I.Q. Puzzle

From Rosetta Code
I.Q. Puzzle 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.

An   IQ Puzzle   is a triangle of 15 golf tee's.


This puzzle is typically seen at Cracker Barrel   (a USA sales store)   where one tee is missing and the remaining tees jump over each other   (with removal of the jumped tee, like checkers)   until one tee is left.

The fewer tees left,   the higher the IQ score.

Peg   #1   is the top centre through to the bottom row which are pegs 11 through to 15.

         ^
        / \        
       /   \
      /     \
     /   1   \     
    /  2   3  \
   / 4   5  6  \ 
  / 7  8  9  10 \
 /11 12 13 14  15\
/_________________\

Reference picture:   http://www.joenord.com/puzzles/peggame/


Task

Print a solution to solve the puzzle leaving one peg not implemented variations.

Start with empty peg in   X   and solve with one peg in position   Y.

D[edit]

Translation of: Ruby
import std.stdio, std.array, std.string, std.range, std.algorithm;
 
immutable N = [0,1,1,1,1,1,1,1,1,1,1,1,1,1,1];
immutable G = [[0,1,3],[0,2,5],[1,3,6],[1,4,8],[2,4,7],[2,5,9],
[3,4,5],[3,6,10],[3,7,12],[4,7,11],[4,8,13],[5,8,12],
[5,9,14],[6,7,8],[7,8,9],[10,11,12],[11,12,13],[12,13,14]];
 
string b2s(in int[] n) pure @safe {
static immutable fmt = 6.iota
.map!(i => " ".replicate(5 - i) ~ "%d ".replicate(i))
.join('\n');
return fmt.format(n[0], n[1], n[2], n[3], n[4], n[5], n[6],
n[7], n[8], n[9], n[10], n[11], n[12], n[13], n[14]);
}
 
string solve(in int[] n, in int i, in int[] g) pure @safe {
if (i == N.length - 1)
return "\nSolved";
if (n[g[1]] == 0)
return null;
string s;
if (n[g[0]] == 0) {
if (n[g[2]] == 0)
return null;
s = "\n%d to %d\n".format(g[2], g[0]);
} else {
if (n[g[2]] == 1)
return null;
s = "\n%d to %d\n".format(g[0], g[2]);
}
 
auto a = n.dup;
foreach (const gi; g)
a[gi] = 1 - a[gi];
string l;
foreach (const gi; G) {
l = solve(a, i + 1, gi);
if (!l.empty)
break;
}
return l.empty ? l : (s ~ b2s(a) ~ l);
}
 
void main() @safe {
b2s(N).write;
string l;
foreach (const g; G) {
l = solve(N, 1, g);
if (!l.empty)
break;
}
writeln(l.empty ? "No solution found." : l);
}
Output:
     
    0 
   1 1 
  1 1 1 
 1 1 1 1 
1 1 1 1 1 
3 to 0
     
    1 
   0 1 
  0 1 1 
 1 1 1 1 
1 1 1 1 1 
8 to 1
     
    1 
   1 1 
  0 0 1 
 1 1 0 1 
1 1 1 1 1 
10 to 3
     
    1 
   1 1 
  1 0 1 
 0 1 0 1 
0 1 1 1 1 
1 to 6
     
    1 
   0 1 
  0 0 1 
 1 1 0 1 
0 1 1 1 1 
11 to 4
     
    1 
   0 1 
  0 1 1 
 1 0 0 1 
0 0 1 1 1 
2 to 7
     
    1 
   0 0 
  0 0 1 
 1 1 0 1 
0 0 1 1 1 
9 to 2
     
    1 
   0 1 
  0 0 0 
 1 1 0 0 
0 0 1 1 1 
0 to 5
     
    0 
   0 0 
  0 0 1 
 1 1 0 0 
0 0 1 1 1 
6 to 8
     
    0 
   0 0 
  0 0 1 
 0 0 1 0 
0 0 1 1 1 
13 to 11
     
    0 
   0 0 
  0 0 1 
 0 0 1 0 
0 1 0 0 1 
5 to 12
     
    0 
   0 0 
  0 0 0 
 0 0 0 0 
0 1 1 0 1 
11 to 13
     
    0 
   0 0 
  0 0 0 
 0 0 0 0 
0 0 0 1 1 
14 to 12
     
    0 
   0 0 
  0 0 0 
 0 0 0 0 
0 0 1 0 0 
Solved

Elixir[edit]

Inspired by Ruby

defmodule IQ_Puzzle do
def task(i \\ 0, n \\ 5) do
fmt = Enum.map_join(1..n, fn i ->
String.duplicate(" ", n-i) <> String.duplicate("~w ", i) <> "~n"
end)
pegs = Tuple.duplicate(1, div(n*(n+1),2)) |> put_elem(i, 0)
rest = tuple_size(pegs) - 1
next = next_list(n)
 :io.format fmt, Tuple.to_list(pegs)
result = Enum.find_value(next, fn nxt -> solve(pegs, rest, nxt, next, fmt) end)
IO.puts if result, do: result, else: "No solution found"
end
 
defp solve(_,1,_,_,_), do: "Solved"
defp solve(pegs,rest,{g0,g1,g2},next,fmt) do
if s = jump(pegs, g0, g1, g2) do
peg2 = Enum.reduce([g0,g1,g2], pegs, fn g,acc ->
put_elem(acc, g, 1-elem(acc, g))
end)
result = Enum.find_value(next, fn g -> solve(peg2, rest-1, g, next, fmt) end)
if result do
[(:io_lib.format "~n~s~n", [s]), (:io_lib.format fmt, Tuple.to_list(peg2)) | result]
end
end
end
 
defp jump(pegs, _0, g1, _2) when elem(pegs,g1)==0, do: nil
defp jump(pegs, g0, _1, g2) when elem(pegs,g0)==0, do: if elem(pegs, g2)==1, do: "#{g2} to #{g0}"
defp jump(pegs, g0, _1, g2) , do: if elem(pegs, g2)==0, do: "#{g0} to #{g2}"
 
defp next_list(n) do
points = for x <- 1..n, y <- 1..x, do: {x,y}
board = points |> Enum.with_index |> Enum.into(Map.new)
Enum.flat_map(points, fn {x,y} ->
[ {board[{x,y}], board[{x, y+1}], board[{x, y+2}]},
{board[{x,y}], board[{x+1,y }], board[{x+2,y }]},
{board[{x,y}], board[{x+1,y+1}], board[{x+2,y+2}]} ]
end)
|> Enum.filter(fn {_,_,p} -> p end)
end
end
 
IQ_Puzzle.task
Output:
    0 
   1 1 
  1 1 1 
 1 1 1 1 
1 1 1 1 1 

3 to 0
    1 
   0 1 
  0 1 1 
 1 1 1 1 
1 1 1 1 1 

8 to 1
    1 
   1 1 
  0 0 1 
 1 1 0 1 
1 1 1 1 1 

10 to 3
    1 
   1 1 
  1 0 1 
 0 1 0 1 
0 1 1 1 1 

1 to 6
    1 
   0 1 
  0 0 1 
 1 1 0 1 
0 1 1 1 1 

11 to 4
    1 
   0 1 
  0 1 1 
 1 0 0 1 
0 0 1 1 1 

2 to 7
    1 
   0 0 
  0 0 1 
 1 1 0 1 
0 0 1 1 1 

9 to 2
    1 
   0 1 
  0 0 0 
 1 1 0 0 
0 0 1 1 1 

0 to 5
    0 
   0 0 
  0 0 1 
 1 1 0 0 
0 0 1 1 1 

6 to 8
    0 
   0 0 
  0 0 1 
 0 0 1 0 
0 0 1 1 1 

13 to 11
    0 
   0 0 
  0 0 1 
 0 0 1 0 
0 1 0 0 1 

5 to 12
    0 
   0 0 
  0 0 0 
 0 0 0 0 
0 1 1 0 1 

11 to 13
    0 
   0 0 
  0 0 0 
 0 0 0 0 
0 0 0 1 1 

14 to 12
    0 
   0 0 
  0 0 0 
 0 0 0 0 
0 0 1 0 0 
Solved

Go[edit]

Translation of: Kotlin
package main
 
import "fmt"
 
type solution struct{ peg, over, land int }
 
type move struct{ from, to int }
 
var emptyStart = 1
 
var board [16]bool
 
var jumpMoves = [16][]move{
{},
{{2, 4}, {3, 6}},
{{4, 7}, {5, 9}},
{{5, 8}, {6, 10}},
{{2, 1}, {5, 6}, {7, 11}, {8, 13}},
{{8, 12}, {9, 14}},
{{3, 1}, {5, 4}, {9, 13}, {10, 15}},
{{4, 2}, {8, 9}},
{{5, 3}, {9, 10}},
{{5, 2}, {8, 7}},
{{9, 8}},
{{12, 13}},
{{8, 5}, {13, 14}},
{{8, 4}, {9, 6}, {12, 11}, {14, 15}},
{{9, 5}, {13, 12}},
{{10, 6}, {14, 13}},
}
 
var solutions []solution
 
func initBoard() {
for i := 1; i < 16; i++ {
board[i] = true
}
board[emptyStart] = false
}
 
func (sol solution) split() (int, int, int) {
return sol.peg, sol.over, sol.land
}
 
func (mv move) split() (int, int) {
return mv.from, mv.to
}
 
func drawBoard() {
var pegs [16]byte
for i := 1; i < 16; i++ {
if board[i] {
pegs[i] = fmt.Sprintf("%X", i)[0]
} else {
pegs[i] = '-'
}
}
fmt.Printf("  %c\n", pegs[1])
fmt.Printf("  %c %c\n", pegs[2], pegs[3])
fmt.Printf("  %c %c %c\n", pegs[4], pegs[5], pegs[6])
fmt.Printf("  %c %c %c %c\n", pegs[7], pegs[8], pegs[9], pegs[10])
fmt.Printf("  %c %c %c %c %c\n", pegs[11], pegs[12], pegs[13], pegs[14], pegs[15])
}
 
func solved() bool {
count := 0
for _, b := range board {
if b {
count++
}
}
return count == 1 // just one peg left
}
 
func solve() {
if solved() {
return
}
for peg := 1; peg < 16; peg++ {
if board[peg] {
for _, mv := range jumpMoves[peg] {
over, land := mv.split()
if board[over] && !board[land] {
saveBoard := board
board[peg] = false
board[over] = false
board[land] = true
solutions = append(solutions, solution{peg, over, land})
solve()
if solved() {
return // otherwise back-track
}
board = saveBoard
solutions = solutions[:len(solutions)-1]
}
}
}
}
}
 
func main() {
initBoard()
solve()
initBoard()
drawBoard()
fmt.Printf("Starting with peg %X removed\n\n", emptyStart)
for _, solution := range solutions {
peg, over, land := solution.split()
board[peg] = false
board[over] = false
board[land] = true
drawBoard()
fmt.Printf("Peg %X jumped over %X to land on %X\n\n", peg, over, land)
}
}
Output:
Same as Kotlin entry

J[edit]

 
NB. This is a direct translation of the python program,
NB. except for the display which by move is horizontal.
 
PEGS =: >:i.15
 
move =: 4 : 0 NB. move should have been factored in the 2014-NOV-29 python version
board =. x
'peg over land' =. y
board =. board RemovePeg peg
board =. board RemovePeg over
board =. board AddPeg land
)
 
NB.# Draw board triangle in ascii
NB.#
NB.def DrawBoard(board):
NB. peg = [0,]*16
NB. for n in xrange(1,16):
NB. peg[n] = '.'
NB. if n in board:
NB. peg[n] = "%X" % n
NB. print "  %s" % peg[1]
NB. print "  %s %s" % (peg[2],peg[3])
NB. print "  %s %s %s" % (peg[4],peg[5],peg[6])
NB. print "  %s %s %s %s" % (peg[7],peg[8],peg[9],peg[10])
NB. print " %s %s %s %s %s" % (peg[11],peg[12],peg[13],peg[14],peg[15])
 
HEXCHARS =: Num_j_ , Alpha_j_
 
DrawBoard =: 3 : 0
NB. observe 1 1 0 1 0 0 1 0 0 0 1 0 0 0 0 -: 2#.inv 26896 (== 6910 in base 16)
board =. y
< (-i._5) (|."0 1) 1j1 (#"1) (2#.inv 16b6910)[;.1 }. (board { HEXCHARS) board } 16 # '.'
)
 
 
NB.# remove peg n from board
NB.def RemovePeg(board,n):
NB. board.remove(n)
NB. return board
 
RemovePeg =: i. ({. , (}.~ >:)~) [
 
 
NB.# Add peg n on board
NB.def AddPeg(board,n):
NB. board.append(n)
NB. return board
 
AddPeg =: ,
 
 
NB.# return true if peg N is on board else false is empty position
NB.def IsPeg(board,n):
NB. return n in board
 
IsPeg =: e.~
 
 
NB.# A dictionary of valid jump moves index by jumping peg
NB.# then a list of moves where move has jumpOver and LandAt positions
NB.JumpMoves = { 1: [ (2,4),(3,6) ], # 1 can jump over 2 to land on 4, or jumper over 3 to land on 6
NB. 2: [ (4,7),(5,9) ],
NB. 3: [ (5,8),(6,10) ],
NB. ...
NB. 14: [ (9,5),(13,12) ],
NB. 15: [ (10,6),(14,13) ]
NB. }
 
JumpMoves =: a:,(<@:([\~ _2:)@:".;._2) 0 :0 NB. 1 can jump over 2 to land on 4, or jump over 3 to land on 6
(2,4),(3,6)
(4,7),(5,9)
(5,8),(6,10)
(2,1),(5,6),(7,11),(8,13)
(8,12),(9,14)
(3,1),(5,4),(9,13),(10,15)
(4,2),(8,9)
(5,3),(9,10)
(5,2),(8,7)
(9,8)
(12,13)
(8,5),(13,14)
(8,4),(9,6),(12,11),(14,15)
(9,5),(13,12)
(10,6),(14,13)
)
 
 
NB.Solution = []
NB.#
NB.# Recursively solve the problem
NB.#
NB.def Solve(board):
NB. #DrawBoard(board)
NB. if len(board) == 1:
NB. return board # Solved one peg left
NB. # try a move for each peg on the board
NB. for peg in xrange(1,16): # try in numeric order not board order
NB. if IsPeg(board,peg):
NB. movelist = JumpMoves[peg]
NB. for over,land in movelist:
NB. if IsPeg(board,over) and not IsPeg(board,land):
NB. saveboard = board[:] # for back tracking
NB. board = RemovePeg(board,peg)
NB. board = RemovePeg(board,over)
NB. board = AddPeg(board,land) # board order changes!
NB. Solution.append((peg,over,land))
NB. board = Solve(board)
NB. if len(board) == 1:
NB. return board
NB. ## undo move and back track when stuck!
NB. board = saveboard[:] # back track
NB. del Solution[-1] # remove last move
NB. return board
 
Solution =: 0 3 $ 0
 
Solve =: 3 : 0
board =. y
if. 1 = # board do. return. end.
for_peg. PEGS do.
if. board IsPeg peg do.
movelist =: peg {:: JumpMoves
for_OL. movelist do.
'over land' =. OL
if. (board IsPeg over) (*. -.) (board IsPeg land) do.
saveboard =. board NB. for back tracking
board =. board move peg,over,land
Solution =: Solution , peg, over, land
board =. Solve board
if. 1 = # board do. return. end.
board =. saveboard
Solution =: }: Solution
end.
end.
end.
end.
board
)
 
 
NB.#
NB.# Remove one peg and start solving
NB.#
NB.def InitSolve(empty):
NB. board = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
NB. RemovePeg(board,empty_start)
NB. Solve(board)
 
InitSolve =: [: Solve PEGS RemovePeg ]
 
 
NB.#
NB.empty_start = 1
NB.InitSolve(empty_start)
 
InitSolve empty_start =: 1
 
 
NB.board = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
NB.RemovePeg(board,empty_start)
NB.for peg,over,land in Solution:
NB. RemovePeg(board,peg)
NB. RemovePeg(board,over)
NB. AddPeg(board,land) # board order changes!
NB. DrawBoard(board)
NB. print "Peg %X jumped over %X to land on %X\n" % (peg,over,land)
 
 
(3 : 0) PEGS RemovePeg empty_start
board =. y
horizontal =. DrawBoard board
for_POL. Solution do.
'peg over land' =. POL
board =. board move POL
horizontal =. horizontal , DrawBoard board
smoutput 'Peg ',(":peg),' jumped over ',(":over),' to land on ',(":land)
end.
smoutput horizontal
NB. Solution NB. return Solution however Solution is global.
)
 

Example linux session with program in file CrackerBarrel.ijs

ubuntu$ ijconsole CrackerBarrel.ijs
Peg 4 jumped over 2 to land on 1
Peg 6 jumped over 5 to land on 4
Peg 1 jumped over 3 to land on 6
Peg 7 jumped over 4 to land on 2
Peg 12 jumped over 8 to land on 5
Peg 14 jumped over 13 to land on 12
Peg 6 jumped over 9 to land on 13
Peg 2 jumped over 5 to land on 9
Peg 12 jumped over 13 to land on 14
Peg 15 jumped over 10 to land on 6
Peg 6 jumped over 9 to land on 13
Peg 14 jumped over 13 to land on 12
Peg 11 jumped over 12 to land on 13
┌──────────┬──────────┬──────────┬──────────┬──────────┬──────────┬──────────┬──────────┬──────────┬──────────┬──────────┬──────────┬──────────┬──────────┐
│    .     │    1     │    1     │    .     │    .     │    .     │    .     │    .     │    .     │    .     │    .     │    .     │    .     │    .     │
│   2 3    │   . 3    │   . 3    │   . .    │   2 .    │   2 .    │   2 .    │   2 .    │   . .    │   . .    │   . .    │   . .    │   . .    │   . .    │
│  4 5 6   │  . 5 6   │  4 . .   │  4 . 6   │  . . 6   │  . 5 6   │  . 5 6   │  . 5 .   │  . . .   │  . . .   │  . . 6   │  . . .   │  . . .   │  . . .   │
│ 7 8 9 A  │ 7 8 9 A  │ 7 8 9 A  │ 7 8 9 A  │ . 8 9 A  │ . . 9 A  │ . . 9 A  │ . . . A  │ . . 9 A  │ . . 9 A  │ . . 9 .  │ . . . .  │ . . . .  │ . . . .  │
│B C D E F │B C D E F │B C D E F │B C D E F │B C D E F │B . D E F │B C . . F │B C D . F │B C D . F │B . . E F │B . . E . │B . D E . │B C . . . │. . D . . │
└──────────┴──────────┴──────────┴──────────┴──────────┴──────────┴──────────┴──────────┴──────────┴──────────┴──────────┴──────────┴──────────┴──────────┘
   JVERSION
Engine: j701/2011-01-10/11:25
Library: 8.02.12
Platform: Linux 64
Installer: unknown
InstallPath: /usr/share/j/8.0.2
   exit 0
ubuntu$ 

Kotlin[edit]

Translation of: Python
// version 1.1.3
 
data class Solution(val peg: Int, val over: Int, val land: Int)
 
var board = BooleanArray(16) { if (it == 0) false else true }
 
val jumpMoves = listOf(
listOf(),
listOf( 2 to 4, 3 to 6),
listOf( 4 to 7, 5 to 9),
listOf( 5 to 8, 6 to 10),
listOf( 2 to 1, 5 to 6, 7 to 11, 8 to 13),
listOf( 8 to 12, 9 to 14),
listOf( 3 to 1, 5 to 4, 9 to 13, 10 to 15),
listOf( 4 to 2, 8 to 9),
listOf( 5 to 3, 9 to 10),
listOf( 5 to 2, 8 to 7),
listOf( 9 to 8),
listOf(12 to 13),
listOf( 8 to 5, 13 to 14),
listOf( 8 to 4, 9 to 6, 12 to 11, 14 to 15),
listOf( 9 to 5, 13 to 12),
listOf(10 to 6, 14 to 13)
)
 
val solutions = mutableListOf<Solution>()
 
fun drawBoard() {
val pegs = CharArray(16) { '-' }
for (i in 1..15) if (board[i]) pegs[i] = "%X".format(i)[0]
println("  %c".format(pegs[1]))
println("  %c %c".format(pegs[2], pegs[3]))
println("  %c %c %c".format(pegs[4], pegs[5], pegs[6]))
println("  %c %c %c %c".format(pegs[7], pegs[8], pegs[9], pegs[10]))
println("  %c %c %c %c %c".format(pegs[11], pegs[12], pegs[13], pegs[14], pegs[15]))
}
 
val solved get() = board.count { it } == 1 // just one peg left
 
fun solve() {
if (solved) return
for (peg in 1..15) {
if (board[peg]) {
for ((over, land) in jumpMoves[peg]) {
if (board[over] && !board[land]) {
val saveBoard = board.copyOf()
board[peg] = false
board[over] = false
board[land] = true
solutions.add(Solution(peg, over, land))
solve()
if (solved) return // otherwise back-track
board = saveBoard
solutions.removeAt(solutions.lastIndex)
}
}
}
}
}
 
fun main(args: Array<String>) {
val emptyStart = 1
board[emptyStart] = false
solve()
board = BooleanArray(16) { if (it == 0) false else true }
board[emptyStart] = false
drawBoard()
println("Starting with peg %X removed\n".format(emptyStart))
for ((peg, over, land) in solutions) {
board[peg] = false
board[over] = false
board[land] = true
drawBoard()
println("Peg %X jumped over %X to land on %X\n".format(peg, over, land))
}
}
Output:
       -
      2 3
     4 5 6
    7 8 9 A
   B C D E F
Starting with peg 1 removed

       1
      - 3
     - 5 6
    7 8 9 A
   B C D E F
Peg 4 jumped over 2 to land on 1

       1
      - 3
     4 - -
    7 8 9 A
   B C D E F
Peg 6 jumped over 5 to land on 4

       -
      - -
     4 - 6
    7 8 9 A
   B C D E F
Peg 1 jumped over 3 to land on 6

       -
      2 -
     - - 6
    - 8 9 A
   B C D E F
Peg 7 jumped over 4 to land on 2

       -
      2 -
     - 5 6
    - - 9 A
   B - D E F
Peg C jumped over 8 to land on 5

       -
      2 -
     - 5 6
    - - 9 A
   B C - - F
Peg E jumped over D to land on C

       -
      2 -
     - 5 -
    - - - A
   B C D - F
Peg 6 jumped over 9 to land on D

       -
      - -
     - - -
    - - 9 A
   B C D - F
Peg 2 jumped over 5 to land on 9

       -
      - -
     - - -
    - - 9 A
   B - - E F
Peg C jumped over D to land on E

       -
      - -
     - - 6
    - - 9 -
   B - - E -
Peg F jumped over A to land on 6

       -
      - -
     - - -
    - - - -
   B - D E -
Peg 6 jumped over 9 to land on D

       -
      - -
     - - -
    - - - -
   B C - - -
Peg E jumped over D to land on C

       -
      - -
     - - -
    - - - -
   - - D - -
Peg B jumped over C to land on D

Perl[edit]

Translation of: Perl 6
@start = qw<
0
1 1
1 1 1
1 1 1 1
1 1 1 1 1
>;
 
@moves = (
[ 0, 1, 3], [ 0, 2, 5], [ 1, 3, 6],
[ 1, 4, 8], [ 2, 4, 7], [ 2, 5, 9],
[ 3, 4, 5], [ 3, 6,10], [ 3, 7,12],
[ 4, 7,11], [ 4, 8,13], [ 5, 8,12],
[ 5, 9,14], [ 6, 7, 8], [ 7, 8, 9],
[10,11,12], [11,12,13], [12,13,14]
);
 
$format .= (" " x (5-$_)) . ("%d " x $_) . "\n" for 1..5;
 
sub solve {
my ($move, $turns, @board) = @_;
$turns = 1 unless $turns;
return "\nSolved" if $turns + 1 == @board;
return undef if $board[$$move[1]] == 0;
my $valid = do {
if ($board[$$move[0]] == 0) {
return undef if $board[$$move[2]] == 0;
"\nmove $$move[2] to $$move[0]\n";
} else {
return undef if $board[$$move[2]] == 1;
"\nmove $$move[0] to $$move[2]\n";
}
};
 
my $new_result;
my @new_layout = @board;
@new_layout[$_] = 1 - @new_layout[$_] for @$move;
for $this_move (@moves) {
$new_result = solve(\@$this_move, $turns + 1, @new_layout);
last if $new_result
}
$new_result ? "$valid\n" . sprintf($format, @new_layout) . $new_result : $new_result}
 
$result = "Starting with\n\n" . sprintf($format, @start), "\n";
 
for $this_move (@moves) {
$result .= solve(\@$this_move, 1, @start);
last if $result
}
 
print $result ? $result : "No solution found";
 
Output:
Starting with

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

move 3 to 0

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

move 8 to 1

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

move 10 to 3

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

move 1 to 6

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

move 11 to 4

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

move 2 to 7

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

move 9 to 2

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

move 0 to 5

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

move 6 to 8

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

move 13 to 11

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

move 5 to 12

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

move 11 to 13

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

move 14 to 12

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

Solved

Perl 6[edit]

Works with: Rakudo version 2017.05
Translation of: Sidef
 
constant @start = <
0
1 1
1 1 1
1 1 1 1
1 1 1 1 1
>».Int;
 
constant @moves =
[ 0, 1, 3],[ 0, 2, 5],[ 1, 3, 6],
[ 1, 4, 8],[ 2, 4, 7],[ 2, 5, 9],
[ 3, 4, 5],[ 3, 6,10],[ 3, 7,12],
[ 4, 7,11],[ 4, 8,13],[ 5, 8,12],
[ 5, 9,14],[ 6, 7, 8],[ 7, 8, 9],
[10,11,12],[11,12,13],[12,13,14];
 
my $format = (1..5).map: {' ' x 5-$_, "%d " x $_, "\n"};
 
sub solve(@board, @move) {
return " Solved" if @board.sum == 1;
return Nil if @board[@move[1]] == 0;
my $valid = do given @board[@move[0]] {
when 0 {
return Nil if @board[@move[2]] == 0;
"move {@move[2]} to {@move[0]}\n ";
}
default {
return Nil if @board[@move[2]] == 1;
"move {@move[0]} to {@move[2]}\n ";
}
}
 
my @new-layout = @board;
@new-layout[$_] = 1 - @new-layout[$_] for @move;
my $result;
for @moves -> @this-move {
$result = solve(@new-layout, @this-move);
last if $result
}
$result ?? "$valid\n " ~ sprintf($format, |@new-layout) ~ $result !! $result
}
 
print "Starting with\n ", sprintf($format, |@start);
 
my $result;
for @moves -> @this-move {
$result = solve(@start, @this-move);
last if $result
};
say $result ?? $result !! "No solution found";
Output:
Starting with
      0  
     1 1  
    1 1 1  
   1 1 1 1  
  1 1 1 1 1  
move 3 to 0
 
      1  
     0 1  
    0 1 1  
   1 1 1 1  
  1 1 1 1 1  
move 8 to 1
 
      1  
     1 1  
    0 0 1  
   1 1 0 1  
  1 1 1 1 1  
move 10 to 3
 
      1  
     1 1  
    1 0 1  
   0 1 0 1  
  0 1 1 1 1  
move 1 to 6
 
      1  
     0 1  
    0 0 1  
   1 1 0 1  
  0 1 1 1 1  
move 11 to 4
 
      1  
     0 1  
    0 1 1  
   1 0 0 1  
  0 0 1 1 1  
move 2 to 7
 
      1  
     0 0  
    0 0 1  
   1 1 0 1  
  0 0 1 1 1  
move 9 to 2
 
      1  
     0 1  
    0 0 0  
   1 1 0 0  
  0 0 1 1 1  
move 0 to 5
 
      0  
     0 0  
    0 0 1  
   1 1 0 0  
  0 0 1 1 1  
move 6 to 8
 
      0  
     0 0  
    0 0 1  
   0 0 1 0  
  0 0 1 1 1  
move 13 to 11
 
      0  
     0 0  
    0 0 1  
   0 0 1 0  
  0 1 0 0 1  
move 5 to 12
 
      0  
     0 0  
    0 0 0  
   0 0 0 0  
  0 1 1 0 1  
move 11 to 13
 
      0  
     0 0  
    0 0 0  
   0 0 0 0  
  0 0 0 1 1  
move 14 to 12
 
      0  
     0 0  
    0 0 0  
   0 0 0 0  
  0 0 1 0 0  
   Solved

Phix[edit]

Twee brute-force string-based solution. Backtracks a mere 366 times, whereas starting with the 5th peg missing backtracks 19388 times (all in 0s, obvs).

--
-- demo\rosetta\IQpuzzle.exw
--
constant moves = {-11,-9,2,11,9,-2}
function solve(string board, integer left)
if left=1 then return "" end if
for i=1 to length(board) do
if board[i]='1' then
for j=1 to length(moves) do
integer mj = moves[j], over = i+mj, tgt = i+2*mj
if tgt>=1 and tgt<=length(board)
and board[tgt]='0' and board[over]='1' then
{board[i],board[over],board[tgt]} = "001"
string res = solve(board,left-1)
if length(res)!=4 then return board&res end if
{board[i],board[over],board[tgt]} = "110"
end if
end for
end if
end for
return "oops"
end function
 
sequence start = """
----0----
---1-1---
--1-1-1--
-1-1-1-1-
1-1-1-1-1
"""
puts(1,substitute(join_by(split(start&solve(start,14),'\n'),5,7),"-"," "))
Output:
    0           1           1           0           0           0           0
   1 1         0 1         0 1         0 0         1 0         1 1         1 1
  1 1 1       0 1 1       1 0 0       1 0 1       0 0 1       0 0 0       0 1 0
 1 1 1 1     1 1 1 1     1 1 1 1     1 1 1 1     0 1 1 1     0 1 1 0     0 0 1 0
1 1 1 1 1   1 1 1 1 1   1 1 1 1 1   1 1 1 1 1   1 1 1 1 1   1 1 1 1 1   1 0 1 1 1

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

Adapted to the English game:

constant moves = {-2,15,2,-15}
function solve(string board, integer left)
if left=1 then
-- return "" -- (leaves it on the edge)
if board[3*15+8]='.' then return "" end if
return "oops"
end if
for i=1 to length(board) do
if board[i]='.' then
for j=1 to length(moves) do
integer mj = moves[j], over = i+mj, tgt = i+2*mj
if tgt>=1 and tgt<=length(board)
and board[tgt]='o' and board[over]='.' then
{board[i],board[over],board[tgt]} = "oo."
string res = solve(board,left-1)
if length(res)!=4 then return board&res end if
{board[i],board[over],board[tgt]} = "..o"
end if
end for
end if
end for
return "oops"
end function
 
sequence start = """
-----.-.-.----
-----.-.-.----
-.-.-.-.-.-.-.
-.-.-.-o-.-.-.
-.-.-.-.-.-.-.
-----.-.-.----
-----.-.-.----
"""
puts(1,substitute(join_by(split(start&solve(start,32),'\n'),7,8),"-"," "))
Output:
     . . .            . . .            . . .            o . .            . o o            . o o            . o o            . o .   
     . . .            . o .            . o .            o o .            o o .            o o .            o o .            o o o   
 . . . . . . .    . . . o . . .    . o o . . . .    . o . . . . .    . o . . . . .    . . o o . . .    o o . o . . .    o o . o o . .
 . . . o . . .    . . . . . . .    . . . . . . .    . . . . . . .    . . . . . . .    . . . . . . .    . . . . . . .    . . . . . . .
 . . . . . . .    . . . . . . .    . . . . . . .    . . . . . . .    . . . . . . .    . . . . . . .    . . . . . . .    . . . . . . .
     . . .            . . .            . . .            . . .            . . .            . . .            . . .            . . .   
     . . .            . . .            . . .            . . .            . . .            . . .            . . .            . . .   

     . o .            . o .            o o .            o o .            o o .            o o .            o o .            o o .   
     o o o            . o o            o o o            o o o            . o o            . o o            . o o            . o .   
 o o . o . o o    o o o o . o o    o o . o . o o    o o . o . o o    o o o o . o o    o o o o . o o    o o o o . o o    o o o o o o o
 . . . . . . .    . . o . . . .    . . o . . . .    o o . . . . .    o o o . . . .    o o . o o . .    o o . o . o o    o o . o o o o
 . . . . . . .    . . . . . . .    . . . . . . .    . . . . . . .    . . . . . . .    . . . . . . .    . . . . . . .    . . . . . . .
     . . .            . . .            . . .            . . .            . . .            . . .            . . .            . . .   
     . . .            . . .            . . .            . . .            . . .            . . .            . . .            . . .   

     o o o            o o o            o o o            o o o            o o o            o o o            o o o            o o o   
     . o o            . o o            o o o            o o o            o o o            o o o            o o o            o o o   
 o o o o . o o    o o . o . o o    o o o o . o o    o o o o . o o    o o o o . o o    o o o o . o o    o o o o . o o    o o o o . o o
 o o . o o o o    o o o o o o o    o o . o o o o    o o . o o o o    o o . o o o o    o o . o . o o    o o . o . o o    o o . o . o o
 . . . . . . .    . . o . . . .    . . o . . . .    o o . . . . .    o . o o . . .    o . o o o . .    o . o o . o o    o . . o . o o
     . . .            . . .            . . .            . . .            . . .            . . o            . . o            o . o   
     . . .            . . .            . . .            . . .            . . .            . . .            . . .            o . .   

     o o o            o o o            o o o            o o o            o o o            o o o            o o o            o o o   
     o o o            o o o            o o o            o o o            o o o            o o o            o o o            o o o   
 o o o o . o o    o o o o . o o    o o o o . o o    o o o o . o o    o o o o . o o    o o o o o o o    o o o o o o o    o o o o o o o
 o o o o . o o    o o o o . o o    o o o o . o o    o o o o . o o    o o o o . o o    o o o o o o o    o o o o o o o    o o o . o o o
 o . o o . o o    o . o o . o o    o . . o . o o    o o o . . o o    o o o o o . o    o o o o . . o    o o o . o o o    o o o o o o o
     . . o            . . o            o . o            o . o            o . o            o . o            o . o            o o o   
     o . .            . o o            o o o            o o o            o o o            o o o            o o o            o o o   

Prolog[edit]

Works with SWI-Prolog and module(lambda).

:- use_module(library(lambda)).
 
iq_puzzle :-
iq_puzzle(Moves),
display(Moves).
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% compute solution
%
iq_puzzle(Moves) :-
play([1], [2,3,4,5,6,7,8,9,10,11,12,13,14,15], [], Moves).
 
play(_, [_], Lst, Moves) :-
reverse(Lst, Moves).
 
play(Free, Occupied, Lst, Moves) :-
select(S, Occupied, Oc1),
select(O, Oc1, Oc2),
select(E, Free, F1),
move(S, O, E),
play([S, O | F1], [E | Oc2], [move(S,O,E) | Lst], Moves).
 
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% allowed moves
%
move(S,2,E) :-
member([S,E], [[1,4], [4,1]]).
move(S,3,E) :-
member([S,E], [[1,6], [6,1]]).
move(S,4,E):-
member([S,E], [[2,7], [7,2]]).
move(S,5,E):-
member([S,E], [[2,9], [9,2]]).
move(S,5,E):-
member([S,E], [[3,8], [8,3]]).
move(S,6,E):-
member([S,E], [[3,10], [10,3]]).
move(S,5,E):-
member([S,E], [[4,6], [6,4]]).
move(S,7,E):-
member([S,E], [[4,11], [11,4]]).
move(S,8,E):-
member([S,E], [[4,13], [13,4]]).
move(S,8,E):-
member([S,E], [[5,12], [12,5]]).
move(S,9,E):-
member([S,E], [[5,14], [14,5]]).
move(S,9,E):-
member([S,E], [[6,13], [13,6]]).
move(S,10,E):-
member([S,E], [[6,15], [15,6]]).
move(S,8,E):-
member([S,E], [[9,7], [7,9]]).
move(S,9,E):-
member([S,E], [[10,8], [8,10]]).
move(S,12,E):-
member([S,E], [[11,13], [13,11]]).
move(S,13,E):-
member([S,E], [[12,14], [14,12]]).
move(S,14,E):-
member([S,E], [[15,13], [13,15]]).
 
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display soluce
%
display(Sol) :-
display(Sol, [1]).
 
display([], Free) :-
numlist(1,15, Lst),
maplist(\X^I^(member(X, Free) -> I = 0; I = 1),
Lst,
[I1,I2,I3,I4,I5,I6,I7,I8,I9,I10,I11,I12,I13,I14,I15]),
format(' ~w ~n', [I1]),
format(' ~w ~w ~n', [I2,I3]),
format(' ~w ~w ~w ~n', [I4,I5,I6]),
format(' ~w ~w ~w ~w ~n', [I7,I8,I9,I10]),
format('~w ~w ~w ~w ~w~n', [I11,I12,I13,I14,I15]),
writeln(solved).
 
 
display([move(Start, Middle, End) | Tail], Free) :-
numlist(1,15, Lst),
maplist(\X^I^(member(X, Free) -> I = 0; I = 1),
Lst,
[I1,I2,I3,I4,I5,I6,I7,I8,I9,I10,I11,I12,I13,I14,I15]),
format(' ~w ~n', [I1]),
format(' ~w ~w ~n', [I2,I3]),
format(' ~w ~w ~w ~n', [I4,I5,I6]),
format(' ~w ~w ~w ~w ~n', [I7,I8,I9,I10]),
format('~w ~w ~w ~w ~w~n', [I11,I12,I13,I14,I15]),
format('From ~w to ~w over ~w~n~n~n', [Start, End, Middle]),
select(End, Free, F1),
display(Tail, [Start, Middle | F1]).
 

Output :

 ?- iq_puzzle.
    0        
   1 1      
  1 1 1    
 1 1 1 1  
1 1 1 1 1
From 4 to 1 over 2


    1        
   0 1      
  0 1 1    
 1 1 1 1  
1 1 1 1 1
From 6 to 4 over 5


    1        
   0 1      
  1 0 0    
 1 1 1 1  
1 1 1 1 1
From 1 to 6 over 3


    0        
   0 0      
  1 0 1    
 1 1 1 1  
1 1 1 1 1
From 7 to 2 over 4


    0        
   1 0      
  0 0 1    
 0 1 1 1  
1 1 1 1 1
From 10 to 3 over 6


    0        
   1 1      
  0 0 0    
 0 1 1 0  
1 1 1 1 1
From 12 to 5 over 8


    0        
   1 1      
  0 1 0    
 0 0 1 0  
1 0 1 1 1
From 13 to 6 over 9


    0        
   1 1      
  0 1 1    
 0 0 0 0  
1 0 0 1 1
From 3 to 10 over 6


    0        
   1 0      
  0 1 0    
 0 0 0 1  
1 0 0 1 1
From 2 to 9 over 5


    0        
   0 0      
  0 0 0    
 0 0 1 1  
1 0 0 1 1
From 15 to 6 over 10


    0        
   0 0      
  0 0 1    
 0 0 1 0  
1 0 0 1 0
From 6 to 13 over 9


    0        
   0 0      
  0 0 0    
 0 0 0 0  
1 0 1 1 0
From 14 to 12 over 13


    0        
   0 0      
  0 0 0    
 0 0 0 0  
1 1 0 0 0
From 11 to 13 over 12


    0        
   0 0      
  0 0 0    
 0 0 0 0  
0 0 1 0 0
solved

Bonus : number of solutions :

 ?- setof(L, iq_puzzle(L), LL), length(LL, Len).
LL = [[move(4, 2, 1), move(6, 5, 4), move(1, 3, 6), move(7, 4, 2), move(10, 6, 3), move(12, 8, 5), move(13, 9, 6), move(..., ..., ...)|...], [move(4, 2, 1), move(6, 5, 4), move(1, 3, 6), move(7, 4, 2), move(10, 6, 3), move(12, 8, 5), move(..., ..., ...)|...], [move(4, 2, 1), move(6, 5, 4), move(1, 3, 6), move(7, 4, 2), move(10, 6, 3), move(..., ..., ...)|...], [move(4, 2, 1), move(6, 5, 4), move(1, 3, 6), move(7, 4, 2), move(..., ..., ...)|...], [move(4, 2, 1), move(6, 5, 4), move(1, 3, 6), move(..., ..., ...)|...], [move(4, 2, 1), move(6, 5, 4), move(..., ..., ...)|...], [move(4, 2, 1), move(..., ..., ...)|...], [move(..., ..., ...)|...], [...|...]|...],
Len = 29760.

Python[edit]

#
# Draw board triangle in ascii
#
def DrawBoard(board):
peg = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
for n in xrange(1,16):
peg[n] = '.'
if n in board:
peg[n] = "%X" % n
print "  %s" % peg[1]
print "  %s %s" % (peg[2],peg[3])
print "  %s %s %s" % (peg[4],peg[5],peg[6])
print "  %s %s %s %s" % (peg[7],peg[8],peg[9],peg[10])
print " %s %s %s %s %s" % (peg[11],peg[12],peg[13],peg[14],peg[15])
#
 
# remove peg n from board
def RemovePeg(board,n):
board.remove(n)
 
# Add peg n on board
def AddPeg(board,n):
board.append(n)
 
# return true if peg N is on board else false is empty position
def IsPeg(board,n):
return n in board
 
# A dictionary of valid jump moves index by jumping peg
# then a list of moves where move has jumpOver and LandAt positions
JumpMoves = { 1: [ (2,4),(3,6) ], # 1 can jump over 2 to land on 4, or jumper over 3 to land on 6
2: [ (4,7),(5,9) ],
3: [ (5,8),(6,10) ],
4: [ (2,1),(5,6),(7,11),(8,13) ],
5: [ (8,12),(9,14) ],
6: [ (3,1),(5,4),(9,13),(10,15) ],
7: [ (4,2),(8,9) ],
8: [ (5,3),(9,10) ],
9: [ (5,2),(8,7) ],
10: [ (9,8) ],
11: [ (12,13) ],
12: [ (8,5),(13,14) ],
13: [ (8,4),(9,6),(12,11),(14,15) ],
14: [ (9,5),(13,12) ],
15: [ (10,6),(14,13) ]
}
 
Solution = []
#
# Recursively solve the problem
#
def Solve(board):
#DrawBoard(board)
if len(board) == 1:
return board # Solved one peg left
# try a move for each peg on the board
for peg in xrange(1,16): # try in numeric order not board order
if IsPeg(board,peg):
movelist = JumpMoves[peg]
for over,land in movelist:
if IsPeg(board,over) and not IsPeg(board,land):
saveboard = board[:] # for back tracking
RemovePeg(board,peg)
RemovePeg(board,over)
AddPeg(board,land) # board order changes!
 
Solution.append((peg,over,land))
 
board = Solve(board)
if len(board) == 1:
return board
## undo move and back track when stuck!
board = saveboard[:] # back track
del Solution[-1] # remove last move
return board
 
#
# Remove one peg and start solving
#
def InitSolve(empty):
board = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
RemovePeg(board,empty_start)
Solve(board)
 
#
empty_start = 1
InitSolve(empty_start)
 
board = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
RemovePeg(board,empty_start)
for peg,over,land in Solution:
RemovePeg(board,peg)
RemovePeg(board,over)
AddPeg(board,land) # board order changes!
DrawBoard(board)
print "Peg %X jumped over %X to land on %X\n" % (peg,over,land)
Output:
     1
    . 3
   . 5 6
  7 8 9 A
 B C D E F
Peg 4 jumped over 2 to land on 1

     1
    . 3
   4 . .
  7 8 9 A
 B C D E F
Peg 6 jumped over 5 to land on 4

     .
    . .
   4 . 6
  7 8 9 A
 B C D E F
Peg 1 jumped over 3 to land on 6

     .
    2 .
   . . 6
  . 8 9 A
 B C D E F
Peg 7 jumped over 4 to land on 2

     .
    2 .
   . 5 6
  . . 9 A
 B . D E F
Peg C jumped over 8 to land on 5

     .
    2 .
   . 5 6
  . . 9 A
 B C . . F
Peg E jumped over D to land on C

     .
    2 .
   . 5 .
  . . . A
 B C D . F
Peg 6 jumped over 9 to land on D

     .
    . .
   . . .
  . . 9 A
 B C D . F
Peg 2 jumped over 5 to land on 9

     .
    . .
   . . .
  . . 9 A
 B . . E F
Peg C jumped over D to land on E

     .
    . .
   . . 6
  . . 9 .
 B . . E .
Peg F jumped over A to land on 6

     .
    . .
   . . .
  . . . .
 B . D E .
Peg 6 jumped over 9 to land on D

     .
    . .
   . . .
  . . . .
 B C . . .
Peg E jumped over D to land on C

     .
    . .
   . . .
  . . . .
 . . D . .
Peg B jumped over C to land on D

Racket[edit]

This example is incorrect. Please fix the code and remove this message.
Details: Should the output start 6 jumps 3, then 15 jumps 10 ... rather than 1 jumps 3, then 6 jumps 10 ... ?


Not so fast... The output is correct if one reads the statement differently. The first number is the arrival
position, the second number is the position where the peg is "jumped over" and is to be removed.

The position of where the peg jumps from is not indicated - but it can only be a single possibility in each case.
  • This includes the code to generate the list of available hops (other implementations seem to have the table built in)
  • It produces a full has containing all the possible results from all possible start positions (including ones without valid hops, and unusual starts). It takes no time... and once this is pre-calculated then some of the questions you might want answered about this puzzle can be more easily answered!

Oh and there are some useful triangle numbers functions thrown in for free!

#lang racket
(define << arithmetic-shift)
(define bwbs? bitwise-bit-set?)
;; 1,2,2,3,3,3,4,4,4,4,5,5,5,5,5
;; OEIS: A002024: n appears n times
(define (A002024 n) (exact-floor (+ 1/2 (sqrt (* n 2)))))
;; 1, 1, 2, 1, 2, 3, 1, 2, 3, 4
;; OEIS: A002260: Triangle T(n,k) = k for k = 1..n.
(define (A002260 n) (+ 1 (A002262 (sub1 n))))
;; OEIS: A000217: Triangular numbers: a(n) = C(n+1,2) = n(n+1)/2 = 0+1+2+...+n.
(define (tri n) (* n (sub1 n) 1/2))
;; OEIS: A002262: Triangle read by rows: T(n,k)
(define (A002262 n)
(define trinv (exact-floor (/ (+ 1 (sqrt (+ 1 (* n 8)))) 2)))
(- n (/ (* trinv (- trinv 1)) 2)))
(define row-number A002024)
(define col-number A002260)
(define (r.c->n r c) (and (<= 1 r 5) (<= 1 c r) (+ 1 (tri r) (- c 1))))
 
(define (available-jumps n) ; takes a peg number, and returns a list of (jumped-peg . landing-site)
(define r (row-number n))
(define c (col-number n))
 ;; Six possible directions - although noone gets all six: "J" - landing site, "j" jumped peg
 ;; Triangle Row/column (square edge)
 ;; A . B A.B
 ;; . a b .ab
 ;; C c X d D CcXdD
 ;; . . e f ..ef
 ;;. . E . F ..E.F
(define (N+.n+ r+ c+) (cons (r.c->n (+ r (* 2 r+)) (+ c (* 2 c+))) (r.c->n (+ r r+) (+ c c+))))
(define-values (A.a B.b C.c D.d E.e F.f)
(values (N+.n+ -1 -1) (N+.n+ -1 0) (N+.n+ 0 -1) (N+.n+ 0 1) (N+.n+ 1 0) (N+.n+ 1 1)))
(filter car (list A.a B.b C.c D.d E.e F.f)))
 
(define (available-jumps/bits n0)
(for/list ((A.a (available-jumps (add1 n0))))
(match-define (cons (app sub1 A) (app sub1 a)) A.a)
(list A a (bitwise-ior (<< 1 n0) (<< 1 A) (<< 1 a))))) ; on a hop, these three bits will flip
 
(define avalable-jumps-list/bits (for/vector #:length 15 ((bit 15)) (available-jumps/bits bit)))
 
;; OK -- we'll be complete about this (so it might take a little longer)
;;
;; There are 2^15 possible start configurations; so we'll just systematically go though them, and
;; build an hash of what can go where. Bits are numbered from 0 - peg#1 to 14 - peg#15.
;; It's overkill for finding a single solution, but it seems that Joe Nord needs a lot of questions
;; answered (which should be herein).
(define paths# (make-hash))
(for* ((board (in-range 0 (expt 2 15)))
(peg (in-range 15))
#:when (bwbs? board peg)
(Jjf (in-list (vector-ref avalable-jumps-list/bits peg)))
#:when (bwbs? board (second Jjf)) ; need something to jump
#:unless (bwbs? board (first Jjf))) ; need a clear landing space
(define board- (bitwise-xor board (third Jjf)))
(hash-update! paths# board (λ (old) (cons (cons board- Jjf) old)) null))
 
(define (find-path start end (acc null))
(if (= start end) (reverse acc)
(for*/first
((hop (hash-ref paths# start null))
(inr (in-value (find-path (car hop) end (cons hop acc)))) #:when inr) inr)))
 
(define (display-board board.Jjf)
(match-define (list board (app add1 J) (app add1 j) _) board.Jjf)
(printf "~a jumps ~a ->" J j)
(for* ((r (in-range 1 6))
(c (in-range 1 (add1 r)))
(n (in-value (r.c->n r c))))
(when (= c 1) (printf "~%~a" (make-string (quotient (* 5 (- 5 r)) 2) #\space)))
(printf "[~a] " (~a #:width 2 #:pad-string " " #:align 'right (if (bwbs? board (sub1 n)) n ""))))
(newline))
 
(define (flip-peg p b) (bitwise-xor (<< 1 (sub1 p)) b))
(define empty-board #b000000000000000)
(define full-board #b111111111111111)
 
;; Solve #1 missing -> #13 left alone
(for-each display-board (find-path (flip-peg 1 full-board) (flip-peg 13 empty-board)))
Output:
1 jumps 3 ->
          [ 1] 
       [ 2] [  ] 
     [ 4] [ 5] [  ] 
  [ 7] [ 8] [ 9] [10] 
[11] [12] [13] [14] [15] 
6 jumps 10 ->
          [ 1] 
       [ 2] [  ] 
     [ 4] [ 5] [ 6] 
  [ 7] [ 8] [ 9] [  ] 
[11] [12] [13] [14] [  ] 
10 jumps 9 ->
          [ 1] 
       [ 2] [  ] 
     [ 4] [ 5] [ 6] 
  [ 7] [  ] [  ] [10] 
[11] [12] [13] [14] [  ] 
3 jumps 6 ->
          [ 1] 
       [ 2] [ 3] 
     [ 4] [ 5] [  ] 
  [ 7] [  ] [  ] [  ] 
[11] [12] [13] [14] [  ] 
9 jumps 5 ->
          [ 1] 
       [  ] [ 3] 
     [ 4] [  ] [  ] 
  [ 7] [  ] [ 9] [  ] 
[11] [12] [13] [14] [  ] 
5 jumps 9 ->
          [ 1] 
       [  ] [ 3] 
     [ 4] [ 5] [  ] 
  [ 7] [  ] [  ] [  ] 
[11] [12] [13] [  ] [  ] 
14 jumps 13 ->
          [ 1] 
       [  ] [ 3] 
     [ 4] [ 5] [  ] 
  [ 7] [  ] [  ] [  ] 
[11] [  ] [  ] [14] [  ] 
2 jumps 4 ->
          [ 1] 
       [ 2] [ 3] 
     [  ] [ 5] [  ] 
  [  ] [  ] [  ] [  ] 
[11] [  ] [  ] [14] [  ] 
8 jumps 5 ->
          [ 1] 
       [ 2] [  ] 
     [  ] [  ] [  ] 
  [  ] [ 8] [  ] [  ] 
[11] [  ] [  ] [14] [  ] 
4 jumps 2 ->
          [  ] 
       [  ] [  ] 
     [ 4] [  ] [  ] 
  [  ] [ 8] [  ] [  ] 
[11] [  ] [  ] [14] [  ] 
13 jumps 8 ->
          [  ] 
       [  ] [  ] 
     [  ] [  ] [  ] 
  [  ] [  ] [  ] [  ] 
[11] [  ] [13] [14] [  ] 
12 jumps 13 ->
          [  ] 
       [  ] [  ] 
     [  ] [  ] [  ] 
  [  ] [  ] [  ] [  ] 
[11] [12] [  ] [  ] [  ] 
13 jumps 12 ->
          [  ] 
       [  ] [  ] 
     [  ] [  ] [  ] 
  [  ] [  ] [  ] [  ] 
[  ] [  ] [13] [  ] [  ]

Ruby[edit]

# Solitaire Like Puzzle Solver - Nigel Galloway: October 18th., 2014
G = [[0,1,3],[0,2,5],[1,3,6],[1,4,8],[2,4,7],[2,5,9],[3,4,5],[3,6,10],[3,7,12],[4,7,11],[4,8,13],[5,8,12],[5,9,14],[6,7,8],[7,8,9],[10,11,12],[11,12,13],[12,13,14],
[3,1,0],[5,2,0],[6,3,1],[8,4,1],[7,4,2],[9,5,2],[5,4,3],[10,6,3],[12,7,3],[11,7,4],[13,8,4],[12,8,5],[14,9,5],[8,7,6],[9,8,7],[12,11,10],[13,12,11],[14,13,12]]
FORMAT = (1..5).map{|i| " "*(5-i)+"%d "*i+"\n"}.join+"\n"
def solve n,i,g
return "Solved" if i == 1
return false unless n[g[0]]==0 and n[g[1]]==1 and n[g[2]]==1
e = n.clone; g.each{|n| e[n] = 1 - e[n]}
l=false; G.each{|g| l=solve(e,i-1,g); break if l}
return l ? "#{g[0]} to #{g[2]}\n" + FORMAT % e + l : l
end
puts FORMAT % (N=[0,1,1,1,1,1,1,1,1,1,1,1,1,1,1])
l=false; G.each{|g| l=solve(N,N.inject(:+),g); break if l}
puts l ? l : "No solution found"
 
Output:
    0 
   1 1 
  1 1 1 
 1 1 1 1 
1 1 1 1 1 

3 to 0
    1 
   0 1 
  0 1 1 
 1 1 1 1 
1 1 1 1 1 

8 to 1
    1 
   1 1 
  0 0 1 
 1 1 0 1 
1 1 1 1 1 

10 to 3
    1 
   1 1 
  1 0 1 
 0 1 0 1 
0 1 1 1 1 

1 to 6
    1 
   0 1 
  0 0 1 
 1 1 0 1 
0 1 1 1 1 

11 to 4
    1 
   0 1 
  0 1 1 
 1 0 0 1 
0 0 1 1 1 

2 to 7
    1 
   0 0 
  0 0 1 
 1 1 0 1 
0 0 1 1 1 

9 to 2
    1 
   0 1 
  0 0 0 
 1 1 0 0 
0 0 1 1 1 

0 to 5
    0 
   0 0 
  0 0 1 
 1 1 0 0 
0 0 1 1 1 

6 to 8
    0 
   0 0 
  0 0 1 
 0 0 1 0 
0 0 1 1 1 

13 to 11
    0 
   0 0 
  0 0 1 
 0 0 1 0 
0 1 0 0 1 

5 to 12
    0 
   0 0 
  0 0 0 
 0 0 0 0 
0 1 1 0 1 

11 to 13
    0 
   0 0 
  0 0 0 
 0 0 0 0 
0 0 0 1 1 

14 to 12
    0 
   0 0 
  0 0 0 
 0 0 0 0 
0 0 1 0 0 

Solved

Sidef[edit]

Translation of: Ruby
const N = [0,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
 
const G = [
[ 0, 1, 3],[ 0, 2, 5],[ 1, 3, 6],
[ 1, 4, 8],[ 2, 4, 7],[ 2, 5, 9],
[ 3, 4, 5],[ 3, 6,10],[ 3, 7,12],
[ 4, 7,11],[ 4, 8,13],[ 5, 8,12],
[ 5, 9,14],[ 6, 7, 8],[ 7, 8, 9],
[10,11,12],[11,12,13],[12,13,14],
]
 
const format = ({"#{' '*(5-_)}#{'%d '*_}\n"}.map(1..5).join + "\n")
 
func solve(n, i, g) is cached {
i == N.end && return "Solved"
n[g[1]] == 0 && return nil
 
var s = given(n[g[0]]) {
when(0) {
n[g[2]] == 0 && return nil
"#{g[2]} to #{g[0]}\n"
}
default {
n[g[2]] == 1 && return nil
"#{g[0]} to #{g[2]}\n"
}
}
 
var a = n.clone
g.each {|n| a[n] = 1-a[n] }
var r = ''
G.each {|g| (r = solve(a, i+1, g)) && break }
r ? (s + (format % (a...)) + r) : r
}
 
format.printf(N...)
 
var r = ''
G.each {|g| (r = solve(N, 1, g)) && break }
say (r ? r : "No solution found")
Output:
    0 
   1 1 
  1 1 1 
 1 1 1 1 
1 1 1 1 1 

3 to 0
    1 
   0 1 
  0 1 1 
 1 1 1 1 
1 1 1 1 1 

8 to 1
    1 
   1 1 
  0 0 1 
 1 1 0 1 
1 1 1 1 1 

10 to 3
    1 
   1 1 
  1 0 1 
 0 1 0 1 
0 1 1 1 1 

1 to 6
    1 
   0 1 
  0 0 1 
 1 1 0 1 
0 1 1 1 1 

11 to 4
    1 
   0 1 
  0 1 1 
 1 0 0 1 
0 0 1 1 1 

2 to 7
    1 
   0 0 
  0 0 1 
 1 1 0 1 
0 0 1 1 1 

9 to 2
    1 
   0 1 
  0 0 0 
 1 1 0 0 
0 0 1 1 1 

0 to 5
    0 
   0 0 
  0 0 1 
 1 1 0 0 
0 0 1 1 1 

6 to 8
    0 
   0 0 
  0 0 1 
 0 0 1 0 
0 0 1 1 1 

13 to 11
    0 
   0 0 
  0 0 1 
 0 0 1 0 
0 1 0 0 1 

5 to 12
    0 
   0 0 
  0 0 0 
 0 0 0 0 
0 1 1 0 1 

11 to 13
    0 
   0 0 
  0 0 0 
 0 0 0 0 
0 0 0 1 1 

14 to 12
    0 
   0 0 
  0 0 0 
 0 0 0 0 
0 0 1 0 0 

Solved

Visual Basic .NET[edit]

Notes: This program uses a brute-force method with a string of 25 characters to internally represent the 15 spots on the peg board. One can set the starting removed peg and intended last remaining peg by editing the header variable declarations named Starting and Target. If one doesn't care which spot the last peg lands on, the Target variable can be set to 0. The constant n can be changed for different sized peg boards, for example with n = 6 the peg board would have 21 positions.

 
Imports System, Microsoft.VisualBasic.DateAndTime
 
Public Module Module1
Const n As Integer = 5 ' extent of board
Dim Board As String ' the peg board
Dim Starting As Integer = 1 ' position on board where first peg has been removed
Dim Target As Integer = 13 ' final peg position, use 0 to solve for any postion
Dim Moves As Integer() ' possible offset moves on grid
Dim bi() As Integer ' string position to peg location index
Dim ib() As Integer ' string position to peg location reverse index
Dim nl As Char = Convert.ToChar(10) ' newline character
 
' expands each line of the board properly
Public Function Dou(s As String) As String
Dou = "" : Dim b As Boolean = True
For Each ch As Char In s
If b Then b = ch <> " "
If b Then Dou &= ch & " " Else Dou = " " & Dou
Next : Dou = Dou.TrimEnd()
End Function
 
' formats the string representaion of a board into a viewable item
Public Function Fmt(s As String) As String
If s.Length < Board.Length Then Return s
Fmt = "" : For i As Integer = 1 To n : Fmt &= Dou(s.Substring(i * n - n, n)) &
If(i = n, s.Substring(Board.Length), "") & nl
Next
End Function
 
' returns triangular number of n
Public Function Triangle(n As Integer) As Integer
Return (n * (n + 1)) / 2
End Function
 
' returns an initialized board with one peg missing
Public Function Init(s As String, pos As Integer) As String
Init = s : Mid(Init, pos, 1) = "0"
End Function
 
' initializes string-to-board position indices
Public Sub InitIndex()
ReDim bi(Triangle(n)), ib(n * n) : Dim j As Integer = 0
For i As Integer = 0 To ib.Length - 1
If i = 0 Then
ib(i) = 0 : bi(j) = 0 : j += 1
Else
If Board(i - 1) = "1" Then ib(i) = j : bi(j) = i : j += 1
End If
Next
End Sub
 
' brute-force solver, returns either the steps of a solution, or the string "fail"
Public Function solve(brd As String, pegsLeft As Integer) As String
If pegsLeft = 1 Then ' down to the last one, see if it's the correct one
If Target = 0 Then Return "Completed" ' don't care where the last one is
If brd(bi(Target) - 1) = "1" Then Return "Completed" Else Return "fail"
End If
For i = 1 To Board.Length ' for each possible position...
If brd(i - 1) = "1" Then ' that still has a peg...
For Each mj In Moves ' for each possible move
Dim over As Integer = i + mj ' the position to jump over
Dim land As Integer = i + 2 * mj ' the landing spot
' ensure landing spot is on the board, then check for a valid pattern
If land >= 1 AndAlso land <= brd.Length _
AndAlso brd(land - 1) = "0" _
AndAlso brd(over - 1) = "1" Then
setPegs(brd, "001", i, over, land) ' make a move
' recursively send it out to test
Dim Res As String = solve(brd.Substring(0, Board.Length), pegsLeft - 1)
' check result, returing if OK
If Res.Length <> 4 Then _
Return brd & info(i, over, land) & nl & Res
setPegs(brd, "110", i, over, land) ' not OK, so undo the move
End If
Next
End If
Next
Return "fail"
End Function
 
' returns a text representation of peg movement for each turn
Function info(frm As Integer, over As Integer, dest As Integer) As String
Return " Peg from " & ib(frm).ToString() & " goes to " & ib(dest).ToString() &
", removing peg at " & ib(over).ToString()
End Function
 
' sets three pegs as once, used for making and un-doing moves
Sub setPegs(ByRef board As String, pat As String, a As Integer, b As Integer, c As Integer)
Mid(board, a, 1) = pat(0) : Mid(board, b, 1) = pat(1) : Mid(board, c, 1) = pat(2)
End Sub
 
' limit an integer to a range
Sub LimitIt(ByRef x As Integer, lo As Integer, hi As Integer)
x = Math.Max(Math.Min(x, hi), lo)
End Sub
 
Public Sub Main()
Dim t As Integer = Triangle(n) ' use the nth triangular number for bounds
LimitIt(Starting, 1, t) ' ensure valid parameters for staring and ending positions
LimitIt(Target, 0, t)
Dim stime As Date = Now() ' keep track of start time for performance result
Moves = {-n - 1, -n, -1, 1, n, n + 1} ' possible offset moves on a nxn grid
Board = New String("1", n * n) ' init string representation of board
For i As Integer = 0 To n - 2 ' and declare non-existent spots
Mid(Board, i * (n + 1) + 2, n - 1 - i) = New String(" ", n - 1 - i)
Next
InitIndex() ' create indicies from board's pattern
Dim B As String = Init(Board, bi(Starting)) ' remove first peg
Console.WriteLine(Fmt(B & " Starting with peg removed from " & Starting.ToString()))
Dim res As String() = solve(B.Substring(0, B.Length), t - 1).Split(nl)
Dim ts As String = (Now() - stime).TotalMilliseconds.ToString() & " ms."
If res(0).Length = 4 Then
If Target = 0 Then
Console.WriteLine("Unable to find a solution with last peg left anywhere.")
Else
Console.WriteLine("Unable to find a solution with last peg left at " &
Target.ToString() & ".")
End If
Console.WriteLine("Computation time: " & ts)
Else
For Each Sol As String In res : Console.WriteLine(Fmt(Sol)) : Next
Console.WriteLine("Computation time to first found solution: " & ts)
End If
If Diagnostics.Debugger.IsAttached Then Console.ReadLine()
End Sub
End Module
Output:

A full solution:

    0
   1 1
  1 1 1
 1 1 1 1
1 1 1 1 1  Starting with peg removed from 1

    1
   0 1
  0 1 1
 1 1 1 1
1 1 1 1 1  Peg from 4 goes to 1, removing peg at 2

    1
   0 1
  1 0 0
 1 1 1 1
1 1 1 1 1  Peg from 6 goes to 4, removing peg at 5

    0
   0 0
  1 0 1
 1 1 1 1
1 1 1 1 1  Peg from 1 goes to 6, removing peg at 3

    0
   1 0
  0 0 1
 0 1 1 1
1 1 1 1 1  Peg from 7 goes to 2, removing peg at 4

    0
   1 1
  0 0 0
 0 1 1 0
1 1 1 1 1  Peg from 10 goes to 3, removing peg at 6

    0
   1 1
  0 1 0
 0 0 1 0
1 0 1 1 1  Peg from 12 goes to 5, removing peg at 8

    0
   1 1
  0 1 1
 0 0 0 0
1 0 0 1 1  Peg from 13 goes to 6, removing peg at 9

    0
   0 1
  0 0 1
 0 0 1 0
1 0 0 1 1  Peg from 2 goes to 9, removing peg at 5

    0
   0 0
  0 0 0
 0 0 1 1
1 0 0 1 1  Peg from 3 goes to 10, removing peg at 6

    0
   0 0
  0 0 1
 0 0 1 0
1 0 0 1 0  Peg from 15 goes to 6, removing peg at 10

    0
   0 0
  0 0 0
 0 0 0 0
1 0 1 1 0  Peg from 6 goes to 13, removing peg at 9

    0
   0 0
  0 0 0
 0 0 0 0
1 1 0 0 0  Peg from 14 goes to 12, removing peg at 13

    0
   0 0
  0 0 0
 0 0 0 0
0 0 1 0 0  Peg from 11 goes to 13, removing peg at 12

Completed
Computation time to first found solution: 15.6086 ms.

A failed solution:

    1
   0 1
  1 1 1
 1 1 1 1
1 1 1 1 1  Starting with peg removed from 2

Unable to find a solution with last peg left at 13.
Computation time: 1656.2754 ms.

zkl[edit]

Translation of: D
Translation of: Ruby
var N=T(0,1,1,1,1,1,1,1,1,1,1,1,1,1,1);
var G=T( T(0,1, 3), T(0,2, 5), T(1,3, 6), T( 1, 4, 8), T( 2, 4, 7), T( 2, 5, 9),
T(3,4, 5), T(3,6,10), T(3,7,12), T( 4, 7,11), T( 4, 8,13), T( 5, 8,12),
T(5,9,14), T(6,7, 8), T(7,8, 9), T(10,11,12), T(11,12,13), T(12,13,14));
 
fcn b2s(n){
var fmt=[1..5].pump(String,fcn(i){ String(" "*(5 - i),"%d "*i,"\n") });
fmt.fmt(n.xplode())
}
 
fcn solve(n,i,g){ // --> False|String
if (i==N.len() - 1) return("\nSolved");
if (n[g[1]]==0) return(False);
 
reg s;
if (n[g[0]]==0){
if(n[g[2]]==0) return(False);
s="\n%d to %d\n".fmt(g[2],g[0]);
} else {
if(n[g[2]]==1) return(False);
s="\n%d to %d\n".fmt(g[0],g[2]);
}
 
a:=n.copy();
foreach gi in (g){ a[gi]=1 - a[gi]; }
reg l; // auto sets to Void
foreach gi in (G){ if(l=solve(a,i + 1,gi)) break; }
l and String(s,b2s(a),l)
}
 
b2s(N).print();
 
reg l;
foreach g in (G){ if(l=solve(N,1,g)) break; }
println(l and l or "No solution found.");
Output:
    0 
   1 1 
  1 1 1 
 1 1 1 1 
1 1 1 1 1 

3 to 0
    1 
   0 1 
  0 1 1 
 1 1 1 1 
1 1 1 1 1 

8 to 1
    1 
   1 1 
  0 0 1 
 1 1 0 1 
1 1 1 1 1 

10 to 3
    1 
   1 1 
  1 0 1 
 0 1 0 1 
0 1 1 1 1 

1 to 6
    1 
   0 1 
  0 0 1 
 1 1 0 1 
0 1 1 1 1 

11 to 4
    1 
   0 1 
  0 1 1 
 1 0 0 1 
0 0 1 1 1 

2 to 7
    1 
   0 0 
  0 0 1 
 1 1 0 1 
0 0 1 1 1 

9 to 2
    1 
   0 1 
  0 0 0 
 1 1 0 0 
0 0 1 1 1 

0 to 5
    0 
   0 0 
  0 0 1 
 1 1 0 0 
0 0 1 1 1 

6 to 8
    0 
   0 0 
  0 0 1 
 0 0 1 0 
0 0 1 1 1 

13 to 11
    0 
   0 0 
  0 0 1 
 0 0 1 0 
0 1 0 0 1 

5 to 12
    0 
   0 0 
  0 0 0 
 0 0 0 0 
0 1 1 0 1 

11 to 13
    0 
   0 0 
  0 0 0 
 0 0 0 0 
0 0 0 1 1 

14 to 12
    0 
   0 0 
  0 0 0 
 0 0 0 0 
0 0 1 0 0 

Solved