2004 OIM Problems/Problem 1

Problem

Squares on a $1001 \times 1001$ board must be colored according to the following rules:

  • If two squares have a common side, then at least one of them must be colored.
  • For every six consecutive cells in a row or column, at least two of them that are adjacent must always be colored

Find the minimum number of squares that must be colored.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

OIM Problems and Solutions