A problem that you cannot solve -- A fascinating problem combining set theory, combinatorics, measure theory and distance geometry -- I cant offer money to nice problems of other people, or I will go broke -- I would offer $1000 for its solution. These are just some of the comments from giants like Paul Halmos, Paul Erdos, Ron Graham et. al - about a 60 year old problem whose best results can be proved even by 'epsilons' in the language of Erdos. The life of a mathematician working in colouring can be more colourful than one may guess. A glimpse into their story by following a single problem.