RU-ALLRUSSIAN 1991 Problem 20
Do there exist 4 vectors in the plane so that none is a multiple of another, but the sum of each pair is perpendicular to the sum of the other two? Do there exist 91 non- zero vectors in the plane such that the sum of any 19 is perpendicular to the sum of the others?
Dataset text NuminaMath olympiads. Quoted with source.
Solutions
No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.