IMO 1992 LL POL56

Origin: POL

Problem

A directed graph (any two distinct vertices joined by at most one directed line) has the following property: If x, u, and v are three distinct vertices such that x \tou and x \tov, then u \tow and v \tow for some vertex w. Suppose that x \tou \toy \to\cdot \cdot \cdot \toz is a path of length n, that cannot be extended to the right (no arrow goes away from z). Prove that every path beginning at x arrives after n steps at z.