Coloring Hales-Jewett theorem

Colouring Hales-Jewett theorem (k=3): If n is sufficiently large depending on c, and [math]\displaystyle{ [3]^n }[/math] is partitioned into c colour classes, then one of the colour classes contains a combinatorial line.

This is a consequence of the Density Hales-Jewett theorem.

There are two combinatorial proofs of this theorem: the original one by Hales and Jewett, and a second proof by Shelah.