MathDB
2013 HMIC p1

Source:

September 20, 2019
combinatorics

Problem Statement

Let SS be a set of size nn, and kk be a positive integer. For each 1≤i≤kn1 \le i \le kn, there is a subset Si⊂SS_i \subset S such that ∣Si∣=2|S_i| = 2. Furthermore, for each e∈Se \in S, there are exactly 2k2k values of ii such that e∈Sie \in S_i. Show that it is possible to choose one element from SiS_i for each 1≤i≤kn1 \le i \le kn such that every element of SS is chosen exactly kk times.
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