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Part of 2009 Abels Math Contest (Norwegian MO) Final

Problems(1)

16 words in a language of 2 letters

Source: Norwegian Mathematical Olympiad 2009 - Abel Competition p2

9/5/2019
There are two letters in a language. Every word consists of seven letters, and two different words always have different letters on at least three places. a. Show that such a language cannot have more than 1616 words. b. Can there be 1616 words in the language?
combinatorics