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	},
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24	"approval": "first-time"
25	}