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Turán's tetrahedron problem

Determine the largest fraction of triples on n points with no 4-set covered by all its triples; Turán conjectured 5/9.

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1{
2 "domain": "mathematics",
3 "topics": [
4 "combinatorics",
5 "graph-theory"
6 ],
7 "type": "proof",
8 "also": [
9 "construction"
10 ],
11 "source": {
12 "key": "erdos",
13 "name": "Erdős Problems",
14 "url": "https://www.erdosproblems.com/500",
15 "id": "500",
16 "curator": "Thomas Bloom",
17 "poser": "Pál Turán",
18 "status": "open, $500 prize",
19 "as_of": "2026-10-20",
20 "prize": "$500",
21 "catalog": "0521c19bbd38"
22 }
23}