Question 91
Consider a $2019\times2019$ grid. The cell $C_{i,j}$ is in column $i$ and row $j$. A coloring is wonderful if there are no indices $1\le i\lt \ell\le2019$ and $1\le j\lt k\le2019$ such that $C_{i,j}$, $C_{i,k}$ and $C_{\ell,j}$ all have the same color. Find the smallest integer $N$ for which a wonderful coloring with $N$ colors exists.