MathDB
Game: putting numbers in a grid

Source: Ukraine MO 2021 8.7

May 2, 2021
combinatoricsgame

Problem Statement

Andriy and Bogdan take turns putting integers from 11 to nn inclusive in the cells of an n×nn \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 nn, which player has a winning strategy?
Proposed by Fedir Yudin