Given an m×n table consisting of mn unit cells. Alice and Bob play the following game: Alice goes first and the one who moves colors one of the empty cells with one of the given three colors. Alice wins if there is a figure, such as the ones below, having three different colors. Otherwise Bob is the winner. Determine the winner for all cases of m
and n where m,n≥3.Proposed by Toghrul Abbasov, Azerbaijan JuniorBalkanshortlist2021combinatoricsgameboard coloring