what is the number of 10 × 10 squares in the 100 × 100 image

Question

I read and calculate the answer to be $(n - k + 1)^2$ in general (where $n=100$ and $k=10$ in the example). But have come across a paper where they use $90 \cdot 90$ - so I wanted to check with others on the answer.

Thanks

Answer 1

To understand why, think of the case $n=k=10$.

Then check $n=11$. You'll notice you can count the number of squares by the number of different positions you can place the upper right corner in.