Question 7
Identical square sheets are divided into a $5\times5$ grid on both faces. Color the sheets using $n$ colors so that each cell has the same color on its two faces. Two colored sheets are considered identical if they can be placed one on top of the other so that all corresponding cells have the same colors. Prove that there are at most
$$\frac18\left(n^{25}+4n^{15}+n^{13}+2n^7\right)$$
pairwise distinct colored sheets.
$$\frac18\left(n^{25}+4n^{15}+n^{13}+2n^7\right)$$
pairwise distinct colored sheets.