olymmath

SHARYGIN 2022 Problem 13

    Eight points in a general position are given in the plane. The areas of all 5656 triangles with vertices at these points are written in a row. Prove that it is possible to insert the symbols " ++ " and " −- " between them in such a way that the obtained sum is equal to zero.

    Dataset text AI-MO AoPS. Quoted with source.

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