Mathematical Proof on Max/Min Problem

Seojun Yang

Concord Academy

Abstract

Suppose n is a positive integer. The (imaginary) sea of Babab has islands each of which has an n-letter name that uses only the letters “a” and “b,” and such that for each n-letter name that uses only the letters “a” and “b,” there is an island. For example, if n = 3, then Aaa, Aab, Aba, Baa, Abb, Bab, Bba and Bbb are the islands in the sea of Babab. The transportation system for Babab consists of ferries traveling back and forth between each pair of islands that differ in exactly one letter.

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