Question 9: Let S1, S2,...,S26 be a sequence consisting of 26 subsets of the set {1,2,...,9}. Assume that each of these 26 subsets consists of at most three elements.
Use the Pigeonhole Principle to prove that there exist two distinct indices i and j, such that ∑x∈Si x = ∑x∈Sj x.
Hint: What are the possible values for ∑x?