Star peg solitaire soultion cracker#
Star peg solitaire soultion pro#

Bell s research regarding large boards has been focused on finding the shortest-length solution using either inductive reasoning or graph search techniques. Bell has developed multiple heuristic search techniques for efficiently traversing the peg solitaire state space and has shown by induction how a solution can be constructed for a triangular or a hexagonal board of any size. RELATED WORKS Much of the research that has been done on the peg solitaire puzzle is attributed to mathematician George Bell, who has published dozens of papers on the topic. The reasons for this have been explored at length in prior literature, and thus are excluded from the scope of this paper. It is not necessarily true that there is a solution between every s and e, or that there exists a valid e for every s. The integers s and e are provided as input and the solution is given as output. The start state must have a hole at position s, and the end state must have a peg at position e. In addition, it is necessary to define the inputs and outputs for this formulation of the problem: a solution consists of a sequence of board states in which theģ transition between each state is a valid move. While the latter definition is useful when considering the shortestlength solution (under the former definition all solutions have the same length), this paper is not concerned with that property, so the former definition of the term move is used. For example, some define a move as one peg jumping into one hole, while others consider this action to be a jump and a move can involve multiple consecutive jumps made with the same peg. BACKGROUND Those who have studied peg solitaire have devised slightly different formulations of the problem at hand. The experiments detailed in this paper 2.

Star peg solitaire soultion cracker#

Figure 1 shows the 5-row triangular board (also known as the Cracker Barrel Peg Game) as well as the popular French and English geometries. With these variations come different board geometries. Variations of peg solitaire, such as Chinese Checkers, Hi-Q, and the Cracker Barrel Peg Game can be found throughout popular culture. The game is complete when there is only one peg remaining.

A move consists of jumping one peg over another to land in an empty hole, at which point the jumped peg is removed from the board. The game starts with one hole empty and every other filled.

INTRODUCTION Peg solitaire is a centuries-old board game that involves a single player and a board of holes containing pegs or marbles. Figure 1: (Left to right) The English, triangular, and French board geometries. were performed on the triangular board geometry due to its ability to scale to larger and larger sizes by simply adding more rows. Future uses of this algorithm include application to other search problems in the peg solitaire realm, such as finding the shortest solution for a given board geometry. This program consistently found solutions in a matter of minutes for puzzles as large as the 15-row triangular board, which has potential board positions and requires 118 moves to solve.

Star peg solitaire soultion pro#

I developed and tested this algorithm in C++ on a 2016 MacBook Pro with a 2.7 GHz Quad-Core Intel Core i7 processor.

This algorithm uses a variation of bidirectional breadth-first search to find a path between a given start and end state while keeping a very small number of nodes in the fringe and being agnostic to the geometry of the underlying puzzle. 2 Peg Solitaire: A New Algorithm for an Old Game CS 4991 Capstone Report, 2022 Michael Starego Computer Science The University of Virginia School of Engineering and Applied Science Charlottesville, Virginia USA ABSTRACT I propose a graph search algorithm that can be used to efficiently find solutions to exceptionally large peg solitaire puzzles.