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STRATEGY AND COMPLEXITY OF THE GAME OF SQUARES

Published online by Cambridge University Press:  01 May 1998

FLORIAN BREUER  and
JOHN MICHAEL ROBSON
FLORIAN BREUER
Affiliation:
Department of Mathematics, University of Stellenbosch, Stellenbosch 7600, South Africa
JOHN MICHAEL ROBSON
Affiliation:
LaBRI, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence, France
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Abstract

We introduce a game called Squares where the single player is presented with a pattern of black and white squares and has to reduce the pattern to white by making as few moves as possible. We present a method for solving the game, and show that the following problem is NP-complete.

Problem 1 (Squares-Solvability). Given a pattern X and k∈N, can X be solved in k or less moves?

We demonstrate a reduction to this problem from Not-All-Equal-3SAT. We also present another NP-complete problem that Squares-Solvability can be reduced to.

Type
Notes and Papers
Information
Bulletin of the London Mathematical Society , Volume 30 , Issue 3 , May 1998 , pp. 274 - 282
Copyright
© The London Mathematical Society 1998

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