![]() ![]() Uehara, R., Iwata, S.: Generalized Hi-Q is NP-complete, Trans. Kanno, E.: Linear Programming Algorithm for Peg Solitaire Problems, Bachelor thesis, Department of Mathematical Engineering, Faculty of Engineering, University of Tokyo, 1997 (in Japanese). 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. Journal of Recreational Mathematics, 1 (1968), 121–123. Journal of Recreational Mathematics, 5 (1972), 133–137.Ĭross, D. G.:A Solitaire Game and Its Relation to a Finite Field. Academic Press, London, 1982.ĭe Bruijn, N. KeywordsĪvis, D., and Deza, A.: Solitaire Cones, Technical Report No. Our algorithm can solve all the peg solitaire problem instances we tried and the total computational time is less than 20 minutes on an ordinary notebook personal computer. The performance of these two methods highly depends on the symmetricity and the length of the sequence of required jumps. We proposed two types of backtrack searching, forward-only searching and forward-backward searching. While solving the relaxed problems, we can prove many peg solitaire problems are infeasible. ![]() This upper bound saves much time at the next stage of backtrack searching. The algorithms first solve relaxed problems and get an upper bound of the number of jumps for each jump position. We proposed algorithms based on the backtrack search method and relaxation methods for integer programming problem. In this paper, we dealt with the peg solitaire problem as an integer programming problem. The game is classical, and nowadays sold in many parts of the world under the trade name of Hi-Q. peg in the central square.To make a move: click on a peg and then click on the destination square. Peg solitaire is a one player game using pegs and a board with some holes. English version of peg solitaire puzzle or the patience game.The objective of the game is to empty the board and leave only one. ![]()
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