Solve triangle solitaire puzzle: Difference between revisions

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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

Translation of: Ruby

<lang d>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);

}</lang>

Output:

Elixir

Inspired by Ruby <lang elixir>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</lang>

Output:

Go

Translation of: Kotlin

<lang go>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}},
   Template:9, 8,
   Template: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)
   }

}</lang>

Output:

Same as Kotlin entry

J

<lang J> 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.

) </lang> 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$

Julia

Translation of: Perl 6

<lang julia>moves = [[1, 2, 4], [1, 3, 6], [2, 4, 7], [2, 5, 9], [3, 5, 8], [3, 6, 10], [4, 5, 6],

        [4, 7, 11], [4, 8, 13], [5, 8, 12], [5, 9, 14], [6, 9, 13], [6, 10, 15],
        [7, 8, 9], [8, 9, 10],  [11, 12, 13], [12, 13, 14], [13, 14, 15]]

triangletext(v) = join(map(i -> " "^([6,4,3,1,0][i]) * join(map(x -> rpad(x, 3),

   v[div(i*i-i+2,2):div(i*(i+1),2)]), ""), 1:5), "\n")

const solutiontext = String[]

function solve(mv, turns=1, bd=[0; ones(Int, 14)])

   if turns + 1 == length(bd)
       return true
   elseif bd[mv[2]] == 0 || (bd[mv[1]] == 0 && bd[mv[3]] == 0) || (bd[mv[3]] == 1 && bd[mv[1]] == 1)
       return false
   else
       movetext = "\nmove " * (bd[mv[1]] == 0 ? "$(mv[3]) to $(mv[1])" : "$(mv[1]) to $(mv[3])")
       newboard = deepcopy(bd)
       map(i -> newboard[i] = 1 - newboard[i], mv)
       for move in moves
           if solve(move, turns + 1, newboard)
               push!(solutiontext, (movetext * "\n" * triangletext(newboard) * "\n"))
               return true
           end
       end
   end
   false

end

for (i, move) in enumerate(moves)

   if solve(move)
       println(join(reverse(solutiontext), ""))
       break
   elseif i == length(moves) 
       println("No solution found.")
   end

end

</lang>

Output:

move 4 to 1
      1
    0  1
   0  1  1
 1  1  1  1
1  1  1  1  1

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

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

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

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

move 3 to 8
      1
    0  0
   0  0  1
 1  1  0  1
0  0  1  1  1

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

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

move 7 to 9
      0
    0  0
   0  0  1
 0  0  1  0
0  0  1  1  1

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

move 6 to 13
      0
    0  0
   0  0  0
 0  0  0  0
0  1  1  0  1

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

move 15 to 13
      0
    0  0
   0  0  0
 0  0  0  0
0  0  1  0  0

Kotlin

Translation of: Python

<lang scala>// 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))
   }

}</lang>

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

Translation of: Perl 6

<lang perl>@start = qw<

>;

@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"; </lang>

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

Works with: Rakudo version 2017.05

Translation of: Sidef

<lang perl6> constant @start = <

>».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";</lang>

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

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). <lang Phix>-- -- 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),"-"," "))</lang>

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: <lang Phix>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),"-"," "))</lang>

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

Works with SWI-Prolog and module(lambda).

<lang Prolog>:- 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]). </lang> 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

<lang Python>#

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)</lang>

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

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>#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)))</lang>

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

<lang ruby># 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" </lang>

Output:

Sidef

Translation of: Ruby

<lang 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")</lang>

Output:

Visual Basic .NET

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. <lang vbnet> 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</lang>

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

Translation of: D

Translation of: Ruby

<lang zkl>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.");</lang>

Output: