 Hales–Jewett theorem

For every finite alphabet $X$ and every positive integer $k$, there is $n$ such that every $k$-coloring of $X^n$ contains a monochromatic combinatorial line.

The Hales–Jewett theorem is a result in combinatorial geometry, specifically in the field of Ramsey theory. It addresses the existence of certain types of structured configurations in combinatorial objects, such as hypercubes.