Consider a round-robin chess tournament involving n players that play each other once. A win scores 1 for the winner and 0 for the loser, while a draw scores ½ for each player. We are given a set of final scores (s1,...,sn) for the players, from the range [0, n-1], whose sum is n(n-1)/2, and we want to check whether these scores are feasible [for example, in a four-player tournament, a set of final scores of (3, 3, 0, 0) is impossible]. Show that this is equivalent to checking feasibility of some transportation problem.