Problem of the Week 853

A Nonstandard Coloring of a Checkerboard

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Color each square of a 6x6 checkerboard either black and white so that each square is a neighbor of an odd number of black squares. Here "neighbor" includes squares that touch only on a corner. A square is not considered to be a neighbor of itself.

Variation for enthusiasts: What if 6 is replaced by n?

Source: 1995 Quebec Math Contest, Crux Math. Nov 1997.

© Copyright 1998 Stan Wagon. Reproduced with permission.

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The Math Forum

2 October 1998