English

Solitaire Clobber

Discrete Mathematics 2007-05-23 v2 Computational Geometry Computer Science and Game Theory

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.

Cite

@article{arxiv.cs/0204017,
  title  = {Solitaire Clobber},
  author = {Erik D. Demaine and Martin L. Demaine and Rudolf Fleischer},
  journal= {arXiv preprint arXiv:cs/0204017},
  year   = {2007}
}

Comments

14 pages. v2 fixes small typo