Let a, b denote series with length of 2n
such that for every 1 $\leq$ i $\leq$ 2n: 1 $\leq$ $a_i$ $\leq$ n and 1 $\leq$ $b_i$ $\leq$ n
prove that there are index sets I, J $\subseteq$ [2n] such that
$$\sum_{i \in I} a_i = \sum_{j \in J} b_j$$
That question was taken from homework of combinatorics and graph theory course
