MathDB

There are some papers of the size

5\times 5

with two sides which are divided into unit squares for both sides. One uses

n

colors to paint each cell on the paper, one cell by one color, such that two cells on the same positions for two sides are painted by the same color. Two painted papers are consider as the same if the color of two corresponding cells are the same. Prove that there are no more than

\frac{1}{8}\left( {{n}^{25}}+4{{n}^{15}}+{{n}^{13}}+2{{n}^{7}} \right)

pairwise distinct papers that painted by this way.

Problem Statement