print("Doors open : %s" % [results] )
 
# calling the function from the _ready function
func _ready() -> void :
  Doors(100)
 

Output:

Doors open : 1 4 9 16 25 36 49 64 81 100

Genie

 
// 100 doors problem
// Author: Sinuhe masan (2019)
init
 
	// 100 elements array of boolean type
	doors:bool[100]
 
	for var i = 1 to 100
		doors[i] = false  // set all doors closed
 
 
	for var i = 1 to 100
		j:int = i
		while j <= 100 do
			doors[j] = not doors[j]
			j = j + i
 
	print("Doors open: ")
	for var i = 1 to 100
		if doors[i]
			stdout.printf ("%d ", i)
 
 

Glee

100` *=0=>d                      $$ create vector 1..100, create bit pattern d, marking all equal to 0
:for (1..100[.s]){               $$ loop s from 1 to 100
  d^(100` %s *=0 )=>d;}          $$ d = d xor (bit pattern of vector 1..100 % s)
d                                $$ output d
 

The resulting output is the bit pattern showing the state of the 100 doors:

Result:
10010000 10000001 00000000 10000000 00010000 00000000 10000000 00000001 00000000 00000000 10000000 00000000 0001

GML

var doors,a,i;
//Sets up the array for all of the doors.
for (i = 1; i<=100; i += 1)
    {
    doors[i]=0;
    }
 
//This first for loop goes through and passes the interval down to the next for loop.
for (i = 1; i <= 100; i += 1;)
    {
    //This for loop opens or closes the doors and uses the interval(if interval is 2 it only uses every other etc..)
    for (a = 0; a <= 100; a += i;)
        {
        //Opens or closes a door.
        doors[a] = !doors[a];
        }
    }
open_doors = '';
 
//This for loop goes through the array and checks for open doors.
//If the door is open it adds it to the string then displays the string.
for (i = 1; i <= 100; i += 1;)
    {
    if (doors[i] == 1)
        {
        open_doors += "Door Number "+string(i)+" is open#";
        }
    }
show_message(open_doors);
game_end();

Go

unoptimized

package main
 
import "fmt"
 
func main() {
    doors := [100]bool{}
 
    // the 100 passes called for in the task description
    for pass := 1; pass <= 100; pass++ {
        for door := pass-1; door < 100; door += pass {
            doors[door] = !doors[door]
        }
    }
 
    // one more pass to answer the question
    for i, v := range doors {
        if v {
            fmt.Print("1")
        } else {
            fmt.Print("0")
        }
 
        if i%10 == 9 {
            fmt.Print("\n")
        } else {
            fmt.Print(" ")
        }
 
    }
}

Output:

1 0 0 1 0 0 0 0 1 0
0 0 0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1

optimized

package main
 
import "fmt"
 
func main() {
    var door int = 1
    var incrementer = 0
 
    for current := 1; current <= 100; current++ {
        fmt.Printf("Door %d ", current)
 
        if current == door {
            fmt.Printf("Open\n")
            incrementer++
            door += 2*incrementer + 1
        } else {
            fmt.Printf("Closed\n")
        }
    }
}

optimized 2

// 100 (optimized) doors in Go
 
package main
 
import (
    "fmt"
    "math"
)
 
func main() {
    for i := 1; i <= 100; i++ {
        f := math.Sqrt(float64(i))
        if math.Mod(f, 1) == 0 {
            fmt.Print("O")
        } else {
            fmt.Print("-")
        }
    }
    fmt.Println()
}

Output:

O--O----O------O--------O----------O------------O--------------O----------------O------------------O

Golfscript

100:c;[{0}c*]:d;
c,{.c,>\)%{.d<\.d=1^\)d>++:d;}/}/
[c,{)"door "\+" is"+}%d{{"open"}{"closed"}if}%]zip
{" "*puts}/

optimized with sqrt (Original version of GolfScript has no sqrt operator, but it can be added easily; the code was tested using a work-in-progress C interpreter for a language compatible enough with Golfscript)

100,{)}%
{:d.sqrt 2?=
{"open"}{"close"}if"door "d+" is "+\+puts}/

optimized without sqrt

[{"close"}100*]:d;
10,{)2?(.d<\["open"]\)d>++:d;}/
[100,{)"door "\+" is"+}%d]zip
{" "*puts}/

Gosu

unoptimized

 
uses java.util.Arrays
 
var doors = new boolean[100]
Arrays.fill( doors, false )
 
for( pass in 1..100 ) {
    var counter = pass-1
    while( counter < 100 ) {
        doors[counter] = !doors[counter]
        counter += pass
  }
}
 
for( door in doors index i ) {
    print( "door ${i+1} is ${door ? 'open' : 'closed'}" )
}
 
 

optimized

 
var door = 1
var delta = 0
 
for( i in 1..100 ) {
    if( i == door ) {
        print( "door ${i} is open" )
        delta++
        door += 2*delta + 1
    } else {
        print( "door ${i} is closed" )
    }
}
 

Groovy

unoptimized

doors = [false] * 100
(0..99).each {
   it.step(100, it + 1) {
      doors[it] ^= true
   }
}
(0..99).each {
   println("Door #${it + 1} is ${doors[it] ? 'open' : 'closed'}.")
}

optimized a Using square roots

(1..100).each {
   println("Door #${it} is ${Math.sqrt(it).with{it==(int)it} ? 'open' : 'closed'}.")
}

optimized b Without using square roots

doors = ['closed'] * 100
(1..10).each { doors[it**2 - 1] = 'open' }
(0..99).each {
   println("Door #${it + 1} is ${doors[it]}.")
}

GW-BASIC

10 DIM A(100)
20 FOR OFFSET = 1 TO 100
30      FOR I = 0 TO 100 STEP OFFSET
40              A(I) = A(I) + 1
50      NEXT I
60 NEXT OFFSET
70 ' Print "opened" doors
80 FOR I = 1 TO 100
90      IF A(I) MOD 2 = 1 THEN PRINT I
100 NEXT I

Output:

1
4
9
16
25
36
49
64
81
100

Harbour

Unoptimized code:

#define ARRAY_ELEMENTS 100
PROCEDURE Main()
   LOCAL aDoors := Array( ARRAY_ELEMENTS )
   LOCAL i, j
 
   AFill( aDoors, .F. )
   FOR i := 1 TO ARRAY_ELEMENTS
      FOR j := i TO ARRAY_ELEMENTS STEP i
         aDoors[ j ] = ! aDoors[ j ]
      NEXT
   NEXT
   AEval( aDoors, {|e, n| QQout( Padl(n,3) + " is " + Iif(aDoors[n], "*open*", "closed" ) + "|" ), Iif( n%5 == 0, Qout(), e:=NIL) } )
   RETURN

Optimized code

#define ARRAY_ELEMENTS 100
PROCEDURE Main()
   LOCAL aDoors := Array( ARRAY_ELEMENTS )
 
   AFill( aDoors, .F. )
   AEval( aDoors, {|e, n| aDoors[n] := e := Iif( Int(Sqrt(n))==Sqrt(n), .T., .F. ) } )
   AEval( aDoors, {|e, n| QQout( Padl(n,3) + " is " + Iif(aDoors[n], "*open*", "closed" ) + "|" ), Iif( n%5 == 0, Qout(), e:=NIL )} )
   RETURN

Output:

 1 is *open*|  2 is closed|  3 is closed|  4 is *open*|  5 is closed| 
 6 is closed|  7 is closed|  8 is closed|  9 is *open*| 10 is closed| 
11 is closed| 12 is closed| 13 is closed| 14 is closed| 15 is closed| 
16 is *open*| 17 is closed| 18 is closed| 19 is closed| 20 is closed| 
21 is closed| 22 is closed| 23 is closed| 24 is closed| 25 is *open*| 
26 is closed| 27 is closed| 28 is closed| 29 is closed| 30 is closed| 
31 is closed| 32 is closed| 33 is closed| 34 is closed| 35 is closed| 
36 is *open*| 37 is closed| 38 is closed| 39 is closed| 40 is closed| 
41 is closed| 42 is closed| 43 is closed| 44 is closed| 45 is closed| 
46 is closed| 47 is closed| 48 is closed| 49 is *open*| 50 is closed| 
51 is closed| 52 is closed| 53 is closed| 54 is closed| 55 is closed| 
56 is closed| 57 is closed| 58 is closed| 59 is closed| 60 is closed| 
61 is closed| 62 is closed| 63 is closed| 64 is *open*| 65 is closed| 
66 is closed| 67 is closed| 68 is closed| 69 is closed| 70 is closed| 
71 is closed| 72 is closed| 73 is closed| 74 is closed| 75 is closed| 
76 is closed| 77 is closed| 78 is closed| 79 is closed| 80 is closed| 
81 is *open*| 82 is closed| 83 is closed| 84 is closed| 85 is closed| 
86 is closed| 87 is closed| 88 is closed| 89 is closed| 90 is closed| 
91 is closed| 92 is closed| 93 is closed| 94 is closed| 95 is closed| 
96 is closed| 97 is closed| 98 is closed| 99 is closed|100 is *open*|

Haskell

unoptimized

data Door
  = Open
  | Closed
  deriving (Eq, Show)
 
toggle :: Door -> Door
toggle Open = Closed
toggle Closed = Open
 
toggleEvery :: Int -> [Door] -> [Door]
toggleEvery k = zipWith toggleK [1 ..]
  where
    toggleK n door
      | n `mod` k == 0 = toggle door
      | otherwise = door
 
run :: Int -> [Door]
run n = foldr toggleEvery (replicate n Closed) [1 .. n]
 
main :: IO ()
main = print $ filter ((== Open) . snd) $ zip [1 ..] (run 100)

Output:

[(1,Open),(4,Open),(9,Open),(16,Open),(25,Open),(36,Open),(49,Open),(64,Open),(81,Open),(100,Open)]

optimized (without using square roots)

gate :: Eq a => [a] -> [a] -> [Door]
gate (x:xs) (y:ys) | x == y  =  Open   : gate xs ys
gate (x:xs) ys               =  Closed : gate xs ys
gate []     _                =  []
 
run n = gate [1..n] [k*k | k <- [1..]]

alternatively, returning a list of all open gates, it's a one-liner:

run n = takeWhile (< n) [k*k | k <- [1..]]

Haxe

class RosettaDemo
{
    static public function main()
    {
        findOpenLockers(100);
    }
 
    static function findOpenLockers(n : Int)
    {
        var i = 1;
 
        while((i*i) <= n)
        {
            Sys.print(i*i + "\n");
            i++;
        }
    }
}

HicEst

Unoptimized

REAL :: n=100, open=1, door(n)
 
door = 1 - open ! = closed
DO i = 1, n
  DO j = i, n, i
    door(j) = open - door(j)
  ENDDO
ENDDO
DLG(Text=door, TItle=SUM(door)//" doors open") 

Optimized

door = 1 - open ! = closed
DO i = 1, n^0.5
  door(i*i) = open
ENDDO
DLG(Text=door, TItle=SUM(door)//" doors open") 

HolyC

Translation of: C

U8 is_open[100];
U8 pass = 0, door = 0;
 
/* do the 100 passes */
for (pass = 0; pass < 100; ++pass)
  for (door = pass; door < 100; door += pass + 1)
    is_open[door] = !is_open[door];
 
/* output the result */
for (door = 0; door < 100; ++door)
  if (is_open[door])
    Print("Door #%d is open.\n", door + 1);
  else
    Print("Door #%d is closed.\n", door + 1);
 

Hoon

|^
=/  doors=(list ?)  (reap 100 %.n)
=/  passes=(list (list ?))  (turn (gulf 1 100) pass-n)
|-
?~  passes  doors
$(doors (toggle doors i.passes), passes t.passes)
++  pass-n
  |=  [email protected]
  (turn (gulf 1 100) |=([email protected] =((mod k n) 0)))
++  toggle
  |=  [a=(list ?) b=(list ?)]
  =|  c=(list ?)
  |-
  ?:  |(?=(~ a) ?=(~ b))  (flop c)
  $(a t.a, b t.b, c [=((mix i.a i.b) 1) c])
--

Huginn

#! /bin/sh
exec huginn --no-argv -E "${0}"
#! huginn
 
import Algorithms as algo;
 
main() {
        doorCount = 100;
        doors = [].resize( doorCount, false );
 
        for ( pass : algo.range( doorCount ) ) {
                i = 0;
                step = pass + 1;
                while ( i < doorCount ) {
                        doors[i] = ! doors[i];
                        i += step;
                }
        }
 
        for ( i : algo.range( doorCount ) ) {
                if ( doors[i] ) {
                        print( "door {} is open\n".format( i ) );
                }
        }
        return ( 0 );
}

Hy

Translation of: Coco

(setv doors (* [False] 100))
 
(for [pass (range (len doors))]
  (for [i (range pass (len doors) (inc pass))]
    (assoc doors i (not (get doors i)))))
 
(for [i (range (len doors))]
  (print (.format "Door {} is {}."
    (inc i)
    (if (get doors i) "open" "closed"))))

I

software {
	var doors = len(100)
 
	for pass over [1, 100]
		var door = pass - 1
		loop door < len(doors) {
			doors[door] = doors[door]/0
			door += pass
		}
	end
 
	for door,isopen in doors
		if isopen
			print("Door ",door+1,": open")
		end
	end
	print("All other doors are closed")
}

Icon and Unicon

Icon and Unicon don't have a boolean type because most often, logic is expressed in terms of success or failure, which affects flow at run time.

Unoptimized solution.

 
procedure main()
    door := table(0)    # default value of entries is 0
    every pass := 1 to 100 do
        every door[i := pass to 100 by pass] := 1 - door[i]
 
    every write("Door ", i := 1 to 100, " is ", if door[i] = 1 then "open" else "closed")
end
 

Optimized solution.

 
procedure main()
    every write("Door ", i := 1 to 100, " is ", if integer(sqrt(i)) = sqrt(i) then "open" else "closed")
end
 

or

procedure main(args)
    dMap := table("closed")
    every dMap[(1 to sqrt(100))^2] := "open"
    every write("Door ",i := 1 to 100," is ",dMap[i])
end

Idris

import Data.Vect
 
-- Creates list from 0 to n (not including n) 
upTo : (m : Nat) -> Vect m (Fin m)
upTo Z = []
upTo (S n) = 0 :: (map FS (upTo n))
 
data DoorState = DoorOpen | DoorClosed
 
toggleDoor : DoorState -> DoorState
toggleDoor DoorOpen = DoorClosed
toggleDoor DoorClosed = DoorOpen
 
isOpen : DoorState -> Bool
isOpen DoorOpen = True
isOpen DoorClosed = False
 
initialDoors : Vect 100 DoorState
initialDoors = fromList $ map (\_ => DoorClosed) [1..100]
 
iterate : (n : Fin m) -> Vect m DoorState -> Vect m DoorState
iterate n doors {m} = 
  map (\(idx, doorState) => 
          if ((S (finToNat idx)) `mod` (S (finToNat n))) == Z 
              then toggleDoor doorState 
              else doorState)  
      (zip (upTo m) doors)
 
-- Returns all doors left open at the end
solveDoors : List (Fin 100)
solveDoors = 
  findIndices isOpen $ foldl (\doors,val => iterate val doors) initialDoors (upTo 100)
 
main : IO ()
main = print $ map (\n => S (finToNat n)) solveDoors

Inform 7

Works with: Z-machine version 8

Works with: Glulx virtual machine

Hallway is a room.
 
A toggle door is a kind of thing.
A toggle door can be open or closed. It is usually closed.
A toggle door has a number called the door number.
Understand the door number property as referring to a toggle door.
Rule for printing the name of a toggle door: say "door #[door number]".
 
There are 100 toggle doors.
 
When play begins (this is the initialize doors rule):
	let the next door number be 1;
	repeat with D running through toggle doors:
		now the door number of D is the next door number;
		increment the next door number.
 
To toggle (D - open toggle door): now D is closed.
To toggle (D - closed toggle door): now D is open.
 
When play begins (this is the solve puzzle rule):
	let the door list be the list of toggle doors;
	let the door count be the number of entries in the door list;
	repeat with iteration running from 1 to 100:
		let N be the iteration;
		while N is less than the door count:
			toggle entry N in the door list;
			increase N by the iteration;
	say "Doors left open: [list of open toggle doors].";
	end the story.

Informix 4GL

 
MAIN
    DEFINE
        i, pass SMALLINT,
        doors ARRAY[100] OF SMALLINT
 
    FOR i = 1 TO 100
        LET doors[i] = FALSE
    END FOR
 
    FOR pass = 1 TO 100
        FOR i = pass TO 100 STEP pass
            LET doors[i] = NOT doors[i]
        END FOR
    END FOR
 
    FOR i = 1 TO 100
        IF doors[i]
          THEN DISPLAY i USING "Door <<& is open"
          ELSE DISPLAY i USING "Door <<& is closed"
        END IF
    END FOR
END MAIN
 

Io

simple boolean list solution:

doors := List clone
100 repeat(doors append(false))
for(i,1,100,
    for(x,i,100, i, doors atPut(x - 1, doors at(x - 1) not))
)
doors foreach(i, x, if(x, "Door #{i + 1} is open" interpolate println))

Optimized solution:

(Range 1 to(10) asList) foreach(v, "Door #{v ** 2} is open." interpolate println)

Sample output:

Door 1 is open.
Door 4 is open.
Door 9 is open.
Door 16 is open.
Door 25 is open.
Door 36 is open.
Door 49 is open.
Door 64 is open.
Door 81 is open.
Door 100 is open.

Ioke

Unoptimized Object Oriented solution.

NDoors = Origin mimic
 
NDoors Toggle = Origin mimic do(
  initialize = method(toggled?, @toggled? = toggled?)
  toggle! = method(@toggled? = !toggled?. self)
)
 
NDoors Doors = Origin mimic do(
  initialize = method(n,
    @n = n
    @doors = {} addKeysAndValues(1..n, (1..n) map(_, NDoors Toggle mimic(false)))
  )
  numsToToggle = method(n, for(x <- ([email protected]), (x % n) zero?, x))
  toggleThese = method(nums, nums each(x, @doors[x] = @doors at(x) toggle))
  show = method(@doors filter:dict(value toggled?) keys sort println)
)
 
; Test code
x = NDoors Doors mimic(100)
(1..100) each(n, x toggleThese(x numsToToggle(n)))
x show

Isabelle

theory Scratch
  imports Main
begin
 
section‹100 Doors›
 
  datatype doorstate = Open | Closed
 
  fun toggle :: "doorstate ⇒ doorstate" where
    "toggle Open   = Closed"
  | "toggle Closed = Open"
 
  fun walk :: "('a ⇒ 'a) ⇒ nat ⇒ nat ⇒ 'a list ⇒ 'a list" where
    "walk f _     _       []     = []"
  | "walk f every 0       (x#xs) = (f x) # walk f every every xs"
  | "walk f every (Suc n) (x#xs) = x # walk f every n xs"
 
  text‹Example: \<^const>‹toggle› every second door. (second = 1, because of 0 indexing)›
  lemma "walk toggle 1 1 [Open, Open, Open, Open, Open, Open] =
                         [Open, Closed, Open, Closed, Open, Closed]" by code_simp
 
  text‹Example: \<^const>‹toggle› every third door.›
  lemma "walk toggle 2 2 [Open, Open, Open, Open, Open, Open] =
                         [Open, Open, Closed, Open, Open, Closed]" by code_simp
 
  text‹Walking each door is essentially the same as the common \<^const>‹map› function.›
  lemma "walk f 0 0 xs = map f xs"
    by(induction xs) (simp)+
 
  lemma walk_beginning:
    "walk f every n xs = (walk f every n (take (Suc n) xs)) @ (walk f every every (drop (Suc n) xs))"
    by(induction f every n xs rule:walk.induct) (simp)+
 
  text‹A convenience definition to take the off-by-one into account and setting the starting position.›
  definition visit_every :: "('a ⇒ 'a) ⇒ nat ⇒ 'a list ⇒ 'a list" where
    "visit_every f every xs ≡ walk f (every - 1) (every - 1) xs"
 
 
  fun iterate :: "nat ⇒ (nat ⇒ 'a ⇒ 'a) ⇒ nat ⇒ 'a ⇒ 'a" where
    "iterate 0       _ _ a = a"
  | "iterate (Suc i) f n a = iterate i f (Suc n) (f n a)"
 
  text‹The 100 doors problem.›
  definition "onehundred_doors ≡ iterate 100 (visit_every toggle) 1 (replicate 100 Closed)"
 
  lemma "onehundred_doors =
    [Open, Closed, Closed, Open, Closed, Closed, Closed,
     Closed, Open, Closed, Closed, Closed, Closed, Closed,
     Closed, Open, Closed, Closed, Closed, Closed, Closed,
     Closed, Closed, Closed, Open, Closed, Closed, Closed,
     Closed, Closed, Closed, Closed, Closed, Closed, Closed,
     Open, Closed, Closed, Closed, Closed, Closed, Closed,
     Closed, Closed, Closed, Closed, Closed, Closed, Open,
     Closed, Closed, Closed, Closed, Closed, Closed, Closed,
     Closed, Closed, Closed, Closed, Closed, Closed, Closed,
     Open, Closed, Closed, Closed, Closed, Closed, Closed,
     Closed, Closed, Closed, Closed, Closed, Closed, Closed,
     Closed, Closed, Closed, Open, Closed, Closed, Closed,
     Closed, Closed, Closed, Closed, Closed, Closed, Closed,
     Closed, Closed, Closed, Closed, Closed, Closed, Closed,
     Closed, Open]" by code_simp
 
  text‹Filtering for the open doors, we get the same result as the Haskell implementation.›
  lemma
    "[(i, door) ← enumerate 1 onehundred_doors. door = Open] =
     [(1,Open),(4,Open),(9,Open),(16,Open),(25,Open),(36,Open),(49,Open),(64,Open),(81,Open),(100,Open)]"
    by code_simp
 
section‹Equivalence to Haskell Implementation›
text‹
We will now present an alternative implementation, which is similar to the Haskell implementation
on 🌐‹https://rosettacode.org/wiki/100_doors#Haskell›. We will prove, that the two behave the same;
in general, not just for a fixed set of 100 doors.
›
 
  definition map_every_start :: "('a ⇒ 'a) ⇒ nat ⇒ nat ⇒ 'a list ⇒ 'a list" where
    "map_every_start f every start xs ≡
      map (λ(i, x). if i mod every = 0 then f x else x) (enumerate start xs)"
 
  definition visit_every_alt :: "('a ⇒ 'a) ⇒ nat ⇒ 'a list ⇒ 'a list" where
    "visit_every_alt f every xs ≡ map_every_start f every 1 xs"
 
  text‹Essentially, \<^term>‹start› and \<^term>‹start mod every› behave the same.›
  lemma map_every_start_cycle:
    "map_every_start f every (start + k*every) xs = map_every_start f every start xs"
    proof(induction xs arbitrary: start)
      case Nil
      show "map_every_start f every (start + k * every) [] = map_every_start f every start []"
        by(simp add: map_every_start_def)
    next
      case (Cons x xs)
      from Cons.IH[of "Suc start"]
        show "map_every_start f every (start + k * every) (x # xs) =
              map_every_start f every start (x # xs)"
        by(simp add: map_every_start_def)
    qed
  corollary map_every_start_cycle_zero:
    "map_every_start f every every xs = map_every_start f every 0 xs"
    using map_every_start_cycle[where k=1 and start=0, simplified] by blast
 
  lemma map_every_start_fst_zero:
    "map_every_start f every 0 (x # xs) = f x # map_every_start f every (Suc 0) xs"
    by(simp add: map_every_start_def)
 
  text‹
  The first \<^term>‹n› elements are not processed by \<^term>‹f›,
  as long as \<^term>‹n› is less than the \<^term>‹every› cycle.
  ›
  lemma map_every_start_skip_first: "Suc n < every ⟹
         map_every_start f every (every - (Suc n)) (x # xs) = 
         x # map_every_start f every (every - n) xs"
    by(simp add: map_every_start_def Suc_diff_Suc)
 
  lemma map_every_start_append:
    "map_every_start f n s (ds1 @ ds2) =
     map_every_start f n s ds1 @ map_every_start f n (s + length ds1) ds2"
    by(simp add: map_every_start_def enumerate_append_eq)
 
  text‹
  The \<^const>‹walk› function and \<^const>‹map_every_start› behave the same,
  as long as the starting \<^term>‹n› is less than the \<^term>‹every› cycle,
  because \<^const>‹walk› allows pushing the start arbitrarily far and
  \<^const>‹map_every_start› only allows deferring the start within
  the \<^term>‹every› cycle.
  This generalization is needed to strengthen the induction hypothesis
  for the proof.
  ›
  lemma walk_eq_map_every_start:
    "n ≤ every ⟹ walk f every n xs = map_every_start f (Suc every) (Suc every - n) xs"
    proof(induction xs arbitrary: n)
      case Nil
      show "walk f every n [] = map_every_start f (Suc every) (Suc every - n) []"
        by(simp add: map_every_start_def)
    next
      case (Cons x xs)
      then show "walk f every n (x # xs) = map_every_start f (Suc every) (Suc every - n) (x # xs)"
      proof(cases n)
        case 0
        with Cons.IH show ?thesis 
          by(simp add: map_every_start_cycle_zero map_every_start_fst_zero)
      next
        case (Suc n2)
        with Cons.prems map_every_start_skip_first[of n2 "Suc every"] have
          "map_every_start f (Suc every) (Suc every - Suc n2) (x # xs) =
           x # map_every_start f (Suc every) (Suc every - n2) xs"
          by fastforce
        with Suc Cons show ?thesis
          by(simp)
      qed
    qed
 
  corollary walk_eq_visit_every_alt:
    "walk f every every xs = visit_every_alt f (Suc every) xs"
    unfolding visit_every_alt_def
    using walk_eq_map_every_start by fastforce
 
  text‹
  Despite their very different implementations, our alternative visit function behaves the same
  as our original visit function.
  Text the theorem includes \<^term>‹Suc every› to express that we exclude \<^term>‹every = 0›.
  ›
  theorem visit_every_eq_visit_every_alt:
    "visit_every f (Suc every) xs = visit_every_alt f (Suc every) xs"
    unfolding visit_every_def
    using walk_eq_visit_every_alt by fastforce
 
  text‹Also, the \<^const>‹iterate› function we implemented above can be implemented by a simple \<^const>‹fold›.›
  lemma fold_upt_helper: assumes n_geq_1: "Suc 0 ≤ n"
    shows "fold f [Suc s..<n + s] (f s xs) = fold f [s..<n + s] xs"
  proof -
    from n_geq_1 have "[s..<n + s] = s#[Suc s..<n + s]" by (simp add: Suc_le_lessD upt_rec)
    from this have "fold f [s..<n + s] xs = fold f (s#[Suc s..<n + s]) xs" by simp
    also have "fold f (s#[Suc s..<n + s]) xs = fold f [Suc s..<n + s] (f s xs)" by(simp)
    ultimately show ?thesis by simp
  qed
 
  theorem iterate_eq_fold: "iterate n f s xs = fold f [s ..< n+s] xs"
  proof(induction n arbitrary: s xs)
    case 0
    then show "iterate 0 f s xs = fold f [s..<0 + s] xs" by simp
  next
    case (Suc n)
    from Suc show "iterate (Suc n) f s xs = fold f [s..<Suc n + s] xs" 
      by(simp add: fold_upt_helper not_less_eq_eq)
  qed
 
section‹Efficient Implementation›
text ‹
As noted on this page, the only doors that remain open are those whose numbers are perfect squares.
Yet, rosettacode does not want us to take this shortcut, since we want to compare implementations
across programming languages. But we can prove that our code computes the same result as reporting
all doors with a perfect square number as open:
›
  theorem "[(i, door) ← enumerate 1 onehundred_doors. door = Open] =
           [(i*i, Open). i ← [1..<11]]"
    by code_simp
end

J

unoptimized

   ~:/ (100 $ - {. 1:)"0 >:i.100
1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ...
   ~:/ 0=|/~ >:i.100  NB. alternative
1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ...

optimized

   (e. *:) 1+i.100
1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ...
   1 (<:*:i.10)} 100$0  NB. alternative
1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ...

with formatting

   'these doors are open: ',": I. (i.101) e. *: 1+i.10
these doors are open: 1 4 9 16 25 36 49 64 81 100
 

Janet

 
(def doors (seq [_ :range [0 100]] false))
 
(loop [pass :range [0 100]
       door :range [pass 100 (inc pass)]]
  (put doors door (not (doors door))))
 
(print "open doors: " ;(seq [i :range [0 100] :when (doors i)] (string (inc i) " ")))
 

Output:

open doors: 1 4 9 16 25 36 49 64 81 100

Java

With an array of boolean

class HundredDoors {
    public static void main(String[] args) {
        boolean[] doors = new boolean[101];
 
        for (int i = 1; i < doors.length; i++) {
            for (int j = i; j < doors.length; j += i) {
                doors[j] = !doors[j];
            }
        }
 
        for (int i = 1; i < doors.length; i++) {
            if (doors[i]) {
                System.out.printf("Door %d is open.%n", i);
            }
        }
    }
}

With a BitSet

import java.util.BitSet;
 
public class HundredDoors {
    public static void main(String[] args) {
        final int n = 100;
        var a = new BitSet(n);
        for (int i = 1; i <= n; i++) {
            for (int j = i - 1; j < n; j += i) {
                a.flip(j);
            }
        }
        a.stream().map(i -> i + 1).forEachOrdered(System.out::println);
    }
}

Only print the result

class HundredDoors {
    public static void main(String[] args) {
        for (int i = 1; i <= 10; i++)
            System.out.printf("Door %d is open.%n", i * i);
    }
}

Output:

Door 1 is open.
Door 4 is open.
Door 9 is open.
Door 16 is open.
Door 25 is open.
Door 36 is open.
Door 49 is open.
Door 64 is open.
Door 81 is open.
Door 100 is open.

If only printing the result is required, using streams.

import java.util.stream.Collectors;
import java.util.stream.IntStream;
 
class HundredDoors {
    public static void main(String args[]) {
        String openDoors = IntStream.rangeClosed(1, 100)
                .filter(i -> Math.pow((int) Math.sqrt(i), 2) == i)
                .mapToObj(Integer::toString)
                .collect(Collectors.joining(", "));
        System.out.printf("Open doors: %s%n", openDoors);
    }
}
 

Output:

Open doors: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100

JavaScript

ES5

Iterative

var doors=[];
for (var i=0;i<100;i++)
    doors[i]=false;
for (var i=1;i<=100;i++)
    for (var i2=i-1,g;i2<100;i2+=i)
        doors[i2]=!doors[i2];
for (var i=1;i<=100;i++)
    console.log("Door %d is %s",i,doors[i-1]?"open":"closed")

Functional Composition

Naive search

(function (n) {
    "use strict";
    function finalDoors(n) {
        var lstRange = range(1, n);
        return lstRange
            .reduce(function (a, _, k) {
                var m = k + 1;
                return a.map(function (x, i) {
                    var j = i + 1;
                    return [j, j % m ? x[1] : !x[1]];
                });
            }, zip(
                lstRange,
                replicate(n, false)
            ));
    };
    function zip(xs, ys) {
        return xs.length === ys.length ? (
            xs.map(function (x, i) {
                return [x, ys[i]];
            })
        ) : undefined;
    }
    function replicate(n, a) {
        var v = [a],
            o = [];
        if (n < 1) return o;
        while (n > 1) {
            if (n & 1) o = o.concat(v);
            n >>= 1;
            v = v.concat(v);
        }
        return o.concat(v);
    }
    function range(m, n, delta) {
        var d = delta || 1,
            blnUp = n > m,
            lng = Math.floor((blnUp ? n - m : m - n) / d) + 1,
            a = Array(lng),
            i = lng;
        if (blnUp)
            while (i--) a[i] = (d * i) + m;
        else
            while (i--) a[i] = m - (d * i);
        return a;
    }
    return finalDoors(n)
        .filter(function (tuple) {
            return tuple[1];
        })
        .map(function (tuple) {
            return {
                door: tuple[0],
                open: tuple[1]
            };
        });
 
})(100);

Optimized (iterative)

for (var door = 1; door <= 100; door++) {
  var sqrt = Math.sqrt(door);
  if (sqrt === (sqrt | 0)) {
    console.log("Door %d is open", door);
  }
}

Simple for loop. Optimizing the optimized?

for(var door=1;i<10/*Math.sqrt(100)*/;i++){
 console.log("Door %d is open",i*i);
}

Optimized (functional)

The question of which doors are flipped an odd number of times reduces to the question of which numbers have an odd number of integer factors. We can simply search for these:

(function (n) {
    "use strict";
    return range(1, 100)
        .filter(function (x) {
            return integerFactors(x)
                .length % 2;
        });
    function integerFactors(n) {
        var rRoot = Math.sqrt(n),
            intRoot = Math.floor(rRoot),
            lows = range(1, intRoot)
            .filter(function (x) {
                return (n % x) === 0;
            });
        return lows.concat(lows.map(function (x) {
                return n / x;
            })
            .reverse()
            .slice((rRoot === intRoot) | 0));
    }
    function range(m, n, delta) {
        var d = delta || 1,
            blnUp = n > m,
            lng = Math.floor((blnUp ? n - m : m - n) / d) + 1,
            a = Array(lng),
            i = lng;
        if (blnUp)
            while (i--) a[i] = (d * i) + m;
        else
            while (i--) a[i] = m - (d * i);
        return a;
    }
})(100);

Or we can note, on inspection and further reflection, that only perfect squares have odd numbers of integer factors - all other numbers have only matched pairs of factors - low factors below the non-integer square root, and the corresponding quotients above the square root. In the case of perfect squares, the additional integer square root (not paired with any other factor than itself) makes the total number of distinct factors odd.

(function (n) {
    "use strict";
    return perfectSquaresUpTo(100);
    function perfectSquaresUpTo(n) {
        return range(1, Math.floor(Math.sqrt(n)))
            .map(function (x) {
                return x * x;
            });
    }
    function range(m, n, delta) {
        var d = delta || 1,
            blnUp = n > m,
            lng = Math.floor((blnUp ? n - m : m - n) / d) + 1,
            a = Array(lng),
            i = lng;
        if (blnUp)
            while (i--) a[i] = (d * i) + m;
        else
            while (i--) a[i] = m - (d * i);
        return a;
    }
})(100);

ES6

 
Array.apply(null, { length: 100 })
  .map((v, i) => i + 1)
    .forEach(door => { 
      var sqrt = Math.sqrt(door); 
 
      if (sqrt === (sqrt | 0)) {
        console.log("Door %d is open", door);
      } 
    });

// Array comprehension style
[ for (i of Array.apply(null, { length: 100 })) i ].forEach((_, i) => { 
  var door = i + 1
  var sqrt = Math.sqrt(door); 
 
  if (sqrt === (sqrt | 0)) {
    console.log("Door %d is open", door);
  } 
});

The result is always:

Door 1 is open
Door 4 is open
Door 9 is open
Door 16 is open
Door 25 is open
Door 36 is open
Door 49 is open
Door 64 is open
Door 81 is open
Door 100 is open

Or using a more general function for listing perfect squares:

(function (n) {
 
 
    // ONLY PERFECT SQUARES HAVE AN ODD NUMBER OF INTEGER FACTORS
    // (Leaving the door open at the end of the process) 
 
    return perfectSquaresUpTo(n);
 
 
    // perfectSquaresUpTo :: Int -> [Int]
    function perfectSquaresUpTo(n) {
        return range(1, Math.floor(Math.sqrt(n)))
            .map(x => x * x);
    }
 
 
    // GENERIC
 
    // range(intFrom, intTo, optional intStep)
    // Int -> Int -> Maybe Int -> [Int]
    function range(m, n, step) {
        let d = (step || 1) * (n >= m ? 1 : -1);
 
        return Array.from({
            length: Math.floor((n - m) / d) + 1
        }, (_, i) => m + (i * d));
    }
 
})(100);

Output:

[1, 4, 9, 16, 25, 36, 49, 64, 81, 100]

School example

Works with: JavaScript version Node.js 16.13.0 (LTS)

"use strict";
 
// Doors can be open or closed.
const open = "O";
const closed = "C";
 
// There are 100 doors in a row that are all initially closed.
const doorsCount = 100;
const doors = [];
for (let i = 0; i < doorsCount; doors[i] = closed, i++);
 
// You make 100 passes by the doors, visiting every door and toggle the door (if
// the door is closed, open it; if it is open, close it), according to the rules
// of the task.
for (let pass = 1; pass <= doorsCount; pass++)
    for (let i = pass - 1; i < doorsCount; i += pass)
        doors[i] = doors[i] == open ? closed : open;
 
// Answer the question: what state are the doors in after the last pass?
doors.forEach((v, i) =>
    console.log(`Doors ${i + 1} are ${v == open ? 'opened' : 'closed'}.`));
 
// Which are open, which are closed?
let openKeyList = [];
let closedKeyList = [];
for (let door of doors.entries())
    if (door[1] == open)
        openKeyList.push(door[0] + 1);
    else
        closedKeyList.push(door[0] + 1);
console.log("These are open doors: " + openKeyList.join(", ") + ".");
console.log("These are closed doors: " + closedKeyList.join(", ") + ".");
 
// Assert:
const expected = [];
for (let i = 1; i * i <= doorsCount; expected.push(i * i), i++);
if (openKeyList.every((v, i) => v === expected[i]))
    console.log("The task is solved.")
else
    throw "These aren't the doors you're looking for.";

jq

jq arrays have 0 as their index origin, but in the following, the 100 doors are numbered from 1 to 100.

Solution by simulation

# Solution for n doors:
def doors(n):
 
  def print:
    . as $doors
    | range(1; length+1)
    | if $doors[.] then "Door \(.) is open" else empty end;
 
    [range(n+1)|null] as $doors
  | reduce range(1; n+1) as $run
      ( $doors; reduce range($run; n+1; $run ) as $door
                  ( .; .[$door] = (.[$door] | not) ) )
  | print ;
 
 

Analytical solution

# Solution for 100 doors:
def solution:
  range(1;11) | "Door \(. * .) is open";
 

Julia

Simple:

• falses(100) creates a 100-element Bool array filled with false values,
• 'b in a:a:100' translates to 'start:step:end',
• string concatenation by '*'.

doors = falses(100)
for a in 1:100, b in a:a:100
    doors[b] = !doors[b]
end
for a = 1:100
    println("Door $a is " * (doors[a] ? "open." : "closed.")) 
end

Gimmicky-optimized:

for i in 1:10 println("Door $(i^2) is open.") end

K

unoptimized / converted from Q .

 `closed `open ![ ; 2 ] @ #:' 1 _ = ,/ &:' 0 = t !\:/: t : ! 101

optimized / 1 origin indices

 ( 1 + ! 10 ) ^ 2

/ As parameterized function :

 { ( 1 + ! _ x ^ % 2 ) ^ 2 } 100 

Klingphix

include ..\Utilitys.tlhy
 
%n 100 !n
0 $n repeat
 
$n [dup sqrt int dup * over
== ( [1 swap set] [drop] ) if] for
 
$n [ ( "The door " over  " is " ) lprint get ( ["OPEN"] ["closed"] ) if print nl] for
 
( "Time elapsed: " msec " seconds" ) lprint nl
 
pstack
" " input

Klong

unoptimized

 
flip::{,/{(1-*x),1_x}'x:#y}
i::0;(100{i::i+1;flip(i;x)}:*100:^0)?1
 

optimized

 
(1+!9)^2
 

Kotlin

fun oneHundredDoors(): List<Int> {
    val doors = BooleanArray(100, { false })
    for (i in 0..99) {
        for (j in i..99 step (i + 1)) {
            doors[j] = !doors[j]
        }
    }
    return doors
        .mapIndexed { i, b -> i to b }
        .filter { it.second }
        .map { it.first + 1 }
}

KQL

range InitialDoor from 1 to 100 step 1
| extend DoorsVisited=range(InitialDoor, 100, InitialDoor)
| mvexpand DoorVisited=DoorsVisited to typeof(int)
| summarize VisitCount=count() by DoorVisited
| project Door=DoorVisited, IsOpen=(VisitCount % 2) == 1

LabVIEW

This image is a VI Snippet, an executable image of LabVIEW code. The LabVIEW version is shown on the top-right hand corner. You can download it, then drag-and-drop it onto the LabVIEW block diagram from a file browser, and it will appear as runnable, editable code.

Optimized

This image is a VI Snippet, an executable image of LabVIEW code. The LabVIEW version is shown on the top-right hand corner. You can download it, then drag-and-drop it onto the LabVIEW block diagram from a file browser, and it will appear as runnable, editable code.

langur

not optimized

Works with: langur version 0.8.11

var .doors = arr 100, false
 
for .i of .doors {
    for .j = .i; .j <= len(.doors); .j += .i {
        .doors[.j] = not .doors[.j]
    }
}
 
writeln wherekeys .doors

We could also use a for loop value to produce the output (instead of the wherekeys function), as in the following example.

Works with: langur version 0.8.1

writeln for[=[]] .i of .doors { if(.doors[.i]: _for ~= [.i]) }

Or, we could use the foldfrom() function to produce the output.

writeln foldfrom(f if(.b: .a~[.c]; .a), [], .doors, series 1..len .doors)

optimized

writeln map(f .x ^ 2, series 1..10)

Works with: langur version 0.8.11

writeln map f{^2}, 1..10

Output:

[1, 4, 9, 16, 25, 36, 49, 64, 81, 100]

lambdatalk

Translation from Python

 
1) unoptimized version
 
{def doors
 {A.new
  {S.map {lambda {} false} {S.serie 1 100}}}}
-> doors
 
{def toggle
 {lambda {:i :a}
  {let { {_ {A.set! :i {not {A.get :i :a}} :a} }}}}}
-> toggle
 
{S.map {lambda {:b} 
 {S.map {lambda {:i} {toggle :i {doors}}} 
  {S.serie :b 99 {+ :b 1}}}}
   {S.serie 0 99}} 
->
 
{S.replace \s by space in 
 {S.map {lambda {:i} {if {A.get :i {doors}} then {+ :i 1} else}} 
  {S.serie 0 99}}}
 
-> 1 4 9 16 25 36 49 64 81 100
 
2.2) optimized version
 
{S.replace \s by space in 
 {S.map {lambda {:i}
         {let { {:root {sqrt :i}} } 
              {if {= :root {round :root}} 
               then {* :root :root}
               else}}}
        {S.serie 1 100}}}
 
-> 1 4 9 16 25 36 49 64 81 100
 

Lasso

Loop

loop(100) => {^
	local(root = math_sqrt(loop_count))
	local(state = (#root == math_ceil(#root) ? '<strong>open</strong>' | 'closed'))
	#state != 'closed' ? 'Door ' + loop_count + ': ' + #state + '<br>'
^}

Output:

Door 1: open
Door 4: open
Door 9: open
Door 16: open
Door 25: open
Door 36: open
Door 49: open
Door 64: open
Door 81: open
Door 100: open

Latitude

use 'format importAllSigils.
 
doors := Object clone.
doors missing := { False. }.
doors check := {
  self slot ($1 ordinal).
}.
doors toggle := {
  self slot ($1 ordinal) = self slot ($1 ordinal) not.
}.
1 upto 101 do {
  takes '[i].
  local 'j = i.
  while { j <= 100. } do {
    doors toggle (j).
    j = j + i.
  }.
}.
$stdout printf: ~fmt "The open doors are: ~A", 1 upto 101 filter { doors check. } to (Array).

Lhogho

This implementation defines 100 variables, named "1 through "100, rather than using a list. Thanks to Pavel Boytchev, the author of Lhogho, for help with the code.

to doors
	;Problem 100 Doors 
	;Lhogho
 
	for "p [1 100] 
	[
		make :p "false
	]
 
	for "a [1 100 1]
	[
		for "b [:a 100 :a]
		[
			if :b < 101 
			[
				make :b not thing :b
			]
		]
	]
 
	for "c [1 100]
	[
		if thing :c 
		[ 
			(print "door :c "is "open) 
		]
	] 
end
 
doors

Liberty BASIC

dim doors(100)
for pass = 1 to 100
    for door = pass to 100 step pass
        doors(door) = not(doors(door))
    next door
next pass
print "open doors ";
for door = 1 to 100
    if doors(door) then print door;"  ";
next door

Lily

var doors = List.fill(100, false)
 
for i in 0...99:
    for j in i...99 by i + 1:
        doors[j] = !doors[j]
 
# The type must be specified since the list starts off empty.
var open_doors: List[Integer] = []
 
doors.each_index{|i|
    if doors[i]:
        open_doors.push(i + 1)
}
 
print($"Open doors: ^(open_doors)")

Output:

Open doors: [1, 4, 9, 16, 25, 36, 49, 64, 81, 100]

xTalk

Works with: HyperCard

Works with: LiveCode

 
on mouseUp   
   repeat with tStep = 1 to 100
      repeat with tDoor = tStep to 100 step tStep
         put not tDoors[tDoor] into tDoors[tDoor]
      end repeat
      if tDoors[tStep] then put "Door " & tStep & " is open" & cr after tList
   end repeat
   set the text of field "Doors" to tList
end mouseUp
 

Logo

to doors
;Problem 100 Doors 
;FMSLogo
;lrcvs 2010
 
make "door (vector 100 1) 
for [p 1 100][setitem :p :door 0] 
 
for [a 1 100 1][for [b :a 100 :a][make "x item :b :door 
	                          ifelse :x  = 0 [setitem :b :door 1][setitem :b :door 0] ] ] 
 
for [c 1 100][make "y item :c :door 
	      ifelse :y = 0 [pr (list :c "Close)] [pr (list :c "Open)] ] 
end

LOLCODE

HAI 1.3
 
I HAS A doors ITZ A BUKKIT
IM IN YR hallway UPPIN YR door TIL BOTH SAEM door AN 100
    doors HAS A SRS door ITZ FAIL BTW, INISHULIZE ALL TEH DOORZ AS CLOZD
IM OUTTA YR hallway
 
IM IN YR hallway UPPIN YR pass TIL BOTH SAEM pass AN 100
    I HAS A door ITZ pass
    IM IN YR passer
        doors'Z SRS door R NOT doors'Z SRS door
        door R SUM OF door AN SUM OF pass AN 1
        DIFFRINT door AN SMALLR OF door AN 99, O RLY?
            YA RLY, GTFO
        OIC
    IM OUTTA YR passer
IM OUTTA YR hallway
 
IM IN YR printer UPPIN YR door TIL BOTH SAEM door AN 100
    VISIBLE "Door #" SUM OF door AN 1 " is "!
    doors'Z SRS door, O RLY?
        YA RLY, VISIBLE "open."
        NO WAI, VISIBLE "closed."
    OIC
IM OUTTA YR printer
 
KTHXBYE

Lua

local is_open = {}
 
for pass = 1,100 do
    for door = pass,100,pass do
        is_open[door] = not is_open[door]
    end
end
 
for i,v in next,is_open do
    print ('Door '..i..':',v and 'open' or 'close')
end

M2000 Interpreter

Second dim preserve values except explicit assign a value for each item using = or a different value using << and a lambda function as generator.

Here we use =false to make all items false (which is a double value of 0).

M2000 use True and False as -1 and 0 (type of double), but from comparisons return Boolean True and False, which used as -1 and 0 also. Using =1=1 we get Boolean True and =1=0 we get Boolean False. We can check type from a variable using Type$(), so x=1=1 : Print Type$(x)="Boolean". We can chack type of an expression using a function: Def ExpressionType$(x)=Type$(x)

 
Module Doors100 {
      Dim Doors(1 to 100)
      For i=1 to 100
            For j=i to 100 step i
                  Doors(j)~
            Next j
      Next i
      DispAll()
      ' optimization
      Dim Doors(1 to 100)=False
      For i=1 to 10
            Doors(i**2)=True
      Next i
      Print
      DispAll()
      Sub DispAll()
            Local i
            For i=1 to 100
                  if Doors(i) then print i,
            Next i
            Print
      End Sub
}
Doors100
 

M4

define(`_set', `define(`$1[$2]', `$3')')dnl
define(`_get', `defn(`$1[$2]')')dnl
define(`for',`ifelse($#,0,``$0'',`ifelse(eval($2<=$3),1,
`pushdef(`$1',$2)$5`'popdef(`$1')$0(`$1',eval($2+$4),$3,$4,`$5')')')')dnl
define(`opposite',`_set(`door',$1,ifelse(_get(`door',$1),`closed',`open',`closed'))')dnl
define(`upper',`100')dnl
for(`x',`1',upper,`1',`_set(`door',x,`closed')')dnl
for(`x',`1',upper,`1',`for(`y',x,upper,x,`opposite(y)')')dnl
for(`x',`1',upper,`1',`door x is _get(`door',x)
')dnl

MAD

            NORMAL MODE IS INTEGER
            DIMENSION OPEN(100)
            PRINT COMMENT $ $
 
          R MAKE SURE ALL DOORS ARE CLOSED AT BEGINNING
            THROUGH CLOSE, FOR DOOR=1, 1, DOOR.G.100
CLOSE       OPEN(DOOR) = 0
 
          R MAKE 100 PASSES
            THROUGH TOGGLE, FOR PASS=1, 1, PASS.G.100
            THROUGH TOGGLE, FOR DOOR=PASS, PASS, DOOR.G.100
TOGGLE      OPEN(DOOR) = 1 - OPEN(DOOR) 
 
          R PRINT THE DOORS THAT ARE OPEN
            THROUGH SHOW, FOR DOOR=1, 1, DOOR.G.100
SHOW        WHENEVER OPEN(DOOR).E.1, PRINT FORMAT ISOPEN, DOOR
 
            VECTOR VALUES ISOPEN = $5HDOOR ,I3,S1,8HIS OPEN.*$     
            END OF PROGRAM

Output:

DOOR   1 IS OPEN.
DOOR   4 IS OPEN.
DOOR   9 IS OPEN.
DOOR  16 IS OPEN.
DOOR  25 IS OPEN.
DOOR  36 IS OPEN.
DOOR  49 IS OPEN.
DOOR  64 IS OPEN.
DOOR  81 IS OPEN.
DOOR 100 IS OPEN.

Maple

 
NDoors := proc( N :: posint )
        # Initialise, using 0 to represent "closed"
        local pass, door, doors := Array( 1 .. N, 'datatype' = 'integer'[ 1 ] );
        # Now do N passes
        for pass from 1 to N do
                for door from pass by pass while door <= N do
                        doors[ door ] := 1 - doors[ door ]
                end do
        end do;
        # Output
        for door from 1 to N do
                printf( "Door %d is %s.\n", door, `if`( doors[ door ] = 0, "closed", "open" ) )
        end do;
        # Since this is a printing routine, return nothing.
        NULL
end proc:
 

To solve the problem, call it with 100 as argument (output not shown here).

 
> NDoors( 100 );
 

Here is the optimised version, which outputs only the open doors.

 
> seq( i^2, i = 1 .. isqrt( 100 ) );
                  1, 4, 9, 16, 25, 36, 49, 64, 81, 100
 

Alternatively,

 
> [seq]( 1 .. 10 )^~2;
                 [1, 4, 9, 16, 25, 36, 49, 64, 81, 100]
 

Mathematica/Wolfram Language

unoptimized 1

n=100;
tmp=ConstantArray[-1,n];
Do[tmp[[i;;;;i]]*=-1;,{i,n}];
Do[Print["door ",i," is ",If[tmp[[i]]==-1,"closed","open"]],{i,1,Length[tmp]}]

unoptimized 2

f[n_] = "Closed"; 
Do[Do[If[f[n] == "Closed", f[n] = "Open", f[n] = "Closed"], {n, k, 100, k}], {k, 1, 100}]; 
Table[f[n], {n, 1, 100}]

unoptimized 3

Mathematica also supports immutable data paradigms, like so:

 
Fold[
 ReplacePart[#1, (i_ /; Mod[i, #2] == 0) :> (-#1[[i]])] &,
 ConstantArray[-1, {100}],
 Range[100]
] /. {1 -> "Open", -1 -> "Closed"}
 

optimized 1

Do[Print["door ",i," is ",If[IntegerQ[Sqrt[i]],"open","closed"]],{i,100}]

optimized 2

n=100;
a=Range[1,Sqrt[n]]^2
Do[Print["door ",i," is ",If[MemberQ[a,i],"open","closed"]],{i,100}]

optimized 3

n=100
nn=1
a=0
For[i=1,i<=n,i++,
 If[i==nn,
  Print["door ",i," is open"];
  a++;
  nn+=2a+1;
 ,
  Print["door ",i," is closed"];
 ];
]

These will only give the indices for the open doors: unoptimized 2

Pick[Range[100], [email protected]@@Array[Divisible[#1,#2]&, {100,100}]]

optimized 4

Range[Sqrt[100]]^2

MATLAB / Octave

Iterative Method

Unoptimized

a = false(1,100);
for b=1:100
  for i = b:b:100
    a(i) = ~a(i);
  end
end
a
 

Optimized

 
for x=1:100;
  if sqrt(x) == floor(sqrt(x))
    a(i)=1;
  end
end
a
 

More Optimized

 
a = zeros(100,1);
for counter = 1:sqrt(100);
  a(counter^2) = 1;
end
a
 

Vectorized Method

function [doors,opened,closed] = hundredDoors()
 
    %Initialize the doors, make them booleans for easy vectorization
    doors = logical( (1:1:100) );
 
    %Go through the flipping process, ignore the 1 case because the doors
    %array is already initialized to all open
    for initialPosition = (2:100)
        doors(initialPosition:initialPosition:100) = not( doors(initialPosition:initialPosition:100) );
    end
 
    opened = find(doors); %Stores the numbers of the open doors
    closed = find( not(doors) ); %Stores the numbers of the closed doors
 
end

Known-Result Method

 
doors((1:10).^2) = 1;
 
doors
 

Maxima

doors(n) := block([v], local(v),
  v: makelist(true, n),
  for i: 2 thru n do
  for j: i step i thru n do v[j]: not v[j],
  sublist_indices(v, 'identity));

Usage:

doors(100);
/* [1, 4, 9, 16, 25, 36, 49, 64, 81, 100] */

MAXScript

unoptimized

doorsOpen = for i in 1 to 100 collect false
 
for pass in 1 to 100 do
(
    for door in pass to 100 by pass do
    (
        doorsOpen[door] = not doorsOpen[door]
    )
)
 
for i in 1 to doorsOpen.count do
(
    format ("Door % is open?: %\n") i doorsOpen[i]
)

optimized

for i in 1 to 100 do
(
    root = pow i 0.5
    format ("Door % is open?: %\n") i (root == (root as integer))
)

Mercury

:- module doors.
:- interface.
:- import_module io.
:- pred main(io::di, io::uo) is det.
:- implementation.
:- import_module bitmap, bool, list, string, int.
 
:- func doors = bitmap.
doors = bitmap.init(100, no).
 
:- pred walk(int, bitmap, bitmap).
:- mode walk(in, bitmap_di, bitmap_uo) is det.
walk(Pass, !Doors) :-
    walk(Pass, Pass, !Doors).
 
:- pred walk(int, int, bitmap, bitmap).
:- mode walk(in, in, bitmap_di, bitmap_uo) is det.
walk(At, By, !Doors) :-
    ( if bitmap.in_range(!.Doors, At - 1) then
        bitmap.unsafe_flip(At - 1, !Doors),
        walk(At + By, By, !Doors)
    else
        true
    ).
 
:- pred report(bitmap, int, io, io).
:- mode report(bitmap_di, in, di, uo) is det.
report(Doors, N, !IO) :-
    ( if is_set(Doors, N - 1) then
        State = "open"
    else
        State = "closed"
    ),
    io.format("door #%d is %s\n",
        [i(N), s(State)], !IO).
 
main(!IO) :-
    list.foldl(walk, 1 .. 100, doors, Doors),
    list.foldl(report(Doors), 1 .. 100, !IO).

Metafont

boolean doors[];
for i = 1 upto 100: doors[i] := false; endfor
for i = 1 upto 100:
  for j = 1 step i until 100:
    doors[j] := not doors[j];
  endfor
endfor
for i = 1 upto 100:
  message decimal(i) & " " & if doors[i]: "open" else: "close" fi;
endfor
end

Microsoft Small Basic

Translation of: GW-BASIC

 
For offset = 1 To 100
  For i = 0 To 100 Step offset
    a[i] = a[i] + 1
  EndFor
EndFor
' Print "opened" doors
For i = 1 To 100
  If math.Remainder(a[i], 2) = 1 Then 
    TextWindow.WriteLine(i)
  EndIf  
EndFor
 

Output:

1
4
9
16
25
36
49
64
81
100

MiniScript

Using a map to hold the set of open doors:

d = {}
for p in range(1, 100)
    for t in range(p, 100, p)
        if d.hasIndex(t) then d.remove t else d.push t
    end for
end for
 
print d.indexes.sort

Output:

[1, 4, 9, 16, 25, 36, 49, 64, 81, 100]

Using an array of boolean values to keep track of door state, and a separate list of indexes of the open doors:

d = [false] * 101
open = []
for p in range(1, 100)
    for t in range(p, 100, p)
        d[t] = not d[t]
    end for
    if d[p] then open.push p
end for
 
print open

(Output same as above.)

MIPS Assembly

.data
  doors:     .space 100
  num_str:   .asciiz "Number "
  comma_gap: .asciiz " is "
  newline:   .asciiz "\n"
 
.text
main:
# Clear all the cells to zero
  li $t1, 100
  la $t2, doors
clear_loop:
  sb $0, ($t2)
  add $t2, $t2, 1
  sub $t1, $t1, 1
  bnez $t1, clear_loop
 
# Now start the loops
  li $t0, 1         # This will the the step size
  li $t4, 1         # just an arbitrary 1
loop1:
  move $t1, $t0      # Counter
  la $t2, doors      # Current pointer
  add $t2, $t2, $t0
  addi $t2, $t2, -1
loop2:
  lb $t3, ($t2)
  sub $t3, $t4, $t3
  sb $t3, ($t2)
  add $t1, $t1, $t0
  add $t2, $t2, $t0
  ble $t1, 100, loop2
 
  addi $t0, $t0, 1
  ble $t0, 100, loop1
 
  # Now display everything
  la $t0, doors
  li $t1, 1
loop3:
  li $v0, 4
  la $a0, num_str
  syscall
 
  li $v0, 1
  move $a0, $t1
  syscall
 
  li $v0, 4
  la $a0, comma_gap
  syscall
 
  li $v0, 1
  lb $a0, ($t0)
  syscall
 
  li $v0, 4,
  la $a0, newline
  syscall
 
  addi $t0, $t0, 1
  addi $t1, $t1, 1
  bne $t1, 101 loop3
 

Mirah

import java.util.ArrayList
 
class Door
	:state
 
	def initialize
		@state=false
	end
 
	def closed?; [email protected]; end
	def open?; @state; end
 
	def close; @state=false; end
	def open; @state=true; end
 
	def toggle
		if closed?
			open
		else
			close
		end
	end
 
	def toString; Boolean.toString(@state); end
end
 
doors=ArrayList.new
1.upto(100) do
    doors.add(Door.new)
end 
 
1.upto(100) do |multiplier|
    index = 0
    doors.each do |door|
        Door(door).toggle if (index+1)%multiplier == 0
        index += 1
    end
end
 
i = 0
doors.each do |door| 
    puts "Door #{i+1} is #{door}."
    i+=1
end
 

mIRC Scripting Language

var %d = $str(0 $+ $chr(32),100), %m = 1
while (%m <= 100) {
  var %n = 1
  while ($calc(%n * %m) <= 100) {
    var %d = $puttok(%d,$iif($gettok(%d,$calc(%n * %m),32),0,1),$calc(%n * %m),32)
    inc %n
  }
  inc %m
}
echo -ag All Doors (Boolean): %d
var %n = 1
while (%n <= $findtok(%d,1,0,32)) {
  var %t = %t $findtok(%d,1,%n,32)
  inc %n
}
echo -ag Open Door Numbers: %t

ML/I

MCSKIP "WITH" NL
"" 100 doors
MCINS %.
MCSKIP MT,<>
"" Doors represented by P1-P100, 0 is closed
MCPVAR 100
"" Set P variables to 0
MCDEF ZEROPS WITHS NL AS <MCSET T1=1
%L1.MCSET PT1=0
MCSET T1=T1+1
MCGO L1 UNLESS T1 EN 101
>
ZEROPS
"" Generate door state
MCDEF STATE WITHS () AS <MCSET T1=%A1.
MCGO L1 UNLESS T1 EN 0
closed<>MCGO L0
%L1.open>
"" Main macro - no arguments
"" T1 is pass number
"" T2 is door number
MCDEF DOORS WITHS NL
AS <MCSET T1=1
"" pass loop
%L1.MCGO L4 IF T1 GR 100
"" door loop
MCSET T2=T1
%L2.MCGO L3 IF T2 GR 100
MCSET PT2=1-PT2
MCSET T2=T2+T1
MCGO L2
%L3.MCSET T1=T1+1
MCGO L1
%L4."" now output the result
MCSET T1=1
%L5.door %T1. is STATE(%PT1.)
MCSET T1=T1+1
MCGO L5 UNLESS T1 GR 100
>
"" Do it
DOORS

MMIX

See 100 doors/MMIX

Modula-2

unoptimized

MODULE Doors;
IMPORT InOut;
 
TYPE State = (Closed, Open);
TYPE List = ARRAY [1 .. 100] OF State;
 
VAR
  Doors: List;
  I, J:  CARDINAL;
 
BEGIN
  FOR I := 1 TO 100 DO
    FOR J := 1 TO 100 DO
      IF J MOD I = 0 THEN
        IF Doors[J] = Closed THEN
          Doors[J] := Open
        ELSE
          Doors[J] := Closed
        END
      END
    END
  END;
 
  FOR I := 1 TO 100 DO
    InOut.WriteCard(I, 3);
    InOut.WriteString(' is ');
 
    IF Doors[I] = Closed THEN
      InOut.WriteString('Closed.')
    ELSE
      InOut.WriteString('Open.')
    END;
 
    InOut.WriteLn
  END
END Doors.

optimized

MODULE DoorsOpt;
IMPORT InOut;
 
TYPE State = (Closed, Open);
TYPE List = ARRAY [1 .. 100] OF State;
 
VAR
  Doors: List;
  I:  CARDINAL;
 
BEGIN
  FOR I := 1 TO 10 DO
    Doors[I*I] := Open
  END;
 
  FOR I := 1 TO 100 DO
    InOut.WriteCard(I, 3);
    InOut.WriteString(' is ');
    IF Doors[I] = Closed THEN
      InOut.WriteString('Closed.')
    ELSE
      InOut.WriteString('Open.')
    END;
    InOut.WriteLn
  END
END DoorsOpt.

Modula-3

unoptimized

MODULE Doors EXPORTS Main;
 
IMPORT IO, Fmt;
 
TYPE State = {Closed, Open};
TYPE List = ARRAY [1..100] OF State;
 
VAR doors := List{State.Closed, ..};
 
BEGIN
  FOR i := 1 TO 100 DO
    FOR j := FIRST(doors) TO LAST(doors) DO
      IF j MOD i = 0 THEN
        IF doors[j] = State.Closed THEN
          doors[j] := State.Open;
        ELSE
          doors[j] := State.Closed;
        END;
      END;
    END;
  END;
 
  FOR i := FIRST(doors) TO LAST(doors) DO
    IO.Put(Fmt.Int(i) & " is ");
    IF doors[i] = State.Closed THEN
      IO.Put("Closed.\n");
    ELSE
      IO.Put("Open.\n");
    END;
  END;
END Doors.

optimized

MODULE DoorsOpt EXPORTS Main;
 
IMPORT IO, Fmt;
 
TYPE State = {Closed, Open};
TYPE List = ARRAY [1..100] OF State;
 
VAR doors := List{State.Closed, ..};
 
BEGIN
  FOR i := 1 TO 10 DO
    doors[i * i] := State.Open;
  END;
 
  FOR i := FIRST(doors) TO LAST(doors) DO
    IO.Put(Fmt.Int(i) & " is ");
    IF doors[i] = State.Closed THEN
      IO.Put("Closed.\n");
    ELSE
      IO.Put("Open.\n");
    END;
  END;
END DoorsOpt.

MontiLang

101 var l .
 
for l 0 endfor
arr
 
0 var i .
for l
    i 1 + var i var j .
    j l < var pass .
    while pass
        get j not insert j .
        j i + var j
        l < var pass .  
    endwhile
endfor
print /# show all doors #/
 
/# show only open doors #/
|| print .
0 var i .
for l
    get i
    if : i out | | out . . endif .
    i 1 + var i .
endfor
 
input . /# pause until ENTER key pressed #/

MOO

is_open = make(100);
for pass in [1..100]
  for door in [pass..100]
    if (door % pass)
      continue;
    endif
    is_open[door] = !is_open[door];
  endfor
endfor
 
"output the result";
for door in [1..100]
  player:tell("door #", door, " is ", (is_open[door] ? "open" : "closed"), ".");
endfor

MoonScript

is_open = [false for door = 1,100]
 
for pass = 1,100 
    for door = pass,100,pass
        is_open[door] = not is_open[door]
 
for i,v in ipairs is_open
    print "Door #{i}: " .. if v then 'open' else 'closed'

MUMPS

doors	new door,pass
	For door=1:1:100 Set door(door)=0
	For pass=1:1:100 For door=pass:pass:100 Set door(door)='door(door)
	For door=1:1:100 If door(door) Write !,"Door",$j(door,4)," is open"
	Write !,"All other doors are closed."
	Quit
Do doors
Door   1 is open
Door   4 is open
Door   9 is open
Door  16 is open
Door  25 is open
Door  36 is open
Door  49 is open
Door  64 is open
Door  81 is open
Door 100 is open
All other doors are closed.

Myrddin

 
use std
 
const main = {
	var isopen	: bool[100]
 
	std.slfill(isopen[:], false)
	for var i = 0; i < isopen.len; i++
		for var j = i; j < isopen.len; j += i + 1
			isopen[j] = !isopen[j]
		;;
	;;
 
	for var i = 0; i < isopen.len; i++
		if isopen[i]
			std.put("door {} is open\n", i + 1)
		;;
	;;
}
 

Output:

door 1 is open
door 4 is open
door 9 is open
door 16 is open
door 25 is open
door 36 is open
door 49 is open
door 64 is open
door 81 is open
door 100 is open

MySQL

 
DROP PROCEDURE IF EXISTS one_hundred_doors;
 
DELIMITER |
 
CREATE PROCEDURE one_hundred_doors (n INT)
BEGIN
  DROP TEMPORARY TABLE IF EXISTS doors; 
  CREATE TEMPORARY TABLE doors (
    id INTEGER NOT NULL,
    open BOOLEAN DEFAULT FALSE,
    PRIMARY KEY (id)
  );
 
  SET @i = 1;
  create_doors: LOOP
    INSERT INTO doors (id, open) values (@i, FALSE);
    SET @i = @i + 1;
    IF @i > n THEN
      LEAVE create_doors;
    END IF;
  END LOOP create_doors;
 
  SET @i = 1;
  toggle_doors: LOOP
    UPDATE doors SET open = NOT open WHERE MOD(id, @i) = 0;
    SET @i = @i + 1;
    IF @i > n THEN
      LEAVE toggle_doors;
    END IF;
  END LOOP toggle_doors;
 
  SELECT id FROM doors WHERE open;
END|
 
DELIMITER ;
 
CALL one_hundred_doors(100);
 

Output:

+-----+
| id  |
+-----+
|   1 |
|   4 |
|   9 |
|  16 |
|  25 |
|  36 |
|  49 |
|  64 |
|  81 |
| 100 |
+-----+
10 rows in set (0.02 sec)

Nanoquery

// allocate a boolean array with all closed doors (false)
// we need 101 since there will technically be a door 0
doors = {false} * 101
 
// loop through all the step lengths (1-100)
for step in range(1, 100)
	// loop through all the doors, stepping by step
	for door in range(0, len(doors) - 1, step)
		// change the state of the current door
		doors[door] = !doors[door]
	end for
end for
 
// loop through and print the doors that are open, skipping door 0
for i in range(1, len(doors) - 1)
	// if the door is open, display it
	if doors[i]
		println "Door " + i + " is open."
	end if
end for

NetRexx

unoptimized

/* NetRexx */
options replace format comments java crossref symbols binary
 
True  = Rexx(1 == 1)
False = Rexx(\True)
 
doors = False
 
loop i_ = 1 to 100
  loop j_ = 1 to 100
    if 0 = (j_ // i_) then doors[j_] = \doors[j_]
    end j_
  end i_
 
loop d_ = 1 to 100
  if doors[d_] then  state = 'open'
  else  state = 'closed'
 
  say 'Door Nr.' Rexx(d_).right(4) 'is' state
  end d_

optimized (Based on the Java 'optimized' version)

Translation of: Java

/* NetRexx */
options replace format comments java crossref symbols binary
 
True  = (1 == 1)
False = \True
 
doors = boolean[100]
 
loop i_ = 0 to 9
  doors[(i_ + 1) * (i_ + 1) - 1] = True;
  end i_
 
loop i_ = 0 to 99
  if doors[i_] then  state = 'open'
  else  state = 'closed'
 
  say 'Door Nr.' Rexx(i_ + 1).right(4) 'is' state
  end i_

optimized 2 (Based on the Java 'optimized 2' version)

Translation of: Java

/* NetRexx */
options replace format comments java crossref savelog symbols binary
 
resultstring = ''
 
loop i_ = 1 to 10
  resultstring = resultstring || 'Door Nr.' Rexx(i_ * i_).right(4) 'is open\n'
  end i_
 
say resultstring

optimized 3

/* NetRexx */
 
loop i = 1 to 10
   say 'Door Nr.' i * i 'is open.'
  end i

newLISP

(define (status door-num)
    (let ((x (int (sqrt door-num))))
     (if
       (= (* x x) door-num) (string "Door " door-num " Open")
       (string "Door " door-num " Closed"))))
 
(dolist (n (map status (sequence 1 100)))
  (println n))
 

Not optimized:

 
(set 'Doors (array 100))  ;; Default value: nil (Closed)
 
(for (x 0 99)
    (for (y x 99 (+ 1 x))
        (setf (Doors y) (not (Doors y)))))
 
(for (x 0 99)  ;; Display open doors
    (if (Doors x)
        (println (+ x 1) " : Open")))
 

Output:

1 : Open
4 : Open
9 : Open
16 : Open
25 : Open
36 : Open
49 : Open
64 : Open
81 : Open
100 : Open

Nial

unoptimized solution (works with Q'Nial7):

Output of the boolean array showing the status of the doors. Truth values in Nial arrays are shown as l(true) and o(false):

     n:=100;reduce xor (count n eachright mod count n eachall<1)
looloooolooooooloooooooolooooooooooloooooooooooolooooooooooooooloooooooooooooooo
 
looooooooooooooooool

Indices of the open doors:

     true findall (n:=100;reduce xor (count n eachright mod count n eachall<1))+1
1 4 9 16 25 36 49 64 81 100

optimized solution:

     count 10 power 2
1 4 9 16 25 36 49 64 81 100

Nim

unoptimized:

from strutils import `%`
 
const numDoors = 100
var doors: array[1..numDoors, bool]
 
for pass in 1..numDoors:
  for door in countup(pass, numDoors, pass):
    doors[door] = not doors[door]
 
for door in 1..numDoors:
  echo "Door $1 is $2." % [$door, if doors[door]: "open" else: "closed"]

Challenging C++'s compile time computation: https://rosettacode.org/wiki/100_doors#C.2B.2B
outputString is evaluated at compile time. Check the resulting binary in case of doubt.

from strutils import `%`
 
const numDoors = 100
var doors {.compileTime.}: array[1..numDoors, bool]
 
proc calcDoors(): string =
  for pass in 1..numDoors:
    for door in countup(pass, numDoors, pass):
      doors[door] = not doors[door] 
  for door in 1..numDoors:
    result.add("Door $1 is $2.\n" % [$door, if doors[door]: "open" else: "closed"])
 
const outputString: string = calcDoors()
 
echo outputString

Oberon

Oberon-07, by Niklaus Wirth.

MODULE Doors;
  IMPORT Out;
 
  PROCEDURE Do*;  (* In Oberon an asterisk after an identifier is an export mark *)
    CONST N = 100; len = N + 1;
    VAR i, j: INTEGER;
      closed: ARRAY len OF BOOLEAN;  (* Arrays in Oberon always start with index 0; closed[0] is not used *)
  BEGIN
    FOR i := 1 TO N DO closed[i] := TRUE END;
    FOR i := 1 TO N DO
      j := 1;
      WHILE j < len DO
        IF j MOD i = 0 THEN closed[j] := ~closed[j] END; INC(j)  (* ~ = NOT *)
      END
    END;
    (* Print a state diagram of all doors *)
    FOR i := 1 TO N DO 
      IF (i - 1) MOD 10 = 0 THEN Out.Ln END;
      IF closed[i] THEN Out.String("- ") ELSE Out.String("+ ") END
    END;  Out.Ln;
    (* Print the numbers of the open doors *)
    FOR i := 1 TO N DO 
      IF ~closed[i] THEN Out.Int(i, 0); Out.Char(" ") END
    END;  Out.Ln
  END Do;
 
END Doors. 

Execute: Doors.Do

Output:

+ – – + – – – – + – 
– – – – – + – – – – 
– – – – + – – – – – 
– – – – – + – – – – 
– – – – – – – – + – 
– – – – – – – – – – 
– – – + – – – – – – 
– – – – – – – – – – 
+ – – – – – – – – – 
– – – – – – – – – + 
1 4 9 16 25 36 49 64 81 100 

Objeck

optimized

 
bundle Default {
  class Doors {
    function : Main(args : String[]) ~ Nil {
      doors := Bool->New[100];
 
      for(pass := 0; pass < 10; pass += 1;) {
        doors[(pass + 1) * (pass + 1) - 1] := true;
      };
 
      for(i := 0; i < 100; i += 1;) {    
        IO.Console->GetInstance()->Print("Door #")->Print(i + 1)->Print(" is ");
        if(doors[i]) {
          "open."->PrintLine();
        }
        else {
          "closed."->PrintLine();
        };
      };
    }
  }
}
 

Objective-C

A basic implementation in Objective-C:

This is a very basic Objective-C sample that shows the usage of standard types and classes such as NSInteger and NSMutableArray.

It uses modern Objective-C syntax such as literals, blocks, and a compiler module import statement.

 
@import Foundation;
 
int main(int argc, const char * argv[]) {
    @autoreleasepool {
 
        // Create a mutable array
        NSMutableArray *doorArray = [@[] mutableCopy];
 
        // Fill the doorArray with 100 closed doors
        for (NSInteger i = 0; i < 100; ++i) {
            doorArray[i] = @NO;
        }
 
        // Do the 100 passes
        for (NSInteger pass = 0; pass < 100; ++pass) {
            for (NSInteger door = pass; door < 100; door += pass+1) {
                doorArray[door] = [doorArray[door]  isEqual: @YES] ? @NO : @YES;
            }
        }
 
        // Print the results
        [doorArray enumerateObjectsUsingBlock:^(id obj, NSUInteger idx, BOOL *stop) {
            if ([obj isEqual: @YES]) {
                NSLog(@"Door number %lu is open", idx + 1);
            }
        }];
    }
}
 

A more typical implementation in Objective-C:

This example is more along the lines of what typical Objective-C program would look like.

Language features used include:

• MVC design pattern with separate classes for the data model, user interface, and controller (Here, main steps in to represent the controller class.)
• Class category to extend the standard NSMutableArray class to add doors without a subclass
• Class inheritance in the DoorViewClass when subclassing NSObject
• Pragma mark statements for IDE navigation in Xcode

In a real world program classes are normally separated into different files.

 
@import Foundation;
 
#pragma mark - Classes
////////////////////////////////////////////////////
// Model class header - A we are using a category to add a method to MSMutableArray
@interface NSMutableArray (DoorModelExtension)
 
- (void)setNumberOfDoors:(NSUInteger)doors;
 
@end
 
// Model class implementation
@implementation NSMutableArray (DoorModelExtension)
 
- (void)setNumberOfDoors:(NSUInteger)doors {
    // Fill the doorArray with 100 closed doors
    for (NSInteger i = 0; i < doors; ++i) {
        self[i] = @NO;
    }
}
@end
////////////////////////////////////////////////////
 
// View class header - A simple class to handle printing our values
@interface DoorViewClass : NSObject
 
- (void)printResultsOfDoorTask:(NSMutableArray *)doors;
 
@end
 
// View class implementation
@implementation DoorViewClass
 
- (void)printResultsOfDoorTask:(NSMutableArray *)doors {
 
    // Print the results, using an enumeration block for easy index tracking
    [doors enumerateObjectsUsingBlock:^(id obj, NSUInteger idx, BOOL *stop) {
        if ([obj isEqual: @YES]) {
            NSLog(@"Door number %lu is open", idx + 1);
        }
    }];
}
 
@end
////////////////////////////////////////////////////
 
#pragma mark - main
// With our classes set we can use them from our controller, in this case main
int main(int argc, const char * argv[]) {
 
    // Init our classes
    NSMutableArray *doorArray = [NSMutableArray array];
    DoorViewClass *doorView = [DoorViewClass new];
 
    // Use our class category to add the doors
    [doorArray setNumberOfDoors:100];
 
    // Do the 100 passes
    for (NSUInteger pass = 0; pass < 100; ++pass) {
        for (NSUInteger door = pass; door < 100; door += pass+1) {
            doorArray[door] = [doorArray[door]  isEqual: @YES] ? @NO : @YES;
        }
    }
 
    // Print the results
    [doorView printResultsOfDoorTask:doorArray];
 
}
 

OCaml

unoptimized

let max_doors = 100
 
let show_doors =
  Array.iteri (fun i x -> Printf.printf "Door %d is %s\n" (i+1)
                                        (if x then "open" else "closed"))
 
let flip_doors doors =
  for i = 1 to max_doors do
    let rec flip idx =
      if idx < max_doors then begin
        doors.(idx) <- not doors.(idx);
        flip (idx + i)
      end
    in flip (i - 1)
  done;
  doors
 
let () =
  show_doors (flip_doors (Array.make max_doors false))

optimized

let optimised_flip_doors doors =
  for i = 1 to int_of_float (sqrt (float_of_int max_doors)) do
    doors.(i*i - 1) <- true
  done;
  doors
 
let () =
  show_doors (optimised_flip_doors (Array.make max_doors false))

This variant is more functional style (loops are recursions), unoptimized, and we do rather 100 passes on first element, then 100 * second, to avoid mutable data structures and many intermediate lists.

type door = Open | Closed    (* human readable code *)
 
let flipdoor = function Open -> Closed | Closed -> Open
 
let string_of_door =       
  function Open -> "is open." | Closed -> "is closed."
 
let printdoors ls =
  let f i d = Printf.printf "Door %i %s\n" (i + 1) (string_of_door d)
  in List.iteri f ls
 
let outerlim = 100
let innerlim = 100
 
let rec outer cnt accu =
  let rec inner i door = match i > innerlim with (* define inner loop *)
    | true  -> door                         
    | false -> inner (i + 1) (if (cnt mod i) = 0 then flipdoor door else door)
  in (* define and do outer loop *)
  match cnt > outerlim with
  | true  -> List.rev accu
  | false -> outer  (cnt + 1)  (inner 1 Closed :: accu) (* generate new entries with inner *)
 
let () = printdoors (outer 1 [])

Octave

doors = false(100,1);
for i = 1:100
  for j = i:i:100
    doors(j) = !doors(j);
  endfor
endfor
for i = 1:100
  if ( doors(i) )
    s = "open";
  else
    s = "closed";
  endif
  printf("%d %s\n", i, s);
endfor

See also the solutions in Matlab. They will work in Octave, too.

Oforth

: doors
| i j l |
   100 false Array newWith dup ->l
   100 loop: i [ 
      i 100 i step: j [ l put ( j , j l at not ) ] 
      ] 
;
 

Ol

 
(define (flip doors every)
   (map (lambda (door num)
            (mod (+ door (if (eq? (mod num every) 0) 1 0)) 2))
      doors
      (iota (length doors) 1)))
 
(define doors
   (let loop ((doors (repeat 0 100)) (n 1))
      (if (eq? n 100)
         doors
         (loop (flip doors n) (+ n 1)))))
 
(print "100th doors: " doors)
 

Output:

100th doors: (1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0)

Onyx

$Door dict def
1 1 100 {Door exch false put} for
$Toggle {dup Door exch get not Door up put} def
$EveryNthDoor {dup 100 {Toggle} for} def
$Run {1 1 100 {EveryNthDoor} for} def
$ShowDoor {dup `Door no. ' exch cvs cat ` is ' cat
  exch Door exch get {`open.\n'}{`shut.\n'} ifelse cat
  print flush} def
Run 1 1 100 {ShowDoor} for

Output:

Door no. 1 is open.
Door no. 2 is shut.
Door no. 3 is shut.
Door no. 4 is open.
Door no. 5 is shut.
Door no. 6 is shut.
Door no. 7 is shut.
Door no. 8 is shut.
Door no. 9 is open.
Door no. 10 is shut.
Door no. 11 is shut.
Door no. 12 is shut.
Door no. 13 is shut.
Door no. 14 is shut.
Door no. 15 is shut.
Door no. 16 is open.
Door no. 17 is shut.
Door no. 18 is shut.
Door no. 19 is shut.
Door no. 20 is shut.
Door no. 21 is shut.
Door no. 22 is shut.
Door no. 23 is shut.
Door no. 24 is shut.
Door no. 25 is open.
Door no. 26 is shut.
Door no. 27 is shut.
Door no. 28 is shut.
Door no. 29 is shut.
Door no. 30 is shut.
Door no. 31 is shut.
Door no. 32 is shut.
Door no. 33 is shut.
Door no. 34 is shut.
Door no. 35 is shut.
Door no. 36 is open.
Door no. 37 is shut.
Door no. 38 is shut.
Door no. 39 is shut.
Door no. 40 is shut.
Door no. 41 is shut.
Door no. 42 is shut.
Door no. 43 is shut.
Door no. 44 is shut.
Door no. 45 is shut.
Door no. 46 is shut.
Door no. 47 is shut.
Door no. 48 is shut.
Door no. 49 is open.
Door no. 50 is shut.
Door no. 51 is shut.
Door no. 52 is shut.
Door no. 53 is shut.
Door no. 54 is shut.
Door no. 55 is shut.
Door no. 56 is shut.
Door no. 57 is shut.
Door no. 58 is shut.
Door no. 59 is shut.
Door no. 60 is shut.
Door no. 61 is shut.
Door no. 62 is shut.
Door no. 63 is shut.
Door no. 64 is open.
Door no. 65 is shut.
Door no. 66 is shut.
Door no. 67 is shut.
Door no. 68 is shut.
Door no. 69 is shut.
Door no. 70 is shut.
Door no. 71 is shut.
Door no. 72 is shut.
Door no. 73 is shut.
Door no. 74 is shut.
Door no. 75 is shut.
Door no. 76 is shut.
Door no. 77 is shut.
Door no. 78 is shut.
Door no. 79 is shut.
Door no. 80 is shut.
Door no. 81 is open.
Door no. 82 is shut.
Door no. 83 is shut.
Door no. 84 is shut.
Door no. 85 is shut.
Door no. 86 is shut.
Door no. 87 is shut.
Door no. 88 is shut.
Door no. 89 is shut.
Door no. 90 is shut.
Door no. 91 is shut.
Door no. 92 is shut.
Door no. 93 is shut.
Door no. 94 is shut.
Door no. 95 is shut.
Door no. 96 is shut.
Door no. 97 is shut.
Door no. 98 is shut.
Door no. 99 is shut.
Door no. 100 is open.

ooRexx

doors = .array~new(100)    -- array containing all of the doors
do i = 1 to doors~size     -- initialize with a collection of closed doors
   doors[i] = .door~new(i)
end
 
do inc = 1 to doors~size
  do d = inc to doors~size by inc
    doors[d]~toggle
  end
end
say "The open doors after 100 passes:"
do door over doors
  if door~isopen then say door
end
 
::class door           -- simple class to represent a door
::method init          -- initialize an instance of a door
  expose id state      -- instance variables of a door
  use strict arg id    -- set the id
  state = .false       -- initial state is closed
 
::method toggle        -- toggle the state of the door
  expose state
  state = \state
 
::method isopen        -- test if the door is open
  expose state
  return state
 
::method string        -- return a string value for a door
  expose state id
  if state then return "Door" id "is open"
  else return "Door" id "is closed"
 
::method state         -- return door state as a descriptive string
  expose state
  if state then return "open"
  else return "closed"

The two programs in the Rexx section run under ooRexx when '#' is replaced by, e.g., 'dd'.
'#' is not supported by ooRexx as part of or as a symbol. Neither are @ and $.

OpenEdge/Progress

DEFINE VARIABLE lopen   AS LOGICAL     NO-UNDO EXTENT 100.
DEFINE VARIABLE idoor   AS INTEGER     NO-UNDO.
DEFINE VARIABLE ipass   AS INTEGER     NO-UNDO.
DEFINE VARIABLE cresult AS CHARACTER   NO-UNDO.
 
DO ipass = 1 TO 100:
   idoor = 0.
   DO WHILE idoor <= 100:
      idoor = idoor + ipass.
      IF idoor <= 100 THEN
         lopen[ idoor ] = NOT lopen[ idoor ].
   END.
END.
 
DO idoor = 1 TO 100:
   cresult = cresult + STRING( lopen[ idoor ], "1  /0  " ).
   IF idoor MODULO 10 = 0 THEN
      cresult = cresult + "~r":U.
END.
 
MESSAGE cresult VIEW-AS ALERT-BOX.
 

OxygenBasic

def    doors 100
int    door[doors],i ,j, c
string cr,tab,pr
'
for i=1 to doors
  for j=i to doors step i
    door[j]=1-door[j]
    if door[j] then c++ else c--
  next
next
'
cr=chr(13) chr(10)
pr="Doors Open: " c cr cr 
'
for i=1 to doors
   if door[i] then pr+=i cr
next
print pr

Oz

declare
  NumDoors = 100
  NumPasses = 100
 
  fun {NewDoor} closed end
 
  fun {Toggle Door}
     case Door of closed then open
     [] open then closed
     end
  end
 
  fun {Pass Doors I}
     {List.mapInd Doors
      fun {$ Index Door}
         if Index mod I == 0 then {Toggle Door}
         else Door
         end
      end}
  end
 
  Doors0 = {MakeList NumDoors}
  {ForAll Doors0 NewDoor}
 
  DoorsN = {FoldL {List.number 1 NumPasses 1} Pass Doors0}
in
  %% print open doors
  {List.forAllInd DoorsN
   proc {$ Index Door}
      if Door == open then
	 {System.showInfo "Door "#Index#" is open."}
      end
   end
  }

Output:

Door 1 is open.
Door 4 is open.
Door 9 is open.
Door 16 is open.
Door 25 is open.
Door 36 is open.
Door 49 is open.
Door 64 is open.
Door 81 is open.
Door 100 is open.

PARI/GP

Unoptimized version.

 
v=vector(d=100);/*set 100 closed doors*/
for(i=1,d,forstep(j=i,d,i,v[j]=1-v[j]));
for(i=1,d,if(v[i],print("Door ",i," is open.")))
 

Optimized version.

for(n=1,sqrt(100),print("Door ",n^2," is open."))

Unoptimized version.

 
doors =vector(100);
print("open doors are : ");
for(i=1,100,for(j=i,100,doors[j]=!doors[j];j +=i-1))
for(k=1,100,if(doors[k]==1,print1(" ",k)))
 

Output:

Open doors are:
 1 4 9 16 25 36 49 64 81 100

Pascal

Program OneHundredDoors;
 
var
   doors : Array[1..100] of Boolean;
   i, j	 : Integer;
 
begin
   for i := 1 to 100 do
      doors[i] := False;
   for i := 1 to 100 do begin
      j := i;
      while j <= 100 do begin
	 doors[j] := not doors[j];
	 j := j + i
      end
   end;
   for i := 1 to 100 do begin
      Write(i, ' ');
      if doors[i] then
	 WriteLn('open')
      else
	 WriteLn('closed');
   end
end.

Optimized version.

program OneHundredDoors;
 
{$APPTYPE CONSOLE}
 
uses
  math, sysutils;
 
var
   AOpendoors  : String;
   ACloseDoors : String;
   i	       : Integer;
 
begin
   for i := 1 to 100 do
   begin
      if (sqrt(i) = floor(sqrt(i))) then
        AOpenDoors := AOpenDoors + IntToStr(i) + ';'
      else
        ACloseDoors := ACloseDoors + IntToStr(i) +';';
   end;
 
   WriteLn('Open doors: ' + AOpenDoors);
   WriteLn('Close doors: ' + ACloseDoors);
end.     

Perl

unoptimized

Works with: Perl version 5.x

my @doors;
for my $pass (1 .. 100) {
    for (1 .. 100) {
        if (0 == $_ % $pass) {
            $doors[$_] = not $doors[$_];
        };
    };
};
 
print "Door $_ is ", $doors[$_] ? "open" : "closed", "\n" for 1 .. 100;

semi-optimized

Works with: Perl version 5.x

This version flips doors, but doesn't visit (iterate over) doors that aren't toggled. Note: I represent open doors as 0 and closed as 1 just for preference. (When I print it as a bit vector, 0 looks more like an open door to me.)

 
#!/usr/bin/perl
use strict;
use warnings;
 
my @doors = (1) x 100;
for my $N (1 .. 100) {
   $doors[$_]=1-$doors[$_] for map { $_*$N - 1 } 1 .. int(100/$N);
}
print join("\n", map { "Door $_ is Open" } grep { ! $doors[$_-1] } 1 .. 100), "\n";
print "The rest are closed\n";
 

optimized

Works with: Perl version 5.x

print "Door $_ is open\n" for map $_**2, 1 .. 10;

print "Door $_ is ", qw"closed open"[int sqrt == sqrt], "\n" for 1..100;

while( ++$i <= 100 )
{
    $root = sqrt($i);
    if ( int( $root ) == $root )
    {
        print "Door $i is open\n";
    }
    else
    {
        print "Door $i is closed\n";
    }
}

Perl5i

 
use perl5i::2;
 
package doors {
 
  use perl5i::2;
  use Const::Fast;
 
  const my $OPEN   => 1;
  const my $CLOSED => 0;
 
  # ----------------------------------------
  # Constructor: door->new( @args );
  # input: N - how many doors?
  # returns: door object
  #
  method new($class: @args ) {
    my $self = bless {}, $class;
    $self->_init( @args );
    return $self;
  }
 
  # ----------------------------------------
  # class initializer.
  # input: how many doors?
  # sets N, creates N+1 doors ( door zero is not used ).
  #
  method _init( $N ) {
    $self->{N} = $N;
    $self->{doors} = [ ($CLOSED) x ($N+1) ];
  }
 
  # ----------------------------------------
  # $self->toggle( $door_number );
  # input: number of door to toggle.
  # OPEN a CLOSED door; CLOSE an OPEN  door.
  #
  method toggle( $which ) {
    $self->{doors}[$which] = ( $self->{doors}[$which] == $OPEN
                               ? $CLOSED
                               : $OPEN
        		     );
  }
 
  # ----------------------------------------
  # $self->toggle_n( $cycle );
  # input: number.
  # Toggle doors 0, $cycle, 2 * $cycle, 3 * $cycle, .. $self->{N}
  #
  method toggle_n( $n ) {
    $self->toggle($_)
      for map { $n * $_ }
          ( 1 .. int( $self->{N} / $n) );
 
  }
 
  # ----------------------------------------
  # $self->toggle_all();
  # Toggle every door, then every other door, every third door, ...
  #
  method toggle_all() {
    $self->toggle_n( $_ ) for ( 1 .. $self->{N} );
  }
 
 
  # ----------------------------------------
  # $self->print_open();
  # Print list of which doors are open.
  #
  method print_open() {
    say join ', ', grep { $self->{doors}[$_] == $OPEN } ( 1 ... $self->{N} );
  }
}
 
# ----------------------------------------------------------------------
# Main Thread
#
my $doors = doors->new(100);
$doors->toggle_all();
$doors->print_open();
 

Phix

unoptimised

sequence doors = repeat(false,100)
 
for i=1 to 100 do
    for j=i to 100 by i do
        doors[j] = not doors[j]
    end for
end for
 
for i=1 to 100 do
    if doors[i] == true then
        printf(1,"Door #%d is open.\n", i)
    end if
end for

Output:

Door #1 is open.
Door #4 is open.
Door #9 is open.
Door #16 is open.
Door #25 is open.
Door #36 is open.
Door #49 is open.
Door #64 is open.
Door #81 is open.
Door #100 is open.

optimised

function doors(integer n)
-- returns the perfect squares<=n
integer door = 1, step = 1
sequence res = {}
    while door<=n do
        res &= door
        step += 2
        door += step
    end while
    return res
end function
 
?doors(100)

Output:

{1,4,9,16,25,36,49,64,81,100}

Phixmonti

101 var l                           
0 l repeat                      
 
l for
    var s
    s l s 3 tolist
    for
        var i
        i get not i set
    endfor
endfor
 
l for
    var i
    i get
    if
        i print " " print
    endif
endfor

Another way

100 var n   /# Number of doors #/
0 n repeat  /# Make the doors #/
 
n for
    dup
    sqrt int
    dup * over == if 1 swap set else drop endif
endfor
 
n for
    "The door " print dup print " is " print
    get if "OPEN." else "closed." endif print nl
endfor

Optimized

100 sqrt for dup * print " " print endfor

PHL

unoptimized

module doors;
 
extern printf;
 
@Integer main [
	@Array<@Boolean> doors = new @Array<@Boolean>.init(100);
	var i = 1;
	while (i <= 100) {
		var j = i-1;
		while (j < 100) {
			doors.set(j, doors.get(j)::not);
			j = j + i;
		}
		i = i::inc;
	}
	i = 0;
	while (i < 100) {
		printf("%i %s\n", i+1, iif(doors.get(i), "open", "closed"));
		i = i::inc;
	}
	return 0;
]

optimized

Translation of: C#

module var;
 
extern printf;
 
@Integer main [
	var door = 1;
	var incrementer = 0;
	var current = 1;
        while (current <= 100)
        {
		printf("Door %i ", current);
		if (current == door)
		{
			printf("open\n");
			incrementer = incrementer::inc;
			door = door + 2 * incrementer + 1;
		}
		else
			printf("closed\n");
 
		current = current + 1;
 
        }
 
	return 0;
]

PHP

See: Demo optimized

<?php
for ($i = 1; $i <= 100; $i++) {
	$root = sqrt($i);
	$state = ($root == ceil($root)) ? 'open' : 'closed';
	echo "Door {$i}: {$state}\n";
}
?>

unoptimized

<?php
$doors = array_fill(1, 100, false);
for ($pass = 1; $pass <= 100; ++$pass) {
	for ($nr = 1; $nr <= 100; ++$nr) {
		if ($nr % $pass == 0) {
			$doors[$nr] = !$doors[$nr];
		}
	}
}
for ($nr = 1; $nr <= 100; ++$nr)
	printf("Door %d: %s\n", $nr, ($doors[$nr])?'open':'closed');
?>

Picat

Non-optimized:

doors(N) => 
   Doors = new_array(N),
   foreach(I in 1..N) Doors[I] := 0 end,
   foreach(I in 1..N)
     foreach(J in I..I..N)
        Doors[J] := 1^Doors[J]
     end,
     if N <= 10 then
        print_open(Doors)
     end
   end,
   println(Doors),
   print_open(Doors),
   nl.
 
print_open(Doors) => println([I : I in 1..Doors.length, Doors[I] == 1]).
 

optimized version 1:

doors_opt(N) =>
  foreach(I in 1..N)
     Root = sqrt(I),
     println([I, cond(Root == 1.0*round(Root), open, closed)])
  end,
  nl.
 

optimized version 2:

doors_opt2(N) => 
  println([I**2 : I in 1..N, I**2 <= N]).   
 

PicoLisp

unoptimized

(let Doors (need 100)
   (for I 100
      (for (D (nth Doors I)  D  (cdr (nth D I)))
         (set D (not (car D))) ) )
   (println Doors) )

optimized

(let Doors (need 100)
   (for I (sqrt 100)
      (set (nth Doors (* I I)) T) )
   (println Doors) )

Output in both cases:

(T NIL NIL T NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL
 NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL
 NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T
 NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL N
IL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T)

With formatting:

(let Doors (need 100)
   (for I (sqrt 100)
      (set (nth Doors (* I I)) T) )
   (make
      (for (N . D) Doors
         (when D (link N)) ) ) )

Output:

(1 4 9 16 25 36 49 64 81 100)

Piet

image

Pike

array onehundreddoors()
{
    array doors = allocate(100);
    foreach(doors; int i;)
        for(int j=i; j<100; j+=i+1)
            doors[j] = !doors[j];
    return doors;
}

optimized version:

array doors = map(enumerate(100,1,1), lambda(int x)
                                      {  
                                          return sqrt((float)x)%1 == 0.0; 
                                      });

write("%{%d %d %d %d %d %d %d %d %d %d\n%}\n", doors/10)

output:

1 0 0 1 0 0 0 0 1 0
0 0 0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1

PL/I

 
declare door(100) bit (1) aligned;
declare closed bit (1) static initial ('0'b),
        open   bit (1) static initial ('1'b);
declare (i, inc) fixed binary;
 
door = closed;
inc = 1;
do until (inc >= 100);
   do i = inc to 100 by inc;
      door(i) = ^door(i); /* close door if open; open it if closed. */
   end;
   inc = inc+1;
end;
 
do i = 1 to 100;
   put skip edit ('Door ', trim(i), ' is ') (a);
   if door(i) then put edit (' open.') (a);
   else put edit (' closed.') (a);
end;
 

See also #Polyglot:PL/I and PL/M

PL/I-80

 
/* Solution to the 100 doors problem in PLI-80 */
 
hundred_doors:
  procedure options (main);
 
    %replace
      open_door by '1'b,
      closed_door by '0'b,
      numdoors by 100;
 
    dcl
      doors(1:numdoors) bit(1),
      (i, j) fixed bin(15);
 
    /* all doors are initially closed */
    do i = 1 to numdoors;
      doors(i) = closed_door;
    end;
 
    /* cycle through at increasing intervals and flip doors */
    do i = 1 to numdoors;
      j = i;
      do while (j <= numdoors);
        doors(j) = ^doors(j);
        j = j + i;
      end;
    end;
 
    /* show results - open doors should all be perfect squares */
    put skip list ('The open doors are:');
    do i = 1 to numdoors;
      if doors(i) = open_door then
        put edit (i) (F(4));
    end;
 
end hundred_doors; 

Output:

The open doors are:   1   4   9  16  25  36  49  64  81 100

See also #Polyglot:PL/I and PL/M

PL/M

Translation of: ALGOL W

100H: /* FIND THE FIRST FEW SQUARES VIA THE UNOPTIMISED DOOR FLIPPING METHOD */
 
    /* BDOS SYSTEM CALL */
    BDOS: PROCEDURE( FN, ARG );
        DECLARE FN BYTE, ARG ADDRESS;
        GO TO 5;
    END BDOS;
 
    /* PRINTS A BYTE AS A CHARACTER */
    PRINT$CHAR: PROCEDURE( CH );
        DECLARE CH BYTE;
        CALL BDOS( 2, CH );
    END PRINT$CHAR;
 
    /* PRINTS A BYTE AS A NUMBER */
    PRINT$BYTE: PROCEDURE( N );
        DECLARE N BYTE;
        DECLARE ( V, D3, D2 ) BYTE;
        V  = N;
        D3 = V MOD 10;
        IF ( V := V / 10 ) <> 0 THEN DO;
            D2 = V MOD 10;
            IF ( V := V / 10 ) <> 0 THEN CALL PRINT$CHAR( '0' + V );
            CALL PRINT$CHAR( '0' + D2 );
        END;
        CALL PRINT$CHAR( '0' + D3 );
    END PRINT$BYTE;
 
    DECLARE DOOR$DCL LITERALLY '101';
    DECLARE FALSE    LITERALLY '0';
    DECLARE CR       LITERALLY '0DH';
    DECLARE LF       LITERALLY '0AH';
 
    /* ARRAY OF DOORS - DOOR( I ) IS TRUE IF OPEN, FALSE IF CLOSED */
    DECLARE DOOR( DOOR$DCL ) BYTE;
    DECLARE ( I, J )         BYTE;
 
    /* SET ALL DOORS TO CLOSED */
    DO I = 0 TO LAST( DOOR ); DOOR( I ) = FALSE; END;
    /* REPEATEDLY FLIP THE DOORS */
    DO I = 1 TO LAST( DOOR );
       DO J = I TO LAST( DOOR ) BY I;
          DOOR( J ) = NOT DOOR( J );
       END;
    END;
    /* DISPLAY THE RESULTS */
    DO I = 1 TO LAST( DOOR );
       IF DOOR( I ) THEN DO;
          CALL PRINT$CHAR( ' ' );
          CALL PRINT$BYTE( I );
       END;
    END;
    CALL PRINT$CHAR( CR );
    CALL PRINT$CHAR( LF );
EOF
 

Output:

 1 4 9 16 25 36 49 64 81 100

See Also #Polyglot:PL/I and PL/M

PL/SQL

Unoptimized

 
DECLARE
  TYPE doorsarray IS VARRAY(100) OF BOOLEAN;
  doors doorsarray := doorsarray();
BEGIN
 
doors.EXTEND(100);  --ACCOMMODATE 100 DOORS
 
FOR i IN 1 .. doors.COUNT  --MAKE ALL 100 DOORS FALSE TO INITIALISE
  LOOP
     doors(i) := FALSE;                    
  END LOOP;
 
FOR j IN 1 .. 100 --ITERATE THRU USING MOD LOGIC AND FLIP THE DOOR RIGHT OPEN OR CLOSE
 LOOP
      FOR k IN 1 .. 100
        LOOP
                  IF MOD(k,j)=0 THEN 
                     doors(k) := NOT doors(k); 
                  END IF;
        END LOOP;
 END LOOP;
 
FOR l IN 1 .. doors.COUNT  --PRINT THE STATUS IF ALL 100 DOORS AFTER ALL ITERATION
  LOOP
       DBMS_OUTPUT.PUT_LINE('DOOR '||l||' IS -->> '||CASE WHEN SYS.DBMS_SQLTCB_INTERNAL.I_CONVERT_FROM_BOOLEAN(doors(l)) = 'TRUE' 
                                                                THEN 'OPEN' 
                                                              ELSE 'CLOSED' 
                                                        END);
  END LOOP;
 
END;
 

Pointless

output =
  range(1, 100)
  |> map(visit(100))
  |> println
 
----------------------------------------------------------
 
toggle(state) =
  if state == Closed then Open else Closed
 
----------------------------------------------------------
-- Door state on iteration i is recursively
-- defined in terms of previous door state
 
visit(i, index) = cond {
  case (i == 0) Closed
  case (index % i == 0) toggle(lastState)
  else lastState
} where lastState = visit(i - 1, index)

Output:

[Open, Closed, Closed, Open, Closed, Closed, Closed, Closed, Open, Closed, Closed, Closed, Closed, Closed, Closed, Open, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Open, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Open, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Open, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Open, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Open, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Open]

Polyglot:PL/I and PL/M

Works with: 8080 PL/M Compiler

... under CP/M (or an emulator)

Should work with many PL/I implementations.
The PL/I include file "pg.inc" can be found on the Polyglot:PL/I and PL/M page. Note the use of text in column 81 onwards to hide the PL/I specifics from the PL/M compiler.

/* FIND THE FIRST FEW SQUARES VIA THE UNOPTIMISED DOOR FLIPPING METHOD */
doors_100H: procedure options                                                   (main);
 
/* PROGRAM-SPECIFIC %REPLACE STATEMENTS MUST APPEAR BEFORE THE %INCLUDE AS */
/* E.G. THE CP/M PL/I COMPILER DOESN'T LIKE THEM TO FOLLOW PROCEDURES      */
   /* PL/I                                                                      */
      %replace dcldoors by         100;
   /* PL/M */                                                                   /*
      DECLARE  DCLDOORS LITERALLY '101';
   /* */
 
/* PL/I DEFINITIONS                                                             */
%include 'pg.inc';
/* PL/M DEFINITIONS: CP/M BDOS SYSTEM CALL AND CONSOLE I/O ROUTINES, ETC. */    /*
   DECLARE BINARY LITERALLY 'ADDRESS', CHARACTER LITERALLY 'BYTE';
   DECLARE FIXED  LITERALLY ' ',       BIT       LITERALLY 'BYTE';
   DECLARE STATIC LITERALLY ' ',       RETURNS   LITERALLY ' ';
   DECLARE FALSE  LITERALLY '0',       TRUE LITERALLY '1';
   DECLARE HBOUND LITERALLY 'LAST',    SADDR  LITERALLY '.';
   BDOSF: PROCEDURE( FN, ARG )BYTE;
                               DECLARE FN BYTE, ARG ADDRESS; GOTO 5;   END; 
   BDOS: PROCEDURE( FN, ARG ); DECLARE FN BYTE, ARG ADDRESS; GOTO 5;   END;
   PRCHAR:   PROCEDURE( C );   DECLARE C BYTE;      CALL BDOS( 2, C ); END;
   PRSTRING: PROCEDURE( S );   DECLARE S ADDRESS;   CALL BDOS( 9, S ); END;
   PRNL:     PROCEDURE;        CALL PRCHAR( 0DH ); CALL PRCHAR( 0AH ); END;
   PRNUMBER: PROCEDURE( N );
      DECLARE N ADDRESS;
      DECLARE V ADDRESS, N$STR( 6 ) BYTE, W BYTE;
      N$STR( W := LAST( N$STR ) ) = '$';
      N$STR( W := W - 1 ) = '0' + ( ( V := N ) MOD 10 );
      DO WHILE( ( V := V / 10 ) > 0 );
         N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
      END; 
      CALL BDOS( 9, .N$STR( W ) );
   END PRNUMBER;
   MODF:     PROCEDURE( A, B )ADDRESS;
      DECLARE ( A, B ) ADDRESS;
      RETURN A MOD B;
   END MODF;
/* END LANGUAGE DEFINITIONS */
 
   /* TASK */
 
   /* ARRAY OF DOORS - DOOR( I ) IS TRUE IF OPEN, FALSE IF CLOSED */
   DECLARE DOOR( DCLDOORS )  BIT;
   DECLARE ( I, J, MAXDOOR ) FIXED BINARY;
 
   MAXDOOR = HBOUND( DOOR                                                       ,1
                   );
 
   /* SET ALL DOORS TO CLOSED */
   DO I = 0 TO MAXDOOR; DOOR( I ) = FALSE; END;
   /* REPEATEDLY FLIP THE DOORS */
   DO I = 1 TO MAXDOOR;
      DO J = I TO MAXDOOR BY I;
         DOOR( J ) = NOT( DOOR( J ) );
      END;
   END;
   /* DISPLAY THE RESULTS */
   DO I = 1 TO MAXDOOR;
      IF DOOR( I ) THEN DO;
         CALL PRCHAR( ' ' );
         CALL PRNUMBER( I );
      END;
   END;
   CALL PRNL;
 
EOF: end doors_100H;

Output:

 1 4 9 16 25 36 49 64 81 100

Pony

Combined Optimized and Unoptimized

Probably also rather pointless in its use of actors, but, after all, they're cheap.

 
actor Toggler
    let doors:Array[Bool]
    let env: Env
    new create(count:USize,_env:Env) =>
        var i:USize=0
        doors=Array[Bool](count)
        env=_env
        while doors.size() < count do
            doors.push(false)
        end
    be togglin(interval : USize)=>
        var i:USize=0
        try
            while i < doors.size() do
                doors.update(i,not doors(i)?)?
                i=i+interval
            end
        else
            env.out.print("Errored while togglin'!")
        end
    be printn(onlyOpen:Bool)=>
        try
            for i in doors.keys() do
                if onlyOpen and not doors(i)? then
                    continue
                end
                env.out.print("Door " + i.string() + " is " +
                    if doors(i)? then
                        "Open"
                    else
                        "closed"
                    end)
            end
        else
            env.out.print("Error!")
        end
        true
 
actor OptimizedToggler
    let doors:Array[Bool]
    let env:Env
    new create(count:USize,_env:Env)=>
        env=_env
        doors=Array[Bool](count)
        while doors.size()<count do
            doors.push(false)
        end
    be togglin()=>
        var i:USize=0
        if alreadydone then
            return
        end
        try
            doors.update(0,true)?
            doors.update(1,true)?
            while i < doors.size() do
                i=i+1
                let z=i*i
                let x=z*z
                if z > doors.size() then
                    break
                else
                    doors.update(z,true)?
                end
                if x < doors.size() then
                    doors.update(x,true)?
                end
            end
        end
    be printn(onlyOpen:Bool)=>
        try
            for i in doors.keys() do
                if onlyOpen and not doors(i)? then
                    continue
                end
                env.out.print("Door " + i.string() + " is " +
                    if doors(i)? then
                        "Open"
                    else
                        "closed"
                    end)
            end
        else
            env.out.print("Error!")
        end
        true
actor Main
    new create(env:Env)=>
        var count: USize =100
        try
            let index=env.args.find("-n",0,0,{(l,r)=>l==r})?
            try
            match env.args(index+1)?.read_int[USize]()?
                | (let x:USize, _)=>count=x
                end
            else
                env.out.print("You either neglected to provide an argument after -n or that argument was not an integer greater than zero.")
                return
            end
        end
        if env.args.contains("optimized",{(l,r)=>r==l}) then
            let toggler=OptimizedToggler(count,env)
            var i:USize = 1
            toggler.togglin()
            toggler.printn(env.args.contains("onlyopen", {(l,r)=>l==r}))
        else
            let toggler=Toggler(count,env)
            var i:USize = 1
            while i < count do
                toggler.togglin(i)
                i=i+1
            end
            toggler.printn(env.args.contains("onlyopen", {(l,r)=>l==r}))
        end
 

Pop11

unoptimized

lvars i;
lvars doors = {% for i from 1 to 100 do false endfor %};
for i from 1 to 100 do
   for j from i by i to 100 do
      not(doors(j)) -> doors(j);
   endfor;
endfor;
;;; Print state
for i from 1 to 100 do
   printf('Door ' >< i >< ' is ' ><
            if doors(i) then 'open' else 'closed' endif, '%s\n');
endfor;

optimized

for i to 100 do
    lvars root = sqrt(i);
    i; if root = round(root) then ' open' ><; else ' closed' ><; endif; =>
endfor;

PostScript

Bruteforce:

/doors [ 100 { false } repeat ] def
 
1 1 100 { dup 1 sub exch 99 {
        dup doors exch get not doors 3 1 roll put
} for } for
doors pstack

Shows:

[true false false true false false false false true false ...<90 doors later>... true]

Potion

square=1, i=3
1 to 100(door):
  if (door == square):
    ("door", door, "is open") say
    square += i
    i += 2.
.

PowerShell

unoptimized

$doors = @(0..99)
for($i=0; $i -lt 100; $i++) {
  $doors[$i] = 0  # start with all doors closed
}
for($i=0; $i -lt 100; $i++) {
  $step = $i + 1
  for($j=$i; $j -lt 100; $j = $j + $step) {
    $doors[$j] = $doors[$j] -bxor 1
  }
}
foreach($doornum in 1..100) {
  if($doors[($doornum-1)] -eq $true) {"$doornum open"}
  else {"$doornum closed"}
}

Alternative Method

function Get-DoorState($NumberOfDoors)
{
   begin 
   {
      $Doors = @()
      $Multiple = 1
   }
 
   process
   {
      for ($i = 1; $i -le $NumberOfDoors; $i++)
      {
         $Door = [pscustomobject]@{
                    Name = $i
                    Open = $false
                 }
 
         $Doors += $Door   
      }
 
      While ($Multiple -le $NumberOfDoors)
      {
	 Foreach ($Door in $Doors)
	 {
	    if ($Door.name % $Multiple -eq 0)
               {
	          If ($Door.open -eq $False){$Door.open = $True}
	          Else {$Door.open = $False}
	       }
	 }
 
         $Multiple++
      }
    }
 
    end {$Doors}
}

unoptimized Pipeline

$doors = 1..100 | ForEach-Object {0}
1..100 | ForEach-Object { $a=$_;1..100 | Where-Object { -not ( $_ % $a )  } | ForEach-Object { $doors[$_-1] = $doors[$_-1] -bxor 1 }; if ( $doors[$a-1] ) { "door opened" } else { "door closed" } }
 

unoptimized Pipeline 2

$doors = 1..100 | ForEach-Object {0}
$visited = 1..100
1..100 | ForEach-Object { $a=$_;$visited[0..([math]::floor(100/$a)-1)] | Where-Object { -not ( $_ % $a )  } | ForEach-Object { $doors[$_-1] = $doors[$_-1] -bxor 1;$visited[$_/$a-1]+=($_/$a) }; if ( $doors[$a-1] ) { "door opened" } else { "door closed" } }
 

unoptimized Pipeline 3 (dynamically build pipeline)

1..100|foreach-object {$pipe += "toggle $_ |"} -begin {$pipe=""}
filter toggle($pass) {$_.door = $_.door -xor !($_.index % $pass);$_}
invoke-expression "1..100| foreach-object {@{index=`$_;door=`$false}} | $pipe  out-host"
 

Using Powershell Workflow for Parallelism

 
 
Workflow Calc-Doors {
    Foreach –parallel ($number in 1..100) {
        "Door " + $number.ToString("0000") + ": " + @{$true="Closed";$false="Open"}[([Math]::pow($number, 0.5)%1) -ne 0]
    }
}
Calc-Doors | sort
 
 

optimized

 
1..10|%{"Door "+ $_*$_ + " is open"}
 

Processing

Unoptimized:

boolean[] doors = new boolean[100];
 
void setup() {
  for (int i = 0; i < 100; i++) {
    doors[i] = false;
  }
  for (int i = 1; i < 100; i++) {
    for (int j = 0; j < 100; j += i) {
      doors[j] = !doors[j];
    }
  }
  println("Open:");
  for (int i = 1; i < 100; i++) {
    if (doors[i]) {
      println(i);
    }
  }
  exit();
}

Output:

Open:
1
4
9
16
25
36
49
64
81

Processing.R

Unoptimized:

setup <- function() {
  for(door in doors(100, 100)) {
    stdout$print(paste(door, ""))
  }
}
 
doors <- function(ndoors=100,passes=100) {
  doors <- rep(FALSE,ndoors)
  for (ii in seq(1,passes)) {
      mask <- seq(0,ndoors,ii)
      doors[mask] <- !doors[mask]  
  }
  return (which(doors == TRUE))
}

Output:

1 4 9 16 25 36 49 64 81 100

ProDOS

Uses math module.

enableextensions 
enabledelayedexpansion
editvar /newvar /value=0 /title=closed
editvar /newvar /value=1 /title=open
editvar /newvar /range=1-100 /increment=1 /from=2
editvar /newvar /value=2 /title=next
:doors
for /alloccurrences (!next!-!102!) do editvar /modify /value=-open-
editvar /modify /value=-next-=+1
if -next- /hasvalue=100 goto :cont else goto :doors
:cont
printline !1!-!102!
stoptask

Prolog

unoptimized

Declarative:

main :-
    forall(between(1,100,Door), ignore(display(Door))).
 
% show output if door is open after the 100th pass
display(Door) :-
    status(Door, 100, open),
    format("Door ~d is open~n", [Door]).
 
% true if Door has Status after Pass is done
status(Door, Pass, Status) :-
    Pass > 0,
    Remainder is Door mod Pass,
    toggle(Remainder, OldStatus, Status),
    OldPass is Pass - 1,
    status(Door, OldPass, OldStatus).
status(_Door, 0, closed).
 
toggle(Remainder, Status, Status) :-
    Remainder > 0.
toggle(0, open, closed).
toggle(0, closed, open).
 

Doors as a list:

doors_unoptimized(N) :-
	length(L, N),
	maplist(init, L),
	doors(N, N, L, L1),
	affiche(N, L1).
 
init(close).
 
doors(Max, 1, L, L1) :-
	!,
       inverse(1, 1, Max, L, L1).
 
doors(Max, N, L, L1) :-
	N1 is N - 1,
	doors(Max, N1, L, L2),
	inverse(N, 1, Max, L2, L1).
 
 
inverse(N, Max, Max, [V], [V1]) :-
	!,
	0 =:= Max mod N -> inverse(V, V1); V1 = V.
 
inverse(N, M, Max, [V|T], [V1|T1]) :-
	M1 is M+1,
	inverse(N, M1, Max, T, T1),
	(   0 =:= M mod N -> inverse(V, V1); V1 = V).
 
 
inverse(open, close).
inverse(close, open).
 
affiche(N, L) :-
	forall(between(1, N, I),
	       (   nth1(I, L, open) -> format('Door ~w is open.~n', [I]); true)).
 

Using dynamic-rules. Tried to be ISO:

doors(Num, Passes) :-
    forall(( everyNth(1,Passes,1,Pass)
           , forall((everyNth(Pass,Num,Pass,Door), toggle(Door)))
           ))
  , show(Num)
  .
 
 
toggle(Door) :-
    Opened = opened(Door)
  , ( clause(Opened,_) -> retract(Opened)
                        ; asserta(Opened)
    ).
 
 
show(Num) :-
    forall(( between(1,Num,Door)
           , (opened(Door) -> State = opened ; State = closed)
           , write(Door), write(' '), write(State), nl
           )).
 
 
% utils
forall(X) :- findall(_, X, _).
 
everyNth(From,To,Step,X) :-
    From =< To
  , ( X = From ; From1 is From + Step, everyNth(From1,To,Step,X) )
  .
 
main :- doors(100,100), halt.

optimized

doors_optimized(N) :-
	Max is floor(sqrt(N)),
	forall(between(1, Max, I),
	       (   J is I*I,format('Door ~w is open.~n',[J]))).
 
 

Pure

using system;
 
// initialize doors as pairs: number, status where 0 means open
let doors = zip (1..100) (repeat 1);
 
toogle (x,y) = x,~y;
 
toogleEvery n d = map (tooglep n) d with
                    tooglep n [email protected]((x,_)) = toogle d if ~(x mod n);
                                        = d otherwise; end;
 
// show description of given doors
status (n,x) = (str n) + (case x of
                            1 = " close";
                            0 = " open"; end);
 
let result = foldl (\a n -> toogleEvery n a) doors (1..100);
 
// pretty print the result (only open doors)
showResult = do (puts.status) final when
               final = filter open result with
                         open (_,x) = ~x;
                       end; end;
 

Output:

 
> showResult;
1 open
4 open
9 open
16 open
25 open
...

Pure Data

100Doors.pd
 
#N canvas 241 375 414 447 10;
#X obj 63 256 expr doors[$f1] = doors[$f1] ^ 1;
#X msg 83 118 \; doors const 0;
#X msg 44 66 bang;
#X obj 44 92 t b b b;
#X obj 43 28 table doors 101;
#X obj 44 360 sel 0;
#X obj 44 336 expr if (doors[$f1] == 1 \, $f1 \, 0);
#X obj 63 204 t b f f;
#X text 81 66 run;
#X obj 71 384 print -n;
#X text 132 310 print results (open doors);
#X obj 63 179 loop 1 100 1;
#X obj 63 231 loop 1 100 1;
#X obj 44 310 loop 1 100 1;
#X text 148 28 create array;
#X text 151 180 100 passes;
#X text 179 123 set values to 0;
#X connect 2 0 3 0;
#X connect 3 0 13 0;
#X connect 3 1 11 0;
#X connect 3 2 1 0;
#X connect 5 1 9 0;
#X connect 6 0 5 0;
#X connect 7 0 12 0;
#X connect 7 1 12 1;
#X connect 7 2 12 3;
#X connect 11 0 7 0;
#X connect 12 0 0 0;
#X connect 13 0 6 0;
 
loop.pd
 
#N canvas 656 375 427 447 10;
#X obj 62 179 until;
#X obj 102 200 f;
#X obj 62 89 inlet;
#X obj 303 158 f \$3;
#X obj 270 339 outlet;
#X obj 223 89 inlet;
#X obj 138 89 inlet;
#X obj 324 89 inlet;
#X obj 117 158 f \$1;
#X text 323 68 step;
#X obj 202 158 f \$2;
#X obj 62 118 t b b b b;
#X obj 270 315 spigot;
#X obj 89 314 sel 0;
#X obj 137 206 +;
#X obj 102 237 expr $f1 \; if ($f3 > 0 \, if ($f1 > $f2 \, 0 \, 1)
\, if ($f3 < 0 \, if ($f1 < $f2 \, 0 \, 1) \, 0)), f 34;
#X text 63 68 run;
#X text 136 68 start;
#X text 227 68 end;
#X text 58 31 loop (abstraction);
#X connect 0 0 1 0;
#X connect 1 0 14 0;
#X connect 1 0 15 0;
#X connect 2 0 11 0;
#X connect 3 0 14 1;
#X connect 3 0 15 2;
#X connect 5 0 10 1;
#X connect 6 0 8 1;
#X connect 7 0 3 1;
#X connect 8 0 1 1;
#X connect 10 0 15 1;
#X connect 11 0 0 0;
#X connect 11 1 8 0;
#X connect 11 2 10 0;
#X connect 11 3 3 0;
#X connect 12 0 4 0;
#X connect 13 0 0 1;
#X connect 14 0 1 1;
#X connect 15 0 12 0;
#X connect 15 1 12 1;
#X connect 15 1 13 0;
 

PureBasic

unoptimized

Dim doors.i(100)
 
For x = 1 To 100
  y = x
  While y <= 100
    doors(y) = 1 - doors(y)
    y + x
  Wend
Next
 
OpenConsole()
PrintN("Following Doors are open:")
For x = 1 To 100
  If doors(x)
    Print(Str(x) + ", ")
  EndIf
Next
Input()

optimized

OpenConsole()
PrintN("Following Doors are open:")
For i = 1 To 100
    root.f = Sqr(i)
    If root = Int(root)
    	Print (Str(i) + ", ")
    EndIf
Next     
Input()

Output:

Following Doors are open:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100,

Pyret

 
data Door:
  | open
  | closed
end
 
fun flip-door(d :: Door) -> Door:
  cases(Door) d:
    | open => closed
    | closed => open
  end
end
 
 
fun flip-doors(doors :: List<Door>) -> List<Door>:
  doc:```Given a list of door positions, repeatedly switch the positions of
      every nth door for every nth pass, and return the final list of door
      positions```
  for fold(flipped-doors from doors, n from range(1, doors.length() + 1)):
    for map_n(m from 1, d from flipped-doors):
      if num-modulo(m, n) == 0:
        flip-door(d)
      else:
        d
      end
    end
  end
where:
    flip-doors([list: closed, closed, closed]) is
  [list: open, closed, closed]
 
  flip-doors([list: closed, closed, closed, closed]) is
  [list: open, closed, closed, open]
 
  flip-doors([list: closed, closed, closed, closed, closed, closed]) is
  [list: open, closed, closed, open, closed, closed]
 
  closed-100 = for map(_ from range(1, 101)): closed end
  answer-100 = for map(n from range(1, 101)):
    if num-is-integer(num-sqrt(n)): open
    else: closed
    end
  end
 
  flip-doors(closed-100) is answer-100
end
 
fun find-indices<A>(pred :: (A -> Boolean), xs :: List<A>) -> List<Number>:
    doc:```Given a list and a predicate function, produce a list of index
      positions where there's a match on the predicate```
  ps = map_n(lam(n,e): if pred(e): n else: -1 end end, 1, xs)
  ps.filter(lam(x): x >= 0 end)
where:
  find-indices((lam(i): i == true end), [list: true,false,true]) is [list:1,3]
end
 
 
fun run(n):
  doc:```Given a list of doors that are closed, make repeated passes 
      over the list, switching the positions of every nth door for 
      each nth pass. Return a list of positions in the list where the
      door is Open.```
  doors = repeat(n, closed)
  ys = flip-doors(doors)
  find-indices((lam(y): y == open end), ys)
where:
  run(4) is [list: 1,4]
end
 
run(100)
 
 

Python

Works with: Python version 2.5+

unoptimized

 
doors = [False] * 100
for i in range(100):
   for j in range(i, 100, i+1):
       doors[j] = not doors[j]
   print("Door %d:" % (i+1), 'open' if doors[i] else 'close')
 

optimized

A version that only visits each door once:

for i in xrange(1, 101):
    root = i ** 0.5
    print "Door %d:" % i, 'open' if root == int(root) else 'close'

One liner using a list comprehension, item lookup, and is_integer

print '\n'.join(['Door %s is %s' % (i, ('closed', 'open')[(i**0.5).is_integer()]) for i in xrange(1, 101)])

One liner using a generator expression, ternary operator, and modulo

print '\n'.join('Door %s is %s' % (i, 'closed' if i**0.5 % 1 else 'open') for i in range(1, 101))

Works with: Python version 3.x

 
for i in range(1, 101):
    if i**0.5 % 1:
        state='closed'
    else:
        state='open'
    print("Door {}:{}".format(i, state))
 

ultra-optimized: ported from Julia version

for i in range(1,101): print("Door %s is open" % i**2)

Q

unoptimized

`closed`open(100#0b){@[x;where y;not]}/100#'(til[100]#'0b),'1b

Binary function {@[x;where y;not]} is applied using Over. The initial state is 100#0b and the right argument is a list of 100 boolean masks. The boolean vector result is used to index the pair of states.

Following expressions simply flag perfect squares.

optimized

`closed`open (1+til 100) in {x*x} 1+til 10

alternative

@[100#`closed; -1+{x*x}1+til 10; :; `open]

QB64

 
Const Opened = -1, Closed = 0
Dim Doors(1 To 100) As Integer, Passes As Integer, Index As Integer
Rem Normal implementation
Print "100doors Normal method"
For Passes = 1 To 100 Step 1
    Doors(Passes) = Closed
Next Passes
For Passes = 1 To 100 Step 1
    For Index = 0 To 100 Step Passes
        If Index > 100 Then Exit For
        If Index > 0 Then If Doors(Index) = Opened Then Doors(Index) = Closed Else Doors(Index) = Opened
    Next Index
Next Passes
Print "OPEN DOORS after 100th passes"
For Passes = 1 To 100 Step 1
    If Doors(Passes) = Opened Then Print Passes; " ";
Next
 
Rem Alternative solution of perfect squares
 
Print "Alternative method"
Passes = 0
For Passes = 1 To 100 Step 1
    Doors(Passes) = Closed
Next Passes
For Passes = 1 To 100 Step 1
    If Sqr(Passes) = Int(Sqr(Passes)) Then Doors(Passes) = Opened
Next
Print "Opened doors found by SQR method"
For Passes = 1 To 100 Step 1
    If Doors(Passes) = Opened Then Print Passes; " ";
Next Passes
End
 

Quackery

unoptimized

/O>  [ bit ^ ]                       is toggle      ( f n --> f )
...   
...  [ 0
...    100 times
...      [ i^ 1+ swap
...        101 times
...          [ i^ toggle over step ]
...      nip ] ]                     is toggledoors (     --> f )
...   
...   [ 100 times
...        [ 1 >> dup 1 &
...          if [ i^ 1+ echo sp ] ]
...     drop ]                       is echodoors   (   f -->   )
...   
...  toggledoors
...  say " These doors are open: " echodoors cr
...  say " The rest are closed." cr
... 
 These doors are open: 1 4 9 16 25 36 49 64 81 100 
 The rest are closed.
 
Stack empty.
 

R

Using a loop

doors_puzzle <- function(ndoors, passes = ndoors) {
    doors <- logical(ndoors)
    for (ii in seq(passes)) {
        mask <- seq(ii, ndoors, ii)
        doors[mask] <- !doors[mask]	
    }
    which(doors)
}
 
doors_puzzle(100)

optimized

x <- rep(1, 100)
for (i in 1:100-1) {
    x <- xor(x, rep(c(rep(0,i),1), length.out=100))
}
which(!x)

Using a **ply function

doors_puzzle <- function(ndoors=100,passes=100) {
names(which(table(unlist(sapply(1:passes, function(X) seq(0, ndoors, by=X)))) %% 2 == 1))
}
 
doors_puzzle()

Using Reduce

H=100
f=rep(F,H)
which(Reduce(function(d,n) xor(replace(f,seq(n,H,n),T),d), 1:H, f))

Output:

1   4   9  16  25  36  49  64  81 100

Racket

 
#lang racket
 
;; Applies fun to every step-th element of seq, leaving the others unchanged.
(define (map-step fun step seq)
  (for/list ([elt seq] [i (in-naturals)])
    ((if (zero? (modulo i step)) fun values) elt)))
 
(define (toggle-nth n seq)
  (map-step not n seq))
 
(define (solve seq)
  (for/fold ([result seq]) ([_ seq] [pass (in-naturals 1)])
    (toggle-nth pass result)))
 
(for ([door (solve (make-vector 101 #f))] [index (in-naturals)]
      #:when (and door (> index 0)))
  (printf "~a is open~%" index))
 

Optimized:

 
#lang racket
(for ([x (in-range 1 101)] #:when (exact-integer? (sqrt x)))
  (printf "~a is open\n" x))
 

Unoptimized imperative, with graphic rendering:

 
#lang slideshow
(define-syntax-rule (vector-neg! vec pos)
  (vector-set! vec pos (not (vector-ref vec pos))))
 
(define (make-doors)
  (define doors (make-vector 100 #f))
  (for* ([i 100] [j (in-range i 100 (add1 i))]) (vector-neg! doors j))
  doors)
 
(displayln (list->string (for/list ([d (make-doors)]) (if d #\o #\-))))
 
(define closed-door (inset (filled-rectangle 4 20) 2))
(define open-door (inset (rectangle 4 20) 2))
 
(for/fold ([doors (rectangle 0 0)]) ([open? (make-doors)])
  (hc-append doors (if open? open-door closed-door)))
 

Output:

Raku

(formerly Perl 6)

unoptimized

Works with: Rakudo version 2015.09"

my @doors = False xx 101;
 
(.=not for @doors[0, $_ ... 100]) for 1..100;
 
say "Door $_ is ", <closed open>[ @doors[$_] ] for 1..100;

optimized

say "Door $_ is open" for map {$^n ** 2}, 1..10;

probably the most compact idiom

say 'Door $_ is open' for (1..10)»²;

Here's a version using the cross meta-operator instead of a map:

 say "Door $_ is open" for 1..10 X** 2;

This one prints both opened and closed doors:

say "Door $_ is ", <closed open>[.sqrt == .sqrt.floor] for 1..100;

verbose version, but uses ordinary components

Works with: Rakudo version 2016.07 Tom Legrady

 
sub  output( @arr, $max ) {
    my $output = 1;
    for 1..^$max -> $index {
	if @arr[$index] {
	    printf "%4d", $index;
	    say '' if $output++ %%  10;
	}
    }
    say '';
}
 
sub MAIN ( Int :$doors = 100 ) {
    my $doorcount = $doors + 1;
    my @door[$doorcount] = 0 xx ($doorcount);
 
    INDEX:
    for 1...^$doorcount -> $index {
        # flip door $index & its multiples, up to last door.
        #
	for ($index, * + $index ... *)[^$doors] -> $multiple {
	    next INDEX if $multiple > $doors;
	    @door[$multiple] =  @door[$multiple] ?? 0 !! 1;
	}
    }
    output @door, $doors+1;
}
 

Output:

$ ./100_doors.pl6 -doors=100
   1   4   9  16  25  36  49  64  81

RapidQ

 
dim x as integer, y as integer
dim door(1 to 100) as byte
 
'initialize array
for x = 1 to 100 : door(x) = 0 : next
 
'set door values
for y = 1 to 100
    for x = y to 100 step y
        door(x) = not door(x)
    next x
next y
 
'print result
for x = 1 to 100
    if door(x) then print "Door " + str$(x) + " = open"
next 
 
while inkey$="":wend
end
 

Output

Door 1 = open
Door 4 = open
Door 9 = open
Door 16 = open
Door 25 = open
Door 36 = open
Door 49 = open
Door 64 = open
Door 81 = open
Door 100 = open

REBOL

Unoptimized

doors: array/initial 100 'closed
repeat i 100 [
    door: at doors i
    forskip door i [change door either 'open = first door ['closed] ['open]]
]

Optimized

doors: array/initial 100 'closed
repeat i 10 [doors/(i * i): 'open]
 

Red

Unoptimized

Red [
  Purpose: "100 Doors Problem (Perfect Squares)"
  Author: "Barry Arthur"
  Date: "07-Oct-2016"
]
doors: make vector! [char! 8 100]
repeat i 100 [change at doors i #"."]
 
repeat i 100 [
    j: i
    while [j <= 100] [
      door: