One major improvement of a classical algorithm can be achieved when instead of arrays, so called bit-boards are used for representing a position. Without the utilization of some advanced approaches, an algorithm could run for many days until a solution is found. Also for backtracking algorithms the computational effort is enormous in order to solve this problem. Since there are many corners on this board it is rather difficult to find a solution where only one peg is left over in the end. In the beginning, only two moves are possible. As I was told - in contrast to the English variant - the only initial empty hole is not located in the center of the board but has to be placed at a slightly different position in order to be able to solve the game (as I found later, the solver was not able to solve the game for an initially empty hole in the center of the board).
Efficiently Solving the Diamond-41 BoardĪs the name suggests, the Diamond-41 board consists of 41 holes. A simple solver for the English variant can be found in english.cpp. The solution for the diamond shaped board is even more tricky. Many players need quite a few attempts in order to find the solution for the English peg solitaire. The English variant is shown in the figure below.Įven though the rules of the game are rather simple, finding a solution is not trivial. The English variant, as shown below, has one additional rule: In order to win, it is not sufficient that only one peg is left in the end this peg also has to be located in the center of the board. This is the case when there is no pair of pegs which are orthogonally adjacent or if only one peg is left. Once no move is possible any longer, the game is over. So, in each move, one peg jumps 2 holes further and the peg in-between is removed. The neighboring peg is then removed, leaving an empty hole.
In each move the player selects one peg and jumps - either vertically or horizontally, not diagonally - with this peg over a directly neighboring one into an empty hole. For example, the English variant consists of 33 holes while the typical diamond variant consists of 41 holes. The number of holes depends on the board variant. Peg solitaire is a one-player game played on a board with $$n$$ holes and $$n-1$$ pegs. Many of us might now the board game peg solitaire and might even have one of its many variants at home.
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