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Difference between revisions of "2024 USAMO Problems/Problem 2"

(Created page with "Let <math>S_1, S_2, \ldots, S_{100}</math> be finite sets of integers whose intersection is not empty. For each non-empty <math>T \subseteq\left\{S_1, S_2, \ldots, S_{100}\rig...")
(No difference)

Revision as of 22:32, 20 March 2024

Let $S_1, S_2, \ldots, S_{100}$ be finite sets of integers whose intersection is not empty. For each non-empty $T \subseteq\left\{S_1, S_2, \ldots, S_{100}\right\}$, the size of the intersection of the sets in $T$ is a multiple of the number of sets in $T$. What is the least possible number of elements that are in at least 50 sets?

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