Question 8
Let us call by an "edge" any segment of length $1$ which is common to two adjacent fields of a given chessboard $8 \times 8$. Consider all possible cuttings of the chessboard into $32$ pieces $2 \times 1$ and denote by $n(e)$ the total number of such cuttings that involve the given edge $e$. Determine the last digit of the sum of the numbers $n(e)$ over all the edges $e$.
(Michal Rolínek)
(Michal Rolínek)