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International Mathematics Competition
for University Students
2015

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IMC 2025
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IMC2015: Day 1, Problem 5

5. Let n2, let A1,A2,,An+1 be n+1 points in the n-dimensional Euclidean space, not lying on the same hyperplane, and let B be a point strictly inside the convex hull of A1,A2,,An+1. Prove that AiBAj>90 holds for at least n pairs (i,j) with 1i<jn+1.

Proposed by Géza Kós, Eötvös University, Budapest

Hint: Use dot-product of vectors.

    

IMC
2015

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