On the combinatorial problems which I would most like to see solved (Q1164626)

I was asked to write a paper about the major unsolved problems in combinatorial mathematics. After some thought it seemed better to modify the title to a less pretentious one. Combinatorial mathematics has grown enormously and a genuine survey would have to include not only topics where I have no real competance but also topics about which I never seriously thought, E.G. algorithmic combinatorics, coding theory and matroid theory.