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So I have this problem: enter image description here and the answers I can choose between are:

a) 1

b) k

c) k+1

d) 2k

I am quite new to rook numbers and rook polynomials so I might be missing something obvious. I have no idea how to start solving this. So far I have simply just tried to draw various k x k chessboards and just simply guessed and tested. Through that testing I have come to the conclusion that the answer is k but I might be completely wrong.

Is there a more methodical way to solve this? Any help is appreciated!

Thanks!

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