The Kotoras alphabet has exactly $11$ letters. It is known that for any positive integer $k$, there are exactly five $k$-letter bad words in the language of this tribe. Prove that it is possible to come up with a word in the Kotoras language with any number of letters that cannot be cut into two smaller words, of which at least one is considered bad. Proposed by Arseniy Nikolaiev
Problem
Source: Ukrainian Mathematical Olympiad 2021. Day 1, Problem 8.2
Tags: Strings, combinatorics