Longest word accepted by DFA

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The length of the longest word that can be accepted by any DFA which satisfies the following two properties is

I) It has $4$ states.

II)It does not accept any word of length $8$ or $9$ or $10$ or $11$ or $12$?

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Hint:

  • If the automaton has only 4 states, then some state has to be revisited at most every 4 parsed letters.

I hope this helps $\ddot\smile$