Eight kings
How many different ways can you place four white kings and four black kings on a 5x5 grid such that every king attacks exactly two kings of it's own color?
Note : A king is a chess piece that can move to (or attack) any adjacent square, including being diagonally adjacent. All kings of the same color are indistinguishable.
The answer is 44.
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1 solution
There is only one way to arrange four kings to suit the criteria. Like this:
And on a 5x5 grid, there are nine different ways you can put the white kings in this arrangement.
For each one, except for them clustered around the middle, there are five different ways to place the black kings in the same arrangement.
For the one where you cluster the white kings around the middle there are four ways to place the black kings.
Therefore the total number of ways is:
5 ⋅ 8 + 4 = 4 4