Question

A square, where s is an odd integer, is divided into unit squares. All the unit squares along the edges and the 2 diagonals of a square are discarded. Find a fully simplified expression, in terms of s, for the number of unit squares remaining answer.

Answer 1

I'll assume that s is the length of a side.

After the borders are discarded, an (s-2)x(s-2) square remains.
There are 2(s-2)-1 = 2s-5 squares on the diagonal, so the remaining squares number

(s-2)^2 - (2s-5) = s^2-6s+9 = (s-3)^2

you can easily check this for small s.