Question 48
Suppose $2n$ non-empty subsets of the set $\{0, 1, \dots, 2n-1\}$ are chosen such that the sum of the cardinals (i.e., total number of elements) of these subsets equals $\binom{2n+1}{2}$. Prove that we can choose exactly one element from each subset such that the sum of the chosen numbers equals $\binom{2n}{2}$.