Problem

Source: Serbia JBMO TST 2024 P3

Tags: combinatorics



a) Is it possible to place $2024$ checkers on a board $70 \times 70$ so that any square $2 \times 2$ contains even number of checkers? b) Is it possible to place $2023$ checkers on a board $70 \times 70$ so that any square $2 \times 2$ contains odd number of checkers?