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An Integer Programming Approach to Solving Tantrix on Fixed Boards

by Fumika Kino 1 and Yushi Uno 2,*
1
Mitsubishi Electric Information Network Corp., 8-1-1 Tsukaguchi-Honmachi, Amagasaki 661-8611, Japan
2
Graduate School of Science, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai 599-8531, Japan
*
Author to whom correspondence should be addressed.
Algorithms 2012, 5(1), 158-175; https://doi.org/10.3390/a5010158
Received: 15 December 2011 / Revised: 9 March 2012 / Accepted: 14 March 2012 / Published: 22 March 2012
(This article belongs to the Special Issue Puzzle/Game Algorithms)
Tantrix (Tantrix R ⃝ is a registered trademark of Colour of Strategy Ltd. in New Zealand, and of TANTRIX JAPAN in Japan, respectively, under the license of M. McManaway, the inventor.) is a puzzle to make a loop by connecting lines drawn on hexagonal tiles, and the objective of this research is to solve it by a computer. For this purpose, we first give a problem setting of solving Tantrix as making a loop on a given fixed board. We then formulate it as an integer program by describing the rules of Tantrix as its constraints, and solve it by a mathematical programming solver to have a solution. As a result, we establish a formulation that can solve Tantrix of moderate size, and even when the solutions are invalid only by elementary constraints, we achieved it by introducing additional constraints and re-solve it. By this approach we succeeded to solve Tantrix of size up to 60.
Keywords: combinatorial game theory; integer programming; mathematical programming solver; recreational mathematics; subloop elimination combinatorial game theory; integer programming; mathematical programming solver; recreational mathematics; subloop elimination
MDPI and ACS Style

Kino, F.; Uno, Y. An Integer Programming Approach to Solving Tantrix on Fixed Boards. Algorithms 2012, 5, 158-175.

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