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Problem 735
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?
Source: erdosproblems.com/735
- Geometry
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Solved, AnsweredAn accepted solution exists. Settled in another form, for example when its parts resolve differently or the question is open-ended.
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.