Problem

Source: Tuymaada 2003, day 1, problem 3.

Tags: combinatorics proposed, combinatorics



Alphabet $A$ contains $n$ letters. $S$ is a set of words of finite length composed of letters of $A$. It is known that every infinite sequence of letters of $A$ begins with one and only one word of $S$. Prove that the set $S$ is finite. Proposed by F. Bakharev