2009 IMO Problems/Problem 6
Problem
Let be distinct positive integers and let
be a set of
positive integers not containing
. A grasshopper is to jump along the real axis, starting at the point
and making
jumps to the right with lengths
in some order. Prove that the order can be chosen in such a way that the grasshopper never lands on any point in
.
Author: Dmitry Khramtsov, Russia