olymmath

IGO 2017 E4

  • Elementary

P1,P2,…,P100P_1,P_2,\ldots,P_{100} are 100100 points on the plane, no three of them are collinear. For each three points, call their triangle clockwise if the increasing order of them is in clockwise order. Can the number of clockwise triangles be exactly 20172017 ?

Proposed by Morteza Saghafian

Dataset text AI-MO AoPS. Quoted with source.

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