International Mathematics Competition
for University Students
2021

IMC2021: Day 2, Problem 8

Problem 8. Let \(\displaystyle n\) be a positive integer. At most how many distinct unit vectors can be selected in \(\displaystyle \RR^n\) such that from any three of them, at least two are orthogonal?

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

  Hint    Solution