Grid game
Source: Czech-Polish-Slovak Match 2022 P1
September 3, 2022
combinatorics
Problem Statement
Let be a positive integer. Alice and Bob play a game on a board. Initially, all cells are white. Alice starts and the players alternate. In her turn, Alice can either color one white cell in red or pass her turn. In his turn, Bob can either color a square of white cells in blue or pass his turn. Once both players pass, the game ends and the person who colored more cells wins (a draw can occur). For each , determine which player (if any) has a winning strategy.