Question 102
Let a grid $2m \times 2n$ be given. Lamin colors each cell of the grid either black or white such that the cells of each color form a polygon. Then Yamal covers the whole grid by $2mn$ dominoes of size $1 \times 2$. The domino is called combined if it covers 1 black and 1 white cell. Find the maximal number of combined dominoes Lamin may guarantee regardless of the strategy of Yamal.