Problem:

23 friends want to play soccer. For this they choose a referee and the others split into two teams of 11 persons each. They want to do this so that the total weight of each team is the same. We know that they all have integer weights and that, regardless of who is the referee, it is possible to make the two teams. Prove that they all have the same weight.

over invariants again. It seems they are the only (mathematical) problems that I’m interested in, now days 😛 …