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Peg Solitaire

Jump a peg over its neighbour to remove it. Keep going until one peg is left.

Type
Logic
Takes
about 3-6 min
Result in
pegs left

Peg Solitaire

~3-6 min

  1. Tap a peg, then tap the empty hole two steps away: it jumps there.
  2. The peg it jumps over comes off the board. Jumps go along lines, never diagonally on the cross board.
  3. Keep going until no jump is left. One peg left is a perfect game.
Board

The triangle is quicker; the English cross is the classic.

Your result: — pegs left

How it's measured

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How do you play peg solitaire?

Peg solitaire starts with a board full of pegs and one empty hole. A move is a jump: a peg leaps over a neighbouring peg into the empty hole straight beyond it, and the peg jumped over is removed. You keep jumping until no jump is possible. The fewer pegs are left, the better, and a single peg is a perfect game.

Which boards can I play?

The English cross has 33 holes in a plus shape, with the centre empty at the start. Jumps go along rows and columns, never diagonally. The classic finish is the last peg in the very centre. The triangle has 15 holes in five rows, with the top hole empty, and jumps also run along its two diagonals. It is the version on the tables of Cracker Barrel restaurants in the US, and a quicker game.

Can peg solitaire always be solved?

Both boards here can be cleared down to one peg, and on the English board that peg can finish in the centre. The site's tests prove it each time the site is built, by searching for a solution and replaying it jump by jump. It is easy to get stuck, though: a few careless jumps can leave pegs stranded where nothing can reach them.

Every jump removes exactly one peg, so clearing the English board always takes 31 jumps. Puzzle books often count a chain of jumps by the same peg as one move instead, and by that count the fewest possible is 18: Ernest Bergholt found an 18-move solution in 1912, and John Beasley proved in 1964 that it can't be done in fewer.

How do you win at peg solitaire?

  • Don't strand pegs. A peg in a corner or along an edge with nothing beside it can never be jumped. Clear the arms of the cross while there are still pegs around them.
  • Work in small groups. Clearing a block of pegs in one area, then moving on, is easier to plan than jumping all over the board.
  • Keep the centre for the end. On the English board the last jumps usually come in towards the middle, so don't leave the centre empty and isolated too early.

How is your result calculated?

Your result is the number of pegs left when no jump remains. You also see how many jumps you made, your undos and your time. Undo is unlimited, so you can learn the board as you go.

For another puzzle with a strict rule about what can move, try the Chinese Rings Puzzle; for one with a proven best, the Tower of Hanoi.

Questions

What is the goal of peg solitaire?
To leave as few pegs as possible, ideally one. On the English board the classic perfect game ends with that peg in the centre hole.
Is it possible to leave only one peg?
Yes, on both boards here. The site's tests find a one-peg solution for each board, and replay it, every time the site is built.
How many solutions does peg solitaire have?
On the English 33-hole board, starting with the centre empty and ending with one peg in the centre, there are 40,861,647,040,079,968 different sequences of jumps. George Bell counted them by computer in 2009, and another count agrees.
How many pegs left is good on the triangle?
One is perfect, and it takes planning. We don't rate other counts, because there is no published standard to compare them with.
Can pegs jump diagonally?
Not on the English cross: only along rows and columns. On the triangle, pegs jump along all three directions of the grid, which includes its two diagonals.
Where is peg solitaire from?
It was being played in France by the late 1600s, and the English board became the standard in Britain. The triangle version is popular in the US.