{c}

The three faces incident to any cube vertex are pairwise adjacent along edges, forcing three colours. Three suffice by giving each pair of opposite faces a common colour, using a different colour for each of the three pairs. Hence \b[the face <chromatic number> is three].

Solution

Past exam of the probability, statistics and options I course of the University of Oxford / 2009 / R / 1 / ii / c / Solution

 Solution (source code)