Peg Solitaire Solver
How to use the peg solitaire solver
Choose the board and where the last peg should end, then set up the position: tap a hole to put a peg in or take one out. Fill every hole and then tap one peg away to make the usual single starting gap. Press Solve. The solver lists every jump, and you can step through them, or press Play to watch. Holes on the English and European boards are named the usual way, columns a to g from the left and rows 1 to 7 from the top, so the classic first move is d2 over d3 to d4. On the triangle they are numbered 1 to 15 from the top.
The rules of peg solitaire
A peg jumps over a peg next to it, in a straight line, into an empty hole just beyond, and the peg it jumped is taken off. On the English and European boards jumps go across and up and down, never diagonally; on the triangle they go along its three directions. The aim is to end with a single peg, and in the classic game that peg sits in the hole that started empty. Every jump removes one peg, so a full English board with one gap always takes 31 jumps.
How to solve peg solitaire
Clear the arms first. Pegs left out in the arms of the cross, or in the triangle's corners, are the ones that get stranded with nothing to jump over. Work in packages. Experienced players clear the board in small groups of moves that remove a block of pegs and leave the rest as it was. Know what cannot work. Every jump changes three holes in a line, and that keeps each position in one of sixteen classes, as John Conway showed. A finish in another class can never be reached, which is why the central game on the European board has no solution at all. The solver checks this first, then searches, skipping every position it has already seen fail and every position too poor in pegs near the goal to finish there.
How it was checked
The solver was run on every start of the daily peg solitaire, all 33 holes of the English board, and finished each with the last peg where the gap began. Every solution was replayed jump by jump under the plain rules. From each single gap on the English and European boards it also decided whether one peg can be left anywhere: on the English board it always can; on the European board 16 gaps can and 21 cannot.
More puzzles
There is a new daily peg solitaire every day. The Tower of Hanoi solver and the 15 puzzle solver play out other classics move by move. For puzzles you hold in your hands, see our mechanical puzzles. There are more solvers on the puzzle tools page.
Puzzles you can hold
More puzzles from the shop.
Frequently Asked Questions
How do you solve peg solitaire?
Clear the arms of the cross first, since pegs left out there get stranded, and work in small groups of jumps that remove a block of pegs and leave the rest as it was. On the English board the classic game, starting from the centre, takes 31 jumps.
What are the rules of peg solitaire?
A peg jumps over a neighbouring peg in a straight line into an empty hole just beyond, and the jumped peg is removed. The aim is to finish with a single peg, in the classic game in the hole that started empty.
Can every peg solitaire start be solved?
No. Every jump keeps the board in one of sixteen classes, as John Conway showed, so some finishes can never be reached. The central game on the 37-hole European board is the famous example; the solver checks the class before it searches.
How many moves does peg solitaire take?
Every jump removes one peg, so a full English board with one gap takes 31 jumps to leave one peg, and the 15-hole triangle takes 13.
What is the difference between English and European peg solitaire?
The English board is a cross of 33 holes. The European, or French, board adds four more holes at the corners of the cross, 37 in all, and that changes which games can be finished.