Difference between revisions of "2024 USAMO Problems/Problem 2"
Anyu-tsuruko (talk | contribs) (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...") |
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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}\right\}</math>, the size of the intersection of the sets in <math>T</math> is a multiple of the number of sets in <math>T</math>. What is the least possible number of elements that are in at least 50 sets? | 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}\right\}</math>, the size of the intersection of the sets in <math>T</math> is a multiple of the number of sets in <math>T</math>. What is the least possible number of elements that are in at least 50 sets? | ||
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| + | ==Video Solution== | ||
| + | https://youtu.be/eguz1OuckH0 | ||
Latest revision as of 08:09, 5 April 2024
Let 
be finite sets of integers whose intersection is not empty. For each non-empty 
, the size of the intersection of the sets in 
is a multiple of the number of sets in . What is the least possible number of elements that are in at least 50 sets?
