Question 25
C2 (UKR) An $(n-1)\times(n-1)$ square is divided into $(n-1)^2$ unit squares in the usual manner. Each of the $n^2$ vertices of these squares is to be colored red or blue. Find the number of different colorings such that each unit square has exactly two red vertices. (Two coloring schemes are regarded as different if at least one vertex is colored differently in the two schemes.)