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Solitaire Clobber

Erik D. Demaine·Martin L. Demaine·Rudolf Fleischer
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Abstract

Clobber is a new two-player board game. In this paper, we introduce the one-player variant Solitaire Clobber where the goal is to remove as many stones as possible from the board by alternating white and black moves. We show that a checkerboard configuration on a single row (or single column) can be reduced to about n/4 stones. For boards with at least two rows and two columns, we show that a checkerboard configuration can be reduced to a single stone if and only if the number of stones is not a multiple of three, and otherwise it can be reduced to two stones. We also show that in general it is NP-complete to decide whether an arbitrary Clobber configuration can be reduced to a single stone.

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Erik D. Demaine, Martin L. Demaine, Rudolf Fleischer. 2002-07-30. Solitaire Clobber. https://arxiv.org/abs/cs/0204017

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