RU-ALLRUSSIAN 1979 Problem 6
Given a finite set X of points in the plane. S is a set of vectors AB where (A, B) are some pairs of points in X. For every point A the number of vectors AB (starting at A) in S equals the number of vectors CA (ending at A) in S. Show that the sum of the vectors in S is zero.
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.