Question 40
Consider a $25 \times 25$ chessboard with cells $C(i, j)$ for $1 \le i, j \le 25$. Find the smallest possible number $n$ of colors with which these cells can be colored subject to the following condition: For $1 \le i \lt j \le 25$ and for $1 \le s \lt t \le 25$, the three cells $C(i, s)$, $C(j, s)$, $C(j, t)$ carry at least two different colors.