8.7

Part of 2021 Ukraine National Mathematical Olympiad

Problems(1)

Game: putting numbers in a grid

Source: Ukraine MO 2021 8.7

Andriy and Bogdan take turns putting integers from

1

n

inclusive in the cells of an

n \times n

board in such a way that no row or column contains two equal numbers. Andriy begins, and the player who cannot make a move loses. Depending on

n

, which player has a winning strategy?
Proposed by Fedir Yudin

combinatoricsgame