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Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
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Problem 101
Statement. Given points in , no five of which are on a line, the number of lines containing four points is .
Status. Open.
Source. erdosproblems.com/101, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #101, https://www.erdosproblems.com/101.
References.
- [BGS74] Burr, Stefan A. and Grünbaum, Branko and Sloane, N. J. A., The orchard problem. Geometriae Dedicata (1974), 397-424.
- [FuPa84] Füredi, Z. and Palásti, I., Arrangements of lines with a large number of triangles. Proc. Amer. Math. Soc. (1984), 561-566.
- [Gr76] Grünbaum, Branko, New views on some old questions of combinatorial geometry. Colloquio Internazionale sulle Teorie Combinatorie (Roma, 1973), Tomo I (1976), 451-468.
- [SoSt13] Solymosi, József and Stojaković, Miloš, Many collinear -tuples with no collinear points. Discrete Comput. Geom. (2013), 811-820.
Formalization. Statement in formal-conjectures.
Progress
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Known Results
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Linked library material
These entries are derived from explicit links on library pages. They are navigation only and do not by themselves record mathematical progress.
Linked from (8)
Problem 669Discrete and Convex Geometrydiscrete_geometry/burr_1974_orchard_problemTheorem 1 (p. 397): t(p) >= 1 + floor(p(p-3)/6) for every p >= 3, by points on a cubic curvediscrete_geometry/erdos_1984_research_problemsConjecture (1) (p. 101): f_k(n)/n tends to infinity and f_k(n)/n^2 tends to 0 for fixed k > 3discrete_geometry/solymosi_2013_many_collinear_k_tuplesTheorem 1 (p. 3): more than n^(2 - c/sqrt(log n)) lines with exactly k points and none with k+1
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