The Erdős–Szekeres happy ending problem

Prove that any 2^{n−2}+1 points in general position in the plane contain a convex n-gon; open from n = 7 on.

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1	{
2	"domain": "mathematics",
3	"topics": [
4	"discrete-geometry",
5	"combinatorics"
6	],
7	"type": "construction",
8	"also": [
9	"proof"
10	],
11	"cover": {
12	"motif": "points",
13	"n": 9
14	},
15	"source": {
16	"key": "erdos",
17	"name": "Erdős Problems",
18	"url": "https://www.erdosproblems.com/107",
19	"id": "107",
20	"curator": "Thomas Bloom",
21	"poser": "Paul Erdős, Esther Klein and George Szekeres",
22	"status": "open, $500 prize",
23	"as_of": "2026-10-20",
24	"prize": "$500",
25	"catalog": "0521c19bbd38"
26	},
27	"review": true,
28	"approval": "first-time"
29	}