# Hales-Jewett Theorem

## Geometric Hales-Jewett Theorem ★★

**Conjecture**For all integers and , there is an integer such that for every set of at least points in the plane, if each point in is assigned one of colours, then:

- \item contains collinear points, or \item contains a monochromatic line (that is, a maximal set of collinear points receiving the same colour)

Keywords: Hales-Jewett Theorem; ramsey theory