Question 124
We have an $8 \times 8$ board. An inner edge is an edge between two $1 \times 1$ cells. We cut the board into $1 \times 2$ dominoes. For an inner edge $k$, $N(k)$ denotes the number of ways to cut the board such that the cut is made along the edge $k$. Compute the last digit of the sum that we obtain when we add up all $N(k)$, where $k$ ranges over the inner edges.