MathDB
Dizzying Set Intersections

Source: USAMO 2024/2

March 20, 2024
USAMOcombinatorics

Problem Statement

Let S1,S2,…,S100S_1, S_2, \ldots, S_{100} be finite sets of integers whose intersection is not empty. For each non-empty T⊆{S1,S2,…,S100},T \subseteq \{S_1, S_2, \ldots, S_{100}\}, the size of the intersection of the sets in TT is a multiple of the number of sets in TT. What is the least possible number of elements that are in at least 5050 sets?
Proposed by Rishabh Das
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