1/17/2024 0 Comments Cool math games peg solitaire![]() The code is attached at the end of this post. Since I could never solve the game myself I decided to write a solver for the problem. When I started programming a few years ago, English peg solitaire was one of my first projects. 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 holes and pegs. Many of us might now the board game peg solitaire and might even have one of its many variants at home. MathWorld-A Wolfram Web Resource.Solving Peg Solitaire with efficient Bit-Board Representations Referenced on Wolfram|Alpha Peg Solitaire Cite this as: "Peg-Solitaire, String Rewriting Systems and Finite Automata." Proc.Ĩth Int. "One-Dimensional Peg Solitaire, and Duotaire." Working To Automata Theory, Languages, and Computation, 2nd ed. R. J. Nowakowski.) Cambridge, England: Cambridge University Press, 1998. MSRI Workshop on Combinatorial Games, July, 1994 (Ed. ![]() "Unsolved Problems in Combinatorial Games." In Games Cambridge, MA: MIT Artificial Intelligence Laboratory, Memo AIM-239, Unexpected Hanging and Other Mathematical Diversions. "A Programming and Problem Solving Seminar." Stanford University Technical Ways for Your Mathematical Plays, Vol. 2: Games in Particular. Oxford, England: Oxford University Press,ġ992. Bell gives necessary and sufficient conditionsįor this problem to be solvable and a simple solution algorithm. To removing peg 3 and flipping the board horizontally. Also because of symmetry, removing peg 2 is equivalent Because of symmetry, only theįirst five pegs need be considered. Numbering hole 1 at the apex of the triangle and thereafterįrom left to right on the next lower row, etc., the following table gives possibleĮnding holes for a single peg removed (Beeler 1972). There is also triangular variant with 15 holes (where 15 is the 5th triangular number )Īnd 14 pegs (Beeler 1972). Strategies and symmetriesĪre discussed by Gosper et al. All holes but the middle one are initially filled with pegs. One of the most common configurations is a cross-shaped board with 33 holes. The goal is to remove all pegs but one by jumping pegs from one side of an occupied peg hole to an empty space, removing the peg which was jumped over. A game played on a board of a given shape consisting of a number of holes of which all but one are initially filled with pegs.
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