MEMO 2012 ekipno problem 3


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June 23, 2013
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Let n be a positive integer. Consider words of length n composed of letters from the set \{ M, E, O \}. Let a be the number of such words containing an even number (possibly 0) of blocks ME and an even number (possibly 0) blocks of MO . Similarly let b the number of such words containing an odd number of blocks ME and an odd number of blocks MO. Prove that a>b.
Source: Srednjoeuropska matematička olimpijada 2012, ekipno natjecanje, problem 3