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Coin-Moving Puzzles

Erik D. Demaine·Martin L. Demaine·Helena A. Verrill
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Abstract

We introduce a new family of one-player games, involving the movement of coins from one configuration to another. Moves are restricted so that a coin can be placed only in a position that is adjacent to at least two other coins. The goal of this paper is to specify exactly which of these games are solvable. By introducing the notion of a constant number of extra coins, we give tight theorems characterizing solvable puzzles on the square grid and equilateral-triangle grid. These existence results are supplemented by polynomial-time algorithms for finding a solution.

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Erik D. Demaine, Martin L. Demaine, Helena A. Verrill. 2002-03-31. Coin-Moving Puzzles. https://arxiv.org/abs/cs/0204002

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