Algorithms 2012, 5(1), 158-175; doi:10.3390/a5010158
Article

An Integer Programming Approach to Solving Tantrix on Fixed Boards

1email and 2,* email
Received: 15 December 2011; in revised form: 9 March 2012 / Accepted: 14 March 2012 / Published: 22 March 2012
(This article belongs to the Special Issue Puzzle/Game Algorithms)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract: 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
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MDPI and ACS Style

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

AMA Style

Kino F, Uno Y. An Integer Programming Approach to Solving Tantrix on Fixed Boards. Algorithms. 2012; 5(1):158-175.

Chicago/Turabian Style

Kino, Fumika; Uno, Yushi. 2012. "An Integer Programming Approach to Solving Tantrix on Fixed Boards." Algorithms 5, no. 1: 158-175.

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