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Good strings

Source: Italian TST 2006 Q1

May 27, 2006
inductionPascal's Trianglecombinatorics unsolvedcombinatorics

Problem Statement

Let SS be a string of 9999 characters, 6666 of which are AA and 3333 are BB. We call SS good if, for each nn such that 1≤n≤991\le n \le 99, the sub-string made from the first nn characters of SS has an odd number of distinct permutations. How many good strings are there? Which strings are good?
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