RU-ALLRUSSIAN 1987 Problem 17
Some lattice points in the plane are marked. S is a set of non- zero vectors. If you take any one of the marked points P and add place each vector in S with its beginning at P, then more vectors will have their ends on marked points than not. Show that there are an infinite number of points.
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.