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Problem 735
claims/: The 1 claim page of Problem 735, one per claimant's result; the problem's standing derives from them.
Statement. Given any points in when can one give positive weights to the points such that the sum of the weights of the points along every line containing at least two points is the same?
Status. Solved. The site credits Ackerman, Buchin, Knauer, Pinchasi and Rote, whose Theorem 1 proves Murty's conjectured list of configurations; the accepted claim is their classification.
Source. erdosproblems.com/735, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #735, https://www.erdosproblems.com/735.
References.
- [ABKPR08] Ackerman, Eyal and Buchin, Kevin and Knauer, Christian and Pinchasi, Rom and Rote, Günter, There are not too many magic configurations. Discrete Comput. Geom. 39 (2008), no. 1-3, 3-16.
Formalization. No formal-conjectures statement file exists for the problem, and the community database lists it as not formalized (2026-10-07). Boris Alexeev's repository of Lean proofs of Erdős problems holds a file that declares itself a formalization of the Ackerman–Buchin–Knauer–Pinchasi–Rote classification, written with the systems Codex and GPT-5.6 Sol; it is a formalization link on the claim page, and this corpus has not built it.
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Linked library material
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