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n points on a circle, find the max nr. of acute triangles

Source: Romanian IMO Team Selection Test TST 1999, problem 13

September 24, 2005
combinatorics proposedcombinatorics

Problem Statement

Let n≥3n\geq 3 and A1,A2,…,AnA_1,A_2,\ldots,A_n be points on a circle. Find the largest number of acute triangles that can be considered with vertices in these points.
G. Eckstein
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