```Date: Jul 19, 2010 2:45 AM
Author: ou, janis
Subject: 6 points in R3 conjecture

Take 6 points in 3D space in general position: no 3 in a line, no 3forming a right angle, no 4 in a plane. Draw all 15 lines between them.This will form 20 distinct triangles. (For each of the six points thereare ten pairs of other points, but the apparent 60 triangles are eachcounted three times.) Each triangle can have at most one obtuse angle,so the maximum number of obtuse angles in the whole figure, over allsuch point sets, is 20.Conjecture: the minimum number of obtuse angles over all 6-point sets in3 dimensions is 2.This has been established experimentally to a high degree of probabilityby creating 28 million (so far) random 6-point sets and counting theobtuse angles in each set. I do not know how to prove it, and I see noway to find a counterexample except by trying additional millions ofpoint sets, which are not likely to turn up any.I think this is a new problem, and I have other similar conjectures.Steve Gray  http://www.usedconecrusher.com
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