Paper by Martin L. Demaine
- Erik D. Demaine, Martin L. Demaine, and Rudolf Fleischer, “Solitaire Clobber”, Theoretical Computer Science, volume 313, number 3, February 2004, pages 325–338. Special issue of selected papers presented at the Schloss Dagstuhl Seminar on Algorithmic Combinatorial Game Theory, 2002.
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
- This paper is also available from ScienceDirect.
- Ivars Peterson wrote an article describing these results, “Getting Clobbered”, Science News 161(17), April 27, 2002.
- The paper is 15 pages.
- The paper is available in PostScript (336k), gzipped PostScript (134k), and PDF (157k).
- See information on file formats.
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- Related papers:
- Clobber_CGames2002 (Solitaire Clobber)
- Clobber_TR2002 (Solitaire Clobber)
See also other papers by Martin Demaine.
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