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string of length 6 composed of three characters

Source: 2007 Korean MO, 2nd Round, A.M.

August 18, 2007
geometry3D geometrycomplex numberscombinatorics unsolvedcombinatorics

Problem Statement

Consider the string of length 6 6 composed of three characters a a, b b, c c. For each string, if two a as are next to each other, or two b bs are next to each other, then replace aa aa by b b, and replace bb bb by a a. Also, if a a and b b are next to each other, or two c cs are next to each other, remove all two of them (i.e. delete ab ab, ba ba, cc cc). Determine the number of strings that can be reduced to c c, the string of length 1, by the reducing processes mentioned above.
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