I am given an $n\times n$ chess board. I have to select $k$ squares of size $1\times1$ so that no two squares share a common side. I have tried for $2\times2 , 3\times3 $ but for big values of $n$ can anyone give an approach to solve this type of problem or suggest any resources about this type of problems?
ex:
For $n=2, k=1$ there are $4$ ways.
For $n=2 ,k=2$ there are $2$ ways.