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Set of 5 Points and Numbers of Acute Triangles

Source: MEMO Team Competition, Question 6

September 24, 2007
combinatorics proposedcombinatorics

Problem Statement

For a set P P of five points in the plane, no three of them being collinear, let s(P) s(P) be the numbers of acute triangles formed by vertices in P P. Find the maximum value of s(P) s(P) over all such sets P P.
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