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words

Source: Bulgarian Math Olympiad MO 2004, problem 4

May 17, 2004
invariantinductionfunctiongeometrygeometric transformationgroup theorycombinatorics proposed

Problem Statement

In a word formed with the letters a,ba,b we can change some blocks: abaaba in bb and back, bbabba in aa and backwards. If the initial word is aaa…abaaa\ldots ab where aa appears 2003 times can we reach the word baaa…abaaa\ldots a, where aa appears 2003 times.
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