Problem

Source: 2018 FKMO Problem 6

Tags: combinatorics, geometry, 3D geometry, icosahedron



Twenty ants live on the faces of an icosahedron, one ant on each side, where the icosahedron have each side with length 1. Each ant moves in a counterclockwise direction on each face, along the side/edges. The speed of each ant must be no less than 1 always. Also, if two ants meet, they should meet at the vertex of the icosahedron. If five ants meet at the same time at a vertex, we call that a collision. Can the ants move forever, in a way that no collision occurs?