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Checkers on a board

Source: Serbia JBMO TST 2024 P3

May 25, 2024
combinatorics

Problem Statement

a) Is it possible to place 20242024 checkers on a board 70×7070 \times 70 so that any square 2×22 \times 2 contains even number of checkers?
b) Is it possible to place 20232023 checkers on a board 70×7070 \times 70 so that any square 2×22 \times 2 contains odd number of checkers?
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