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"Any sequence of length >=7, fizzbuzz will be present."

Are you sure? I don't think the challenge said the sequence could not be gappy.

This is resolved in one of the examples given in the introduction where the interviewer agrees that "buzz buzz" is an invalid sequence.

If sequences could be gappy, wouldn't the solution be just mapping fizz to 3, buzz to 5 and fizbuzz to 15? ( or multiples of those numbers, if duplicates aren't allowed )

But in no case would that be the shortest sequence.

For your example a shorter one would be 9,10,15.

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