If one board position can be rotated and/or flipped into another board position, the board positions are counted as identical. The only place it is possible to end up with a solitary peg, is the centre, or the middle of one of the edges on the last jump, there will always be an option of choosing whether to end in the centre or the edge.įollowing is a table over the number ( Possible Board Positions) of possible board positions after n jumps, and the number ( No Further Jumps) of those board positions, from which no further jumps are possible. , or / ( a slash is used to separate 'chunks' such as a six-purge out).Source peg and destination hole ( you have to work out what it jumps over yourself).As long as the variant has the proper "parity" and is large enough, it will probably be solvable. It has also been played on a triangular board, with jumps allowed in all 3 directions. Peg solitaire has been played on other size boards, although the two given above are the most popular. Thus a hole at a can only leave a single peg at a, p, O or C.Ī thorough analysis of the game is provided in Winning Ways ISBN 01120911027 in the UK and ISBN 156881142 in the US. On a English board, the hole can be anywhere and the final peg can only end up where multiples of three permit. Also starting with one hole here and ending with one peg there. Other alternate games include starting with two empty holes and finishing with two pegs in those holes. This technique can be used with a line of 3, a block of 2*3 and a 6-peg L shape with a base of length 3 and upright of length 4. In the example below, the * is the catalyst.: also works.Ī tactic that can be used is to divide the board into packages of three and to purge (remove) them entirely using one extra peg, the catalyst, that jumps out and then jumps back again. Note that following the solution in reverse, that is, o-x, P-p, D-P, F-D, p-F, d-p, k-I, etc. To see the above solution illustrated, go to Solution to peg solitaire. One solution of the standard English game is: On the English board the equivalent alternative games are to start with a hole and end with a peg at the same position. This mirror image notation is used, amongst other reasons, since on the European board, one set of alternative games is to start with a hole at some position and to end with a single peg in its mirrored position. There are many different solutions to the standard problem, and one notation used to describe them assigns letters to the holes: Template:Solution This article includes one solution to the English standard game. Many people never manage to solve the problem. It is very easy to go wrong and find you have two or three widely spaced lone pegs. On an English board, the first three moves might be: Thus valid moves in each of the four orthogonal directions are: In the diagrams which follow, * is used to indicate a peg (in a hole) and The objective is, making valid moves, to empty the entire board except for a solitary peg in the central hole.Ī valid move is to jump a peg orthogonally over an adjacent peg into a hole two positions away and then to remove the jumped peg. The standard game fills the entire board with pegs except for the central hole. Some sets use marbles in a board with indentations. The game is known simply as Solitaire in the United Kingdom where the card games are called Patience. Peg Solitaire is a solitaire-type puzzle game for one player involving movement of pegs on a board with holes.
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