MathDB

3

Part of 2024 Serbia JBMO TST

Problems(1)

Checkers on a board

Source: Serbia JBMO TST 2024 P3

5/25/2024
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?
combinatorics