Each resident of Dot-town carries a red or blue dot on his (or her) forehead, but if he ever figures out what color it is he kills himself. Each day the residents gather; one day a stranger comes and tells them something—anything—non-trivial about the number of blue dots. Prove that eventually every resident kills himself.

Comment: “Non-trivial” means here that there is some number of blue dots for which the statement would not have been true.