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Matchstick Puzzles on a Grid

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Abstract

In this paper, we consider two kinds of matchstick puzzles. In both puzzles, matchsticks can be placed only on the edges of a square grid. The first problem is to make a given placement of matchsticks by moving the designated number of matchsticks. We show an algorithm to solve this problem using string matching with errors that is faster than exhaustive search. The second problem is to make the designated number of squares by moving the designated number of matchsticks. We show that this problem is NP-complete by reduction from circuit-SAT. We also show that the problem can be solved in polynomial time if the width of the grid is bounded by a constant.

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Acknowledgements

This work was partially supported by JSPS KAKENHI Grant number 15K00505.

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Authors and Affiliations

  1. Department of Computer and Network Engineering, The University of Electro-Communications, Tokyo, Japan

    Yasuhiko Takenaga

  2. Department of Computer Science, The University of Electro-Communications, Tokyo, Japan

    Shohei Mishiba & Haruka Sugiyama

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  1. Yasuhiko Takenaga
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  2. Shohei Mishiba
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  3. Haruka Sugiyama
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Correspondence to Yasuhiko Takenaga.

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Takenaga, Y., Mishiba, S. & Sugiyama, H. Matchstick Puzzles on a Grid. Graphs and Combinatorics 36, 347–357 (2020). https://doi.org/10.1007/s00373-019-02078-3

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  • DOI: https://doi.org/10.1007/s00373-019-02078-3

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