Problem

Source:

Tags: combinatorics, strategy game, winning strategy, game, board



Ana and Beta play a turn-based game on a $m \times n$ board. Ana begins. At the beginning, there is a stone in the lower left square and the objective is to move it to the upper right corner. A move consists of the player moving the stone to the right or up as many squares as the player wants. Find all the values of $(m, n)$ for which Ana can guarantee victory.