IMC 2021 · Problem 8

Day 228th IMC · Online

Statement

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

Official solution

Hidden so you can work on the problem first.

Proposed by Alexander Polyanskii, Moscow Institute of Physics and Technology; based on results of Paul Erdős and Moshe Rosenfeld.