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.

11l

Translation of: Python

<lang 11l>F DrawBoard(board)

  V peg = [‘’] * 16
  L(n) 1.<16
     peg[n] = ‘.’
     I n C board
        peg[n] = hex(n)
  print(‘     #.’.format(peg[1]))
  print(‘    #. #.’.format(peg[2], peg[3]))
  print(‘   #. #. #.’.format(peg[4], peg[5], peg[6]))
  print(‘  #. #. #. #.’.format(peg[7], peg[8], peg[9], peg[10]))
  print(‘ #. #. #. #. #.’.format(peg[11], peg[12], peg[13], peg[14], peg[15]))

F RemovePeg(&board, n)

  board.remove(n)

F AddPeg(&board, n)

  board.append(n)

F IsPeg(board, n)

  R n C board

V JumpMoves = [1 = [(2, 4), (3, 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)]]

[(Int, Int, Int)] Solution

F Solve(=board)

  I board.len == 1
     R board

  L(peg) 1.<16
     I IsPeg(board, peg)
        V movelist = JumpMoves[peg]
        L(over, land) movelist
           I IsPeg(board, over) & !IsPeg(board, land)
              V saveboard = copy(board)
              RemovePeg(&board, peg)
              RemovePeg(&board, over)
              AddPeg(&board, land)

              Solution.append((peg, over, land))

              board = Solve(board)
              I board.len == 1
                 R board
              board = copy(saveboard)
              Solution.pop()

  R board

F InitSolve(empty)

  V board = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
  RemovePeg(&board, empty)
  Solve(board)

V empty_start = 1 InitSolve(empty_start)

V board = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15] RemovePeg(&board, empty_start) L(peg, over, land) Solution

  RemovePeg(&board, peg)
  RemovePeg(&board, over)
  AddPeg(&board, land)
  DrawBoard(board)
  print("Peg #. jumped over #. to land on #.\n".format(hex(peg), hex(over), hex(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

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$

Java

Print the number of solutions for each start and end combination.

Print one possible solution.

<lang Java> import java.util.ArrayList; import java.util.Arrays; import java.util.HashMap; import java.util.List; import java.util.Map; import java.util.Stack;

public class IQPuzzle {

   public static void main(String[] args) {
       System.out.printf("  ");
       for ( int start = 1 ; start < Puzzle.MAX_PEGS ; start++ ) {
           System.out.printf("  %,6d", start);
       }
       System.out.printf("%n");
       for ( int start = 1 ; start < Puzzle.MAX_PEGS ; start++ ) {
           System.out.printf("%2d", start);
           Map<Integer,Integer> solutions = solve(start);    
           for ( int end = 1 ; end < Puzzle.MAX_PEGS ; end++ ) {
               System.out.printf("  %,6d", solutions.containsKey(end) ? solutions.get(end) : 0);
           }
           System.out.printf("%n");
       }
       int moveNum = 0;
       System.out.printf("%nOne Solution:%n");
       for ( Move m : oneSolution ) {
           moveNum++;
           System.out.printf("Move %d = %s%n", moveNum, m);
       }
   }
   
   private static List<Move> oneSolution = null;
   
   private static Map<Integer, Integer> solve(int emptyPeg) {
       Puzzle puzzle = new Puzzle(emptyPeg);
       Map<Integer,Integer> solutions = new HashMap<>();
       Stack<Puzzle> stack = new Stack<Puzzle>();
       stack.push(puzzle);
       while ( ! stack.isEmpty() ) {
           Puzzle p = stack.pop();
           if ( p.solved() ) {
               solutions.merge(p.getLastPeg(), 1, (v1,v2) -> v1 + v2);
               if ( oneSolution == null ) {
                   oneSolution = p.moves;
               }
               continue;
           }
           for ( Move move : p.getValidMoves() ) {
               Puzzle pMove = p.move(move);
               stack.add(pMove);
           }
       }
       //System.out.println("Puzzles tested = " + puzzlesTested);
       return solutions;
   }
   
   private static class Puzzle {
       
       public static int MAX_PEGS = 16;
       private boolean[] pegs = new boolean[MAX_PEGS];  //  true : peg in hole.  false : hole is empty.
       
       private List<Move> moves;

       public Puzzle(int emptyPeg) {
           for ( int i = 1 ; i < MAX_PEGS ; i++ ) {
               pegs[i] = true;
           }
           pegs[emptyPeg] = false;
           moves = new ArrayList<>();
       }

       public Puzzle() {
           for ( int i = 1 ; i < MAX_PEGS ; i++ ) {
               pegs[i] = true;
           }
           moves = new ArrayList<>();
       }

       private static Map<Integer,List<Move>> validMoves = new HashMap<>(); 
       static {
           validMoves.put(1, Arrays.asList(new Move(1, 2, 4), new Move(1, 3, 6)));
           validMoves.put(2, Arrays.asList(new Move(2, 4, 7), new Move(2, 5, 9)));
           validMoves.put(3, Arrays.asList(new Move(3, 5, 8), new Move(3, 6, 10)));
           validMoves.put(4, Arrays.asList(new Move(4, 2, 1), new Move(4, 5, 6), new Move(4, 8, 13), new Move(4, 7, 11)));
           validMoves.put(5, Arrays.asList(new Move(5, 8, 12), new Move(5, 9, 14)));
           validMoves.put(6, Arrays.asList(new Move(6, 3, 1), new Move(6, 5, 4), new Move(6, 9, 13), new Move(6, 10, 15)));
           validMoves.put(7, Arrays.asList(new Move(7, 4, 2), new Move(7, 8, 9)));
           validMoves.put(8, Arrays.asList(new Move(8, 5, 3), new Move(8, 9, 10)));
           validMoves.put(9, Arrays.asList(new Move(9, 5, 2), new Move(9, 8, 7)));
           validMoves.put(10, Arrays.asList(new Move(10, 6, 3), new Move(10, 9, 8)));
           validMoves.put(11, Arrays.asList(new Move(11, 7, 4), new Move(11, 12, 13)));
           validMoves.put(12, Arrays.asList(new Move(12, 8, 5), new Move(12, 13, 14)));
           validMoves.put(13, Arrays.asList(new Move(13, 12, 11), new Move(13, 8, 4), new Move(13, 9, 6), new Move(13, 14, 15)));
           validMoves.put(14, Arrays.asList(new Move(14, 13, 12), new Move(14, 9, 5)));
           validMoves.put(15, Arrays.asList(new Move(15, 14, 13), new Move(15, 10, 6)));
       }
       
       public List<Move> getValidMoves() {
           List<Move> moves = new ArrayList<Move>();
           for ( int i = 1 ; i < MAX_PEGS ; i++ ) {
               if ( pegs[i] ) {
                   for ( Move testMove : validMoves.get(i) ) {
                       if ( pegs[testMove.jump] && ! pegs[testMove.end] ) {
                           moves.add(testMove);
                       }
                   }
               }
           }
           return moves;
       }

       public boolean solved() {
           boolean foundFirstPeg = false;
           for ( int i = 1 ; i < MAX_PEGS ; i++ ) {
               if ( pegs[i] ) {
                   if ( foundFirstPeg ) {
                       return false;
                   }
                   foundFirstPeg = true;
               }
           }
           return true;
       }
       
       public Puzzle move(Move move) {
           Puzzle p = new Puzzle();
           if ( ! pegs[move.start] || ! pegs[move.jump] || pegs[move.end] ) {
               throw new RuntimeException("Invalid move.");
           }
           for ( int i = 1 ; i < MAX_PEGS ; i++ ) {
               p.pegs[i] = pegs[i];
           }
           p.pegs[move.start] = false;
           p.pegs[move.jump] = false;
           p.pegs[move.end] = true;
           for ( Move m : moves ) {
               p.moves.add(new Move(m.start, m.jump, m.end));
           }
           p.moves.add(new Move(move.start, move.jump, move.end));
           return p;
       }
       
       public int getLastPeg() {
           for ( int i = 1 ; i < MAX_PEGS ; i++ ) {
               if ( pegs[i] ) {
                   return i;
               }
           }
           throw new RuntimeException("ERROR:  Illegal position.");
       }
       
       @Override
       public String toString() {
           StringBuilder sb = new StringBuilder();
           sb.append("[");
           for ( int i = 1 ; i < MAX_PEGS ; i++ ) {
               sb.append(pegs[i] ? 1 : 0);
               sb.append(",");
           }
           sb.setLength(sb.length()-1);            
           sb.append("]");
           return sb.toString();
       }
   }
   
   private static class Move {
       int start;
       int jump;
       int end;
       
       public Move(int s, int j, int e) {
           start = s; jump = j; end = e;
       }
       
       @Override
       public String toString() {
           StringBuilder sb = new StringBuilder();
           sb.append("{");
           sb.append("s=" + start);
           sb.append(", j=" + jump);
           sb.append(", e=" + end);
           sb.append("}");
           return sb.toString();
       }
   }

} </lang>

Output:

         1       2       3       4       5       6       7       8       9      10      11      12      13      14      15
 1   6,816       0       0       0       0       0   3,408       0       0   3,408       0       0  16,128       0       0
 2       0     720       0       0       0   8,064       0       0       0       0   3,408       0       0   2,688       0
 3       0       0     720   8,064       0       0       0       0       0       0       0   2,688       0       0   3,408
 4       0       0   8,064  51,452       0       0       0       0   1,550       0       0   8,064       0       0  16,128
 5       0       0       0       0       0       0       0       0       0       0       0       0   1,550       0       0
 6       0   8,064       0       0       0  51,452       0   1,550       0       0  16,128       0       0   8,064       0
 7   3,408       0       0       0       0       0     720       0       0   2,688       0       0   8,064       0       0
 8       0       0       0       0       0   1,550       0       0       0       0       0       0       0       0       0
 9       0       0       0   1,550       0       0       0       0       0       0       0       0       0       0       0
10   3,408       0       0       0       0       0   2,688       0       0     720       0       0   8,064       0       0
11       0   3,408       0       0       0  16,128       0       0       0       0   6,816       0       0   3,408       0
12       0       0   2,688   8,064       0       0       0       0       0       0       0     720       0       0   3,408
13  16,128       0       0       0   1,550       0   8,064       0       0   8,064       0       0  51,452       0       0
14       0   2,688       0       0       0   8,064       0       0       0       0   3,408       0       0     720       0
15       0       0   3,408  16,128       0       0       0       0       0       0       0   3,408       0       0   6,816

One Solution:
Move 1 = {s=6, j=3, e=1}
Move 2 = {s=15, j=10, e=6}
Move 3 = {s=8, j=9, e=10}
Move 4 = {s=10, j=6, e=3}
Move 5 = {s=2, j=5, e=9}
Move 6 = {s=14, j=9, e=5}
Move 7 = {s=12, j=13, e=14}
Move 8 = {s=7, j=4, e=2}
Move 9 = {s=3, j=5, e=8}
Move 10 = {s=1, j=2, e=4}
Move 11 = {s=4, j=8, e=13}
Move 12 = {s=14, j=13, e=12}
Move 13 = {s=11, j=12, e=13}

Julia

Translation of: Raku

<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 = ["Starting board:\n" * triangletext([0; ones(Int, 14)]) * "\n"]

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([solutiontext[1]; reverse(solutiontext[2:end])], ""))
       break
   elseif i == length(moves) 
       println("No solution found.")
   end

end

</lang>

Output:

Starting board:
      0
    1  1
   1  1  1
 1  1  1  1
1  1  1  1  1

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: Raku

<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

Phix

Library: Phix/basics

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 (also in demo\rosetta\IQpuzzle.exw):

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

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] [  ] [  ]

Raku

(formerly 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

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.

Wren

Translation of: Kotlin

Library: Wren-fmt

<lang ecmascript>import "/fmt" for Conv, Fmt

var board = List.filled(16, true) board[0] = false

var jumpMoves = [

   [ ],
   [ [ 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 = []

var drawBoard = Fn.new {

   var pegs = List.filled(16, "-")
   for (i in 1..15) if (board[i]) pegs[i] = Conv.Itoa(i, 16)
   Fmt.print("       $s", pegs[1])
   Fmt.print("      $s $s", pegs[2], pegs[3])
   Fmt.print("     $s $s $s", pegs[4], pegs[5], pegs[6])
   Fmt.print("    $s $s $s $s", pegs[7], pegs[8], pegs[9], pegs[10])
   Fmt.print("   $s $s $s $s $s", pegs[11], pegs[12], pegs[13], pegs[14], pegs[15])

}

var solved = Fn.new { board.count { |peg| peg } == 1 } // just one peg left

var solve // recursive so need to pre-declare solve = Fn.new {

   if (solved.call()) return
   for (peg in 1..15) {
       if (board[peg]) {
           for (ol in jumpMoves[peg]) {
               var over = ol[0]
               var land = ol[1]
               if (board[over] && !board[land]) {
                   var saveBoard = board.toList
                   board[peg]  = false
                   board[over] = false
                   board[land] = true
                   solutions.add([peg, over, land])
                   solve.call()
                   if (solved.call()) return // otherwise back-track
                   board = saveBoard
                   solutions.removeAt(-1)
               }
           }
       }
   }

}

var emptyStart = 1 board[emptyStart] = false solve.call() board = List.filled(16, true) board[0] = false board[emptyStart] = false drawBoard.call() Fmt.print("Starting with peg $X removed\n", emptyStart) for (sol in solutions) {

   var peg =  sol[0]
   var over = sol[1]
   var land = sol[2]
   board[peg]  = false
   board[over] = false
   board[land] = true
   drawBoard.call()
   Fmt.print("Peg $X jumped over $X to land on $X\n", peg, over, land)

}</lang>

Output:

Same as Kotlin entry.

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: