Compute the number of ways to color 3 cells in a grid so that no two colored cells share an edge.
Solution
If the middle square is colored, then two of the four corner squares must be colored, and there are ways to do this. If the middle square is not colored, then after coloring one of the 8 other squares, there are always 6 ways to place the other two squares. However, the number of possibilities is overcounted by a factor of 3, so there are 16 ways where the middle square is not colored. This leads to a total of 22.
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