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IMC 2021 P8: Maximum number of vectors such that for any 3, 2 are orthogonal

Source: IMC 2021 P8

August 5, 2021
IMC 2021vectorcombinatoricslinear algebra

Problem Statement

Let nn be a positive integer. At most how many distinct unit vectors can be selected in Rn\mathbb{R}^n such that from any three of them, at least two are orthogonal?
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