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pieces placed in 8 x 8 board

Source: 2007 Cuba MO 1.1

September 15, 2024
combinatoricstiles

Problem Statement

Pieces are placed in some squares of an 8×88 \times 8 board sothat: a) There is at least one token in any rectangle with sides 2×12 \times 1 or 1×21\times 2. b) There are at least two neighboring pieces in any rectangle with sides 7×17\times 1 or 1×71\times 7. Find the smallest number of tokens that can be taken to fulfill with both conditions.
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