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# Permuted multiples

Permuted multiples is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
Attribution

The following task is taken from Project Euler.

Task

Find the smallest positive integer n such that, when expressed in decimal, 2*n, 3*n, 4*n, 5*n, and 6*n contain exactly the same digits but in a different order.

## AppleScript

Translation of: Phix
— except that the 'steps' figure here is cumulative. Also, for six different numbers to have the same digits, each must have at least three digits, none of which can be 0. So the lowest possible value of n in this respect is 123. But for a number beginning with 1 to stand any chance of containing the same digits as both a number that's 2 times it and another that's 6 times it, it must also contain at least one digit that's no less than 2 and another that's no less than 6. The lowest combination of these is 26, which also produces a multiple of 3 when added to a power of 10. So this makes a slightly better post-power start point than 2, saving eight steps per power.  ;)

Shifting the 26 up against the 1 obviously keeps the "at least" condition satisfied for longer during the subsequent additions of 3 at the low end and gives a start point much closer to the next power. This more than halves the number of steps performed and thus the time taken. It also produces the correct result(s), but I can't see that it's logically bound to do so.  :\

`use AppleScript version "2.3.1" -- Mac OS X 10.9 (Mavericks) or later.use sorter : script "Insertion Sort" -- <https://www.rosettacode.org/wiki/Sorting_algorithms/Insertion_sort#AppleScript> on decDigits(n)    set digits to {n mod 10 as integer}    set n to n div 10    repeat until (n = 0)        set beginning of digits to n mod 10 as integer        set n to n div 10    end repeat    return digitsend decDigits on join(lst, delim)    set astid to AppleScript's text item delimiters    set AppleScript's text item delimiters to delim    set txt to lst as text    set AppleScript's text item delimiters to astid    return txtend join on task()    set {output, n, n10, steps} to {{}, 126, 1000, 0}    repeat        if (n * 6 < n10) then            set steps to steps + 1            set nl to decDigits(n)            tell sorter to sort(nl, 1, -1)            set found to true            repeat with i from 2 to 6                set inl to decDigits(n * i)                tell sorter to sort(inl, 1, -1)                if (inl ≠ nl) then                    set found to false                    exit repeat                end if            end repeat            if (found) then exit repeat            set n to n + 3        else            set end of output to "Nothing below " & n10 & (" (" & steps & " steps)")            set n to n10 + 26 -- set n to n10 * 1.26 as integer            set n10 to n10 * 10            -- set steps to 0        end if    end repeat     set end of output to "    n = " & n & (" (" & steps & " steps altogether)")    repeat with i from 2 to 6        set end of output to (i as text) & " * n = " & i * n    end repeat     return join(output, linefeed)end task task()`
Output:

Using 'set n to n10 + 26':

`"Nothing below 1000 (14 steps)Nothing below 10000 (228 steps)Nothing below 100000 (2442 steps)    n = 142857 (16720 steps altogether)2 * n = 2857143 * n = 4285714 * n = 5714285 * n = 7142856 * n = 857142"`
Output:

Using 'set n to n10 * 1.26 as integer':

`"Nothing below 1000 (14 steps)Nothing below 10000 (150 steps)Nothing below 100000 (1506 steps)    n = 142857 (7126 steps altogether)2 * n = 2857143 * n = 4285714 * n = 5714285 * n = 7142856 * n = 857142" `

## C++

`#include <array>#include <iostream> using digits = std::array<unsigned int, 10>; digits get_digits(unsigned int n) {    digits d = {};    do {        ++d[n % 10];        n /= 10;    } while (n > 0);    return d;} // Returns true if n, 2n, ..., 6n all have the same base 10 digits.bool same_digits(unsigned int n) {    digits d = get_digits(n);    for (unsigned int i = 0, m = n; i < 5; ++i) {        m += n;        if (get_digits(m) != d)            return false;    }    return true;} int main() {    for (unsigned int p = 100; ; p *= 10) {        unsigned int max = (p * 10) / 6;        for (unsigned int n = p + 2; n <= max; n += 3) {            if (same_digits(n)) {                std::cout << " n = " << n << '\n';                for (unsigned int i = 2; i <= 6; ++i)                    std::cout << i << "n = " << n * i << '\n';                return 0;            }        }    }}`
Output:
``` n = 142857
2n = 285714
3n = 428571
4n = 571428
5n = 714285
6n = 857142
```

## F#

` // Permuted multiples. Nigel Galloway: August 18th., 2021let fG n g=let rec fN g=[if g>0 then yield g%10; yield! fN(g/10)] in List.sort(fN n)=List.sort(fN g)let n=Seq.initInfinite((+)2)|>Seq.collect(fun n->seq{(pown 10 n)+2..3..(pown 10 (n+1))/6})|>Seq.find(fun g->let fN=fG g in fN(g*2)&&fN(g*3)&&fN(g*4)&&fN(g*5)&&fN(g*6))printfn \$"The solution to Project Euler 52 is %d{n}" `
Output:
```The solution to Project Euler 52 is 142857
```

## Factor

Works with: Factor version 0.99 2021-06-02
`USING: formatting io kernel lists lists.lazy math math.rangesmath.vectors numspec present prettyprint sequences sets ; : multiples ( n -- seq )    [ 2 * ] [ 6 * ] [ ] tri <range> [ present ] map ; : all-set-eq? ( seq -- ? )    dup ?first [ set= ] curry all? ; ! Ordered lazy list of numbers that start with a '1' digitNUMSPEC: starting-with-one 1 1_ ... ; : smallest-permuted-multiple ( -- n )    starting-with-one [ multiples all-set-eq? ] lfilter car ; { 2 3 4 5 6 } " n: " write smallest-permuted-multiple dup .over n*v [ "×%d: %d\n" printf ] 2each`
Output:
``` n: 142857
×2: 285714
×3: 428571
×4: 571428
×5: 714285
×6: 857142
```

## FreeBASIC

`function sort(s as string) as string    'quick and dirty bubblesort, not the focus of this exercise    dim as string t = s    dim as uinteger i, j, n = len(t)    dim as boolean sw     for i = n to 2 step -1        sw = false        for j = 1 to i-1             if asc(mid(t,j,1))>asc(mid(t,j+1,1)) then                 sw = true                 swap t[j-1], t[j]             end if        next j        if sw = false then return t     next i    return tend function dim as string ns(1 to 6)dim as uinteger n = 0, ido    n+=1    for i = 1 to 6        ns(i) = sort(str(i*n))        if i>1 andalso ns(i)<>ns(i-1) then continue do    next i    print n, 2*n, 3*n, 4*n, 5*n, 6*n    endloop`
Output:
```
142857        285714        428571        571428        714285        857142

```

## Go

Translation of: Wren
Library: Go-rcu
`package main import (    "fmt"    "rcu"    "sort") // assumes l1 is sorted but l2 is notfunc areSame(l1, l2 []int) bool {    if len(l1) != len(l2) {        return false    }    sort.Ints(l2)    for i := 0; i < len(l1); i++ {        if l1[i] != l2[i] {            return false        }    }    return true} func main() {    i := 100 // clearly a 1 or 2 digit number is impossible    nextPow := 1000    for {        digits := rcu.Digits(i, 10)        if digits[0] != 1 {            i = nextPow            nextPow *= 10            continue        }        sort.Ints(digits)        allSame := true        for j := 2; j <= 6; j++ {            digits2 := rcu.Digits(i*j, 10)            if !areSame(digits, digits2) {                allSame = false                break            }        }        if allSame {            fmt.Println("The smallest positive integer n for which the following")            fmt.Println("multiples contain exactly the same digits is:")            fmt.Println("    n =", i)            for k := 2; k <= 6; k++ {                fmt.Printf("%d x n = %d\n", k, k*i)            }            return        }        i = i + 1    }}`
Output:
```The smallest positive integer n for which the following
multiples contain exactly the same digits is:
n = 142857
2 x n = 285714
3 x n = 428571
4 x n = 571428
5 x n = 714285
6 x n = 857142
```

## Java

`import java.util.*; public class PermutedMultiples {    public static void main(String[] args) {        for (int p = 100; ; p *= 10) {            int max = (p * 10) / 6;            for (int n = p + 2; n <= max; n += 3) {                if (sameDigits(n)) {                    System.out.printf(" n = %d\n", n);                    for (int i = 2; i <= 6; ++i)                        System.out.printf("%dn = %d\n", i, n * i);                    return;                }            }        }    }     // Returns true if n, 2n, ..., 6n all have the same base 10 digits.    private static boolean sameDigits(int n) {        int[] digits = getDigits(n);        for (int i = 0, m = n; i < 5; ++i) {            m += n;            if (!Arrays.equals(getDigits(m), digits))                return false;        }        return true;    }     private static int[] getDigits(int n) {        int[] digits = new int[10];        do {            ++digits[n % 10];            n /= 10;        } while (n > 0);        return digits;    }}`
Output:
``` n = 142857
2n = 285714
3n = 428571
4n = 571428
5n = 714285
6n = 857142
```

## jq

Works with: jq

Works with gojq, the Go implementation of jq

The following uses a simple generate-and-test approach but with early backtracking, so it's quite reasonable.

`def digits: tostring | explode; first(range(1; infinite)      | . as \$i      | (digits|sort) as \$reference      | select(all(range(2;7); \$reference == ((. * \$i) | digits | sort))) )`
Output:
```142857
```

## Julia

`n = minimum([n for n in 1:2000000 if sort(digits(2n)) == sort(digits(3n)) == sort(digits(4n)) == sort(digits(5n))== sort(digits(6n))])println("n: \$n, 2n: \$(2n), 3n: \$(3n), 4n: \$(4n), 5n: \$(5n), 6n: \$(6n)") `
Output:
```n: 142857, 2n: 285714, 3n: 428571, 4n: 571428, 5n: 714285, 6n: 857142
```

## Nim

Searching among multiples of 3 between 102 and 1_000 div 6, 1_002 and 10_000 div 6, 10_002 and 100_000 div 6, etc. (see discussion).

`from algorithm import sorted func search(): int =  var start = 100  while true:    for i in countup(start + 2, 10 * start div 6, 3):      let digits = sorted(\$i)      block check:        for j in 2..6:          if sorted(\$(i * j)) != digits:            break check        # Found.        return i    start *= 10 let n = search()echo " n = ", nfor k in 2..6:  echo k, "n = ", k * n`
Output:
``` n = 142857
2n = 285714
3n = 428571
4n = 571428
5n = 714285
6n = 857142```

## Pascal

Create an array of the digits fixed 1 as first digit and 0 "1023456789"
Adding done digit by digit, so no conversion needed.
Using set of tdigit ,so no sort of digits is required.
Don't use the fact, that second digit must be < 6.Runtime negligible.

`program euler52;{\$IFDEF FPC}  {\$MOde DElphi} {\$Optimization On,ALL}{\$else}  {\$Apptype console}{\$ENDIF}  uses  sysutils;const   BaseConvDgt :array[0..35] of char = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ';  MAXBASE = 12;//type  TUsedDigits  =  array[0..MAXBASE-1] of byte;  tDigitsInUse = set of 0..MAXBASE-1;var{\$ALIGN 16}  UsedDigits :tUsedDigits;{\$ALIGN 16}    gblMaxDepth,  steps,  base,maxmul : NativeInt;  found : boolean;   function AddOne(var SumDigits:tUsedDigits;const UsedDigits: tUsedDigits):NativeInt;forward; function ConvBaseToStr(const UsedDigits :tUsedDigits):string;var  i,j:NativeUint;Begin  setlength(result,gblMaxdepth+1);  j := 1;  For i := 0 to gblMaxdepth do   begin    result[j] := BaseConvDgt[UsedDigits[i]];    inc(j);  end;  end;   procedure Out_MaxMul(const UsedDigits :tUsedDigits);var  j : NativeInt;  SumDigits :tUsedDigits;begin  writeln('With ',gblMaxdepth+1,' digits');          sumDigits := UsedDigits;  write(' 1x  :',ConvBaseToStr(UsedDigits));  For j := 2 to MaxMul do  Begin    AddOne(SumDigits,UsedDigits);    write(j:2,'x:',ConvBaseToStr(SumDigits));    end;  writeln;  writeln('steps ',steps);  end; procedure InitUsed;Var i : NativeInt;Begin  For i := 2 to BASE-1 do     UsedDigits[i] := i;  UsedDigits[0] := 1;  UsedDigits[1] := 0;  end; function GetUsedSet(const UsedDigits: tUsedDigits):tDigitsInUse;var  i : NativeInt;begin  result := [];  For i := 0 to gblMaxDepth do    include(result,UsedDigits[i]);end; function AddOne(var SumDigits:tUsedDigits;const UsedDigits: tUsedDigits):NativeInt;//add and return carryvar  s,i: NativeUint;begin  result := 0;    For i := gblMaxdepth downto 0 do    Begin    s := UsedDigits[i]+SumDigits[i]+result;    result := ord(s >= BASE);// 0 or 1//    if result >0 then s -= base;//runtime Base=12 Done in 2.097 -> Done in 1.647    s -= result*base;    SumDigits[i] := s;  end;end;      function CheckMultiples(const UsedDigits: tUsedDigits;OrgInUse:tDigitsInUse):NativeInt;var{\$ALIGN 16}  SumDigits :tUsedDigits;  j : integer;begin  result := 0;    SumDigits := UsedDigits;      j := 2;// first doubled  repeat    if AddOne(SumDigits,UsedDigits) >0 then      break;    if GetUsedSet(SumDigits) <> OrgInUse then      break;    inc(j);    until j > MaxMul;  found := j > MaxMul;  if found then    Out_MaxMul(UsedDigits);end; procedure GetNextUsedDigit(StartIdx:NativeInt);var  i : NativeInt;  DigitTaken: Byte;Begin  For i := StartIDx to BASE-1 do  Begin    //Stop after first found    if found then  BREAK;    DigitTaken := UsedDigits[i];     //swap i with Startidx        UsedDigits[i]:= UsedDigits[StartIdx];    UsedDigits[StartIdx] := DigitTaken;           inc(steps);    IF StartIdx <gblMaxDepth then      GetNextUsedDigit(StartIdx+1)    else      CheckMultiples(UsedDigits,GetUsedSet(UsedDigits));     //undo swap i with Startidx          UsedDigits[StartIdx] := UsedDigits[i];     UsedDigits[i]:= DigitTaken;  end;  end; var  T : INt64;Begin  T := GetTickCount64;//  For base := 4 to MAXBASE do  For base := 4 to 10 do  Begin    Writeln('Base ',base);    MaxMul := Base-2;    If base = 10 then      MaxMul := 6;    InitUsed;      steps := 0;    For gblMaxDepth := 1 to BASE-1 do    Begin      found := false;         GetNextUsedDigit(1);    end;      writeln;  end;    T := GetTickCount64-T;  write('Done in ',T/1000:0:3,' s');  {\$IFDEF WINdows}    readln;  {\$ENDIF}  end.`
Output:
```TIO.RUN
Base 4
With 3 digits
1x  :102 2x:210
steps 5
With 4 digits
1x  :1032 2x:2130
steps 10

Base 5

Base 6
With 5 digits
1x  :10432 2x:21304 3x:32140 4x:43012
steps 139
With 6 digits
1x  :105432 2x:215304 3x:325140 4x:435012
steps 197

Base 7

Base 8
With 7 digits
1x  :1065432 2x:2153064 3x:3240516 4x:4326150 5x:5413602 6x:6501234
steps 5945
With 8 digits
1x  :10765432 2x:21753064 3x:32740516 4x:43726150 5x:54713602 6x:65701234
steps 7793

Base 9

Base 10
With 6 digits
1x  :142857 2x:285714 3x:428571 4x:571428 5x:714285 6x:857142
steps 10725
With 7 digits
1x  :1428570 2x:2857140 3x:4285710 4x:5714280 5x:7142850 6x:8571420
steps 37956
With 8 digits
1x  :14298570 2x:28597140 3x:42895710 4x:57194280 5x:71492850 6x:85791420
steps 128297

Done in 0.044 s```

## Perl

`#!/usr/bin/perl use strict; # https://rosettacode.org/wiki/Permuted_multiplesuse warnings; my \$n = 3;1 while do {  length(\$n += 3) < length 6 * \$n and \$n = 1 . \$n =~ s/./0/gr + 2;  my \$sorted = join '', sort split //, \$n * 6;  \$sorted ne join '', sort split //, \$n * 1 or  \$sorted ne join '', sort split //, \$n * 2 or  \$sorted ne join '', sort split //, \$n * 3 or  \$sorted ne join '', sort split //, \$n * 4 or  \$sorted ne join '', sort split //, \$n * 5  };printf " n  %s\n", \$n;printf "%dn  %s\n", \$_ , \$n * \$_ for 2 .. 6;`
Output:
``` n  142857
2n  285714
3n  428571
4n  571428
5n  714285
6n  857142
```

## Phix

Maintain a limit (n10) and bump the iteration whenever *6 increases the number of digits, which (as [was] shown) cuts the number of iterations by a factor of nearly thirteen and a half times (as in eg [as was] 67 iterations instead of 900 to find nothing in 100..1,000). Also as noted on the talk page, since sum(digits(3n)) is a multiple of 3 and it uses the same digits as n, then sum(digits(n)) will also be the very same multiple of 3 and hence n must (also) be divisible by 3, so we can start each longer-digits iteration on 10^k+2 (since remainder(10^k,3) is always 1) and employ a step of 3, and enjoy a better than 40-fold overall reduction in iterations.

```with javascript_semantics
atom t0 = time()
integer n = 3, n10 = 10, steps = 0
constant fmt="""
%s positive integer n for which (2..6)*n contain the same digits:
n = %,d (%,d steps, hmmm...)
2 x n = %,d
3 x n = %,d
4 x n = %,d
5 x n = %,d
6 x n = %,d
""",
limit = iff(platform()=JS?1e7:1e9)
string nowtelse = "Nothing", smother = "Smallest"
while true do
if n*6>=n10 then
printf(1,"%s less than %,d (%,d steps)\n",{nowtelse,n10,steps})
if n10>=limit then exit end if
n = n10+2
n10 *= 10
steps = 0
else
string ns = sort(sprintf("%d",n))
integer i -- (to test after loop)
for i=2 to 6 do
string ins = sort(sprintf("%d",n*i))
if ins!=ns then exit end if
end for
if i=7 then
printf(1,fmt,{smother,n,steps} & sq_mul(n,tagset(6,2)))
nowtelse = "Nothing else"
smother = "Another"
exit    -- (see below)
end if
n += 3
steps += 1
end if
end while
?elapsed(time()-t0)
```
Output:
```Nothing less than 10 (0 steps)
Nothing less than 100 (2 steps)
Nothing less than 1,000 (22 steps)
Nothing less than 10,000 (222 steps)
Nothing less than 100,000 (2,222 steps)
Smallest positive integer n for which (2..6)*n contain the same digits:
n = 142,857 (14,285 steps, hmmm...)
2 x n = 285,714
3 x n = 428,571
4 x n = 571,428
5 x n = 714,285
6 x n = 857,142
"0.1s"
```

### extended output

If we comment out that "exit -- (see below)", as per the AppleScript comments and the Pascal output, some patterns start to emerge in the values and number of steps: *10 is a bit of a given, whereas "insert 9s before the 8" is (for me) a bit more unexpected. Be warned: on the desktop, 1e8 takes about 9s, 1e9 about 90s, so I'll predict 1e10 would take 15mins (and need 64bit) and I'll not try to compete with Pascal in terms of performance, though I am getting very different results above 1e7. Under pwa/p2js 1e8 takes about 30s (meh) so I've limited it to 1e7 (2.3s).

```Nothing else less than 1,000,000 (22,222 steps)
Another positive integer n for which (2..6)*n contain the same digits:
n = 1,428,570 (142,856 steps, hmmm...)
2 x n = 2,857,140
3 x n = 4,285,710
4 x n = 5,714,280
5 x n = 7,142,850
6 x n = 8,571,420
Another positive integer n for which (2..6)*n contain the same digits:
n = 1,429,857 (143,285 steps, hmmm...)
2 x n = 2,859,714
3 x n = 4,289,571
4 x n = 5,719,428
5 x n = 7,149,285
6 x n = 8,579,142
Nothing else less than 10,000,000 (222,222 steps)
Another positive integer n for which (2..6)*n contain the same digits:
n = 14,285,700 (1,428,566 steps, hmmm...)
2 x n = 28,571,400
3 x n = 42,857,100
4 x n = 57,142,800
5 x n = 71,428,500
6 x n = 85,714,200
Another positive integer n for which (2..6)*n contain the same digits:
n = 14,298,570 (1,432,856 steps, hmmm...)
2 x n = 28,597,140
3 x n = 42,895,710
4 x n = 57,194,280
5 x n = 71,492,850
6 x n = 85,791,420
Another positive integer n for which (2..6)*n contain the same digits:
n = 14,299,857 (1,433,285 steps, hmmm...)
2 x n = 28,599,714
3 x n = 42,899,571
4 x n = 57,199,428
5 x n = 71,499,285
6 x n = 85,799,142
Nothing else less than 100,000,000 (2,222,222 steps)
Another positive integer n for which (2..6)*n contain the same digits:
n = 142,857,000 (14,285,666 steps, hmmm...)
2 x n = 285,714,000
3 x n = 428,571,000
4 x n = 571,428,000
5 x n = 714,285,000
6 x n = 857,142,000
Another positive integer n for which (2..6)*n contain the same digits:
n = 142,985,700 (14,328,566 steps, hmmm...)
2 x n = 285,971,400
3 x n = 428,957,100
4 x n = 571,942,800
5 x n = 714,928,500
6 x n = 857,914,200
Another positive integer n for which (2..6)*n contain the same digits:
n = 142,998,570 (14,332,856 steps, hmmm...)
2 x n = 285,997,140
3 x n = 428,995,710
4 x n = 571,994,280
5 x n = 714,992,850
6 x n = 857,991,420
Another positive integer n for which (2..6)*n contain the same digits:
n = 142,999,857 (14,333,285 steps, hmmm...)
2 x n = 285,999,714
3 x n = 428,999,571
4 x n = 571,999,428
5 x n = 714,999,285
6 x n = 857,999,142
Nothing else less than 1,000,000,000 (22,222,222 steps)
```

I believe that last pattern will be continue to be valid no matter how many 9s are inserted in the middle, and I doubt that any further patterns would emerge.

## Raku

`put display (^∞).map(1 ~ *).race.map( -> \n { next unless [eq] (2,3,4,5,6).map: { (n × \$_).comb.sort.join }; n } ).first; sub display (\$n) { join "\n", " n: \$n", (2..6).map: { "×\$_: {\$n×\$_}" } }`
Output:
``` n: 142857
×2: 285714
×3: 428571
×4: 571428
×5: 714285
×6: 857142
```

## REXX

`/*REXX program  finds and displays  the  smallest positive integer   n   such that  ··· *//*───────────────────────── 2*n, 3*n, 4*5, 5*6, and 6*n contain the same decimal digits.*/        do n=1                                   /*increment  N  from unity 'til answer.*/        b= 2*n                                   /*calculate the product of:     2*n    */        t= 3*n                                   /*    "      "     "     "      3*n    */               if verify(t, b)>0  then iterate   /*T doesn't have required digits?  Skip*/        q= 4*n                                   /*calculate the product of:     4*n    */               if verify(q, b)>0  then iterate   /*Q doesn't have required digits?  Skip*/               if verify(q, t)>0  then iterate   /*"    "      "      "      "        " */        v= 5*n                                   /*calculate the product of:     5*n    */               if verify(v, b)<0  then iterate   /*V doesn't have required digits?  Skip*/               if verify(v, t)>0  then iterate   /*"    "      "      "      "        " */               if verify(v, q)>0  then iterate   /*"    "      "      "      "        " */        s= 6*n                                   /*calculate the product of:     6*n    */               if verify(s, b)>0  then iterate   /*S doesn't have required digits?  Skip*/               if verify(s, t)>0  then iterate   /*"    "      "      "      "        " */               if verify(s, q)>0  then iterate   /*"    "      "      "      "        " */               if verify(s, v)>0  then iterate   /*"    "      "      "      "        " */        say '           n ='  commas(n)          /*display the value of:     n          */        say '         2*n ='  commas(b)          /*   "     "    "    "    2*n          */        say '         3*n ='  commas(t)          /*   "     "    "    "    3*n          */        say '         4*n ='  commas(q)          /*   "     "    "    "    4*n          */        say '         5*n ='  commas(v)          /*   "     "    "    "    5*n          */        say '         6*n ='  commas(s)          /*   "     "    "    "    6*n          */        leave                                    /*found the   N  number, time to leave.*/        end   /*n*/exit 0                                           /*stick a fork in it,  we're all done. *//*──────────────────────────────────────────────────────────────────────────────────────*/commas: parse arg ?;  do jc=length(?)-3  to 1  by -3; ?=insert(',', ?, jc); end;  return ?`
output   when using the internal default input:
```            n = 142,857
2*n = 285,714
3*n = 428,571
4*n = 571,428
5*n = 714,285
6*n = 857,142
```

## Ring

` load "stdlib.ring" see "working..." + nlsee "Permuted multiples are:" + nlper = list(6)perm = list(6) for n = 1 to 1000000    for x = 2 to 6        perm[x] = []    next    perStr = list(6)    for z = 2 to 6        per[z] = n*z        perStr[z] = string(per[z])        for m = 1 to len(perStr[z])            add(perm[z],perStr[z][m])        next    next    for y = 2 to 6        perm[y] = sort(perm[y])        perStr[y] = list2str(perm[y])        perStr[y] = substr(perStr[y],nl,"")    next     if perStr[2] = perStr[3] and perStr[2] = perStr[4] and perStr[2] = perStr[5] and perStr[2] = perStr[6]       see "n   = " + n + nl       see "2*n = " + (n*2) + nl       see "3*n = " + (n*3) + nl       see "4*n = " + (n*4) + nl       see "5*n = " + (n*5) + nl       see "6*n = " + (n*6) + nl       exit    oknext see "done..." + nl `
Output:
```working...
Permuted multiples are:
n   = 142857
2*n = 285714
3*n = 428571
4*n = 571428
5*n = 714285
6*n = 857142
done...
```

## Swift

`func getDigits(_ num: Int) -> Array<Int> {    var n = num    var digits = Array(repeating: 0, count: 10)    while true {        digits[n % 10] += 1        n /= 10        if n == 0 {            break        }    }    return digits} // Returns true if n, 2n, ..., 6n all have the same base 10 digits.func sameDigits(_ n: Int) -> Bool {    let digits = getDigits(n)    for i in 2...6 {        if digits != getDigits(i * n) {            return false        }    }    return true} var p = 100loop: while true {    for n in stride(from: p + 2, through: (p * 10) / 6, by: 3) {        if sameDigits(n) {            print(" n = \(n)")            for i in 2...6 {                print("\(i)n = \(i * n)")            }            break loop        }    }    p *= 10}`
Output:
``` n = 142857
2n = 285714
3n = 428571
4n = 571428
5n = 714285
6n = 857142
```

## Wren

Library: Wren-math

One thing that's immediately clear is that the number must begin with '1' otherwise the higher multiples will have more digits than it has.

`import "/math" for Int // assumes l1 is sorted but l2 is notvar areSame = Fn.new { |l1, l2|    if (l1.count != l2.count) return false    l2.sort()    for (i in 0...l1.count) {        if (l1[i] != l2[i]) return false    }    return true} var i = 100  // clearly a 1 or 2 digit number is impossiblevar nextPow = 1000while (true) {    var digits = Int.digits(i)    if (digits[0] != 1) {        i = nextPow        nextPow = nextPow * 10        continue    }    digits.sort()    var allSame = true    for (j in 2..6) {        var digits2 = Int.digits(i * j)        if (!areSame.call(digits, digits2)) {            allSame = false            break        }    }    if (allSame) {        System.print("The smallest positive integer n for which the following")        System.print("multiples contain exactly the same digits is:")        System.print("    n = %(i)")        for (k in 2..6) System.print("%(k) x n = %(k * i)")        return    }    i = i + 1}`
Output:
```The smallest positive integer n for which the following
multiples contain exactly the same digits is:
n = 142857
2 x n = 285714
3 x n = 428571
4 x n = 571428
5 x n = 714285
6 x n = 857142
```

## XPL0

`func    Digits(N);              \Return counts of digits packed in 30 bitsint     N, Sums;[Sums:= 0;repeat  N:= N/10;        Sums:= Sums + 1<<(rem(0)*3);until   N = 0;return Sums;]; int N, Sums;[N:= 1;loop    [Sums:= Digits(N*2);        if Digits(N*3) = Sums then          if Digits(N*4) = Sums then            if Digits(N*5) = Sums then              if Digits(N*6) = Sums then                quit;        N:= N+1;        ];IntOut(0, N);]`
Output:
```142857
```