Question 58
Let $n$ be a positive integer and suppose a $2n \times 2n$ square grid is given. Suppose we color exactly $2n^2$ square boxes of the grid in such a way that the following condition is satisfied.
Condition: If a box is colored then none of the boxes which share only a vertex with that box is not colored.
How many ways of coloring $2n^2$ square boxes of the grid are there that satisfy the condition stated above? We regard two configurations of colored boxes to be distinct if one configuration can be transposed on the other by rotation or by flipping.
Condition: If a box is colored then none of the boxes which share only a vertex with that box is not colored.
How many ways of coloring $2n^2$ square boxes of the grid are there that satisfy the condition stated above? We regard two configurations of colored boxes to be distinct if one configuration can be transposed on the other by rotation or by flipping.