Play Peg Solitaire Online
The classic single-player board puzzle. Jump pegs over one another to remove them from the board. Choose from 6 board shapes and aim for the perfect solution — one peg remaining.
Created by Brian Hamilton
How to play peg solitaire
Remove pegs by jumping over them, and try to finish with a single peg left.
- A peg jumps over an adjacent peg into an empty hole directly beyond it, and the peg jumped over is removed.
- Jumps are along the board's lines only — never diagonally on the square boards.
- Every jump removes exactly one peg, so the number of moves is fixed from the start: 32 pegs means 31 jumps.
- The game ends when no legal jump remains. One peg left is a win.
- Every board here has been checked: each can be finished from the position it starts in.
Controls: tap a peg to select it, then tap the hole you want it to jump into. Use Undo to take a jump back.
Every jump costs a peg, so the arithmetic is fixed from the start
A peg jumps over a neighbour into an empty hole, and the peg it jumped is removed. That is the whole game. It also means the number of moves is decided before you begin: the English board starts with 32 pegs, and finishing with one takes exactly 31 jumps, no more and no fewer.
You cannot play badly in the sense of taking too long. You can only play into a position where the pegs left cannot reach each other — and that is what makes it hard.
Random play essentially never works
It is worth knowing how unforgiving this is before blaming yourself. Playing entirely at random — picking any legal jump each turn — never once finished the English, French, German or Diamond boards in 20,000 attempts each. Not rarely: not once.
| Board | Pegs | Jumps needed | Random play finishes | Pegs left on average |
|---|---|---|---|---|
| English | 32 | 31 | 0.00% | 6.9 |
| French | 44 | 43 | 0.00% | 9.0 |
| German | 44 | 43 | 0.00% | 9.6 |
| Diamond | 36 | 35 | 0.00% | 10.2 |
| Triangle | 14 | 13 | 6.13% | 3.1 |
| Square | 8 | 7 | 16.59% | 2.4 |
The average random game on the English board strands about seven pegs. Getting to one is not a matter of care; it needs a plan.
Keep the pegs together
The single most useful habit is to think about the shape of what is left rather than the move in front of you. A jump moves one peg two squares away from where its neighbours are, so careless play spreads the pegs outward — and a peg with no neighbour within reach can never be removed and can never move.
Work from the outside in. Clear the arms towards the middle, and let the surviving pegs cluster rather than scatter. The boards here open with only two to four legal jumps, so the first choice matters more than it looks: there is no wide opening book to fall back on.
A useful check while playing: could every remaining peg still be reached by some chain of jumps? If a peg is stranded in a corner with empty holes all around it, the game is already lost, however many pegs are left elsewhere.
Some boards cannot be finished at all — and you can prove it
This is the part worth knowing, because it is not a matter of skill. Certain starting positions have no solution whatsoever, and it can be shown without trying a single move.
Label every square with (row + column) mod 3, giving three classes of square. Any jump spans three squares in a line, so it touches all three classes exactly once: a peg leaves two of the classes and one arrives in the third. Every jump therefore changes the three counts by −1, −1, +1 in some order — which means the differences between the counts never change their parity. Do the same with (row − column) mod 3 and you have four quantities that no legal move can alter.
Now compare the start with the finish. A single peg on a given square has its own signature. If the starting position's signature matches no square on the board, no sequence of jumps can ever leave one peg — and no search is needed to know it.
That argument is why a pure diamond board can never be solved. Every starting hole was checked at radius 2 (13 of 13 impossible) and radius 3 (25 of 25 impossible). Cutting the four extreme tips off the diamond changes the arithmetic and makes it solvable — which is why the board on this page is a clipped diamond rather than a pure one.
Where solvers get stuck
Playing greedily. Taking whatever jump is available is exactly the random strategy measured above, and on the large boards it finishes 0% of the time.
Emptying the middle early. The centre is the most connected part of the board. Strip it and the remaining pegs lose the routes between them.
Not noticing a game is already lost. Once pegs are separated into groups that cannot reach each other, no continuation helps. Spotting that early saves replaying a dead position to its end.
What you can check about these boards
All six can be finished, and each was verified by finding an actual solution. That was not true before. Three of the boards on this page — the French, the Diamond and a five-by-five Plus — were mathematically impossible to complete from the position they started in, by the colouring argument above. A fourth, the German board, could not be settled either way even after tens of millions of positions were searched.
They were fixed rather than removed. The French and German boards now start from a different hole — that choice alone decides the parities — and both are now solvable, with the German board settling in about two million positions. The Diamond has its four tips clipped, for the reason above. The Plus board could not be rescued at all: all nine of its starting holes were proved impossible, so it has been replaced by a three-by-three square, which uses the same nine cells and can be finished in seven jumps.
Peg solitaire and its history
The game is old — the English board dates to at least the seventeenth century — and it has an unusually rich mathematics for something so simple to state. The colouring argument above is the accessible end of it; the full theory of which positions can reach which others was worked out in the twentieth century.
It is also unusual among the puzzles here in having no clues at all. Every other puzzle on this site gives you numbers to reason from. Peg solitaire gives you only a starting position and the rule, and all the constraint comes from the geometry.
More puzzles like this
If you like planning several moves ahead, try these: