  We show that if for all finite $c$ there is a pair of non-isomorphic finite
digraphs satisfying some additional conditions, one of which is that they
cannot be distinguished in a certain $c$-colour node colouring game, then there
can be no axiomatisation of the class of representable relation algebras in any
first-order theory of arbitrary quantifier-depth using only finitely many
variables. This corrects the proposed strategy of Hirsch and Hodkinson,
\emph{Relation algebras by games}, North-Holland (2002), Problem 1. However,
even for $c=2$, no pair of non-isomorphic graphs indistinguishable in the game
is currently known.
