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8.2

Part of 2021 Ukraine National Mathematical Olympiad

Problems(1)

Kotoras tribe

Source: Ukrainian Mathematical Olympiad 2021. Day 1, Problem 8.2

12/20/2023
The Kotoras alphabet has exactly 1111 letters. It is known that for any positive integer kk, there are exactly five kk-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
Stringscombinatorics