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Proof of existing assignment for a line of letters

Source: Japan Mathematical Olympiad Finals 1997, Problem 5

April 24, 2007
combinatorics proposedcombinatorics

Problem Statement

The letters AA or BB are assigned on the points divided equally into 2n (n=1, 2,⋯ )2^{n}\ (n=1,\ 2,\cdots) parts of a circumference.If you choose nn letters from any succesively arranging points directed clockwise, prove that there exists the way of assignning for which the line of letters are mutually distinct.
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