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IMO 1974 — Shortlisted problems Question 12

IMO Shortlist · IMO 1974 — Shortlisted problems

Question 12

II 6 (USS 1)

In a certain language words are formed using an alphabet of three letters. Some words of two or more letters are not allowed, and any two such distinct words are of different lengths. Prove that one can form a word of arbitrary length that does not contain any nonallowed word.