Problem

Source: 2009 Romania JBMO TST 3.3

Tags: combinatorics, Equilateral, combinatorial geometry



The plane is divided into a net of equilateral triangles of side length $1$, with disjoint interiors. A checker is placed initialy inside a triangle. The checker can be moved into another triangle sharing a common vertex (with the triangle hosting the checker) and having the opposite sides (with respect to this vertex) parallel. A path consists in a finite sequence of moves. Prove that there is no path between two triangles sharing a common side.