We study a colourful generalization of the linear programming feasibility
problem, comparing the algorithms introduced by Barany and Onn with new
methods. We perform benchmarking on generic and ill-conditioned problems, as
well as as recently introduced highly structured problems. We show that some
algorithms can lead to cycling or slow convergence, but we provide extensive
numerical experiments which show that others perform much better than predicted
by complexity arguments. We conclude that the most efficient method for all but
the most ill-conditioned problems is a proposed multi-update algorithm.