Question 84
Let $(m, n)$ be a pair of positive integers. Julia has carefully planted $m$ rows of $n$ dandelions in an $m \times n$ array in her back garden. Now, Jana and Viviane decide to play a game with a lawnmower they just found. Taking alternating turns and starting with Jana, they can mow down all the dandelions in a straight horizontal or vertical line (and they must mow down at least one dandelion!). The winner is the player who mows down the final dandelion. Determine all pairs $(m, n)$ for which Jana has a winning strategy.