MathDB

A tribe called Ababab uses only letters

A

and

B

, and they create words according to the following rules: (1)

A

is a word; (2) if

w

is a word, then

ww

and

w\overline{w}

are also words, where

\overline{w}

is obtained from

w

by replacing all letters

A

with

B

and all letters

B

with

A

(

xy

denotes the concatenation of

x

and

y

) (3) all words are created by rules (1) and (2). Prove that any two words with the same number of letters differ exactly in half of their letters.

Problem Statement