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HMMT 2003 U40

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All the sequences consisting of five letters from the set {T,U,R,N,I,P}\{T, U, R, N, I, P\} (with repetitions allowed) are arranged in alphabetical order in a dictionary. Two sequences are called "anagrams" of each other if one can be obtained by rearranging the letters of the other. How many pairs of anagrams are there that have exactly 100 other sequences between them in the dictionary?

Dataset text NuminaMath olympiads. Quoted with source.

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