Question

In space, there are 30 non-degenerate vectors. Prove that there are at least 2 such that the angle between them is no greater than 45 degrees. 
A. Tulpigo

Difficulty level (1 very easy - 10 very hard): 8

Topics:
Geometry -> Trigonometry Geometry -> Spherical Geometry Combinatorics -> Pigeonhole Principle Combinatorics -> Combinatorial Geometry Geometry -> Plane Geometry -> Angle Calculation Geometry -> Vectors
Sources:
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