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MathNet 2004 — Part 01 Question 75

Math Olympiad Vault · MathNet 2004 — Part 01

Question 75

In any word with letters $a$ and $b$ the following changes are allowed: $a b a \rightarrow b$, $b \rightarrow a b a$, $b b a \rightarrow a$ and $a \rightarrow b b a$. Is it possible to obtain the word $b \underbrace{a a \ldots a}_{2003}$ from the word $\underbrace{a a \ldots a}_{2003} b$?