  The Hales-Jewett theorem for alphabet of size 3 states that whenever the
Hales-Jewett cube [3]^n is r-coloured there is a monochromatic line (for n
large). Conlon and Kamcev conjectured that, for any n, there is a 2-colouring
of [3]^n for which there is no monochromatic line whose active coordinate set
is an interval. In this note we disprove this conjecture.
