Prince and The Princess

This is another version of the previous 7 cats puzzle.

On the top floor of a castle lives a princess. The floor has 17 bedrooms arranged in a row. Each bedroom has doors connecting to the adjoining bedrooms as well as to the outside corridor. The princess sleeps in a different bedroom each night by opening the door to an adjoining bedroom and spending the night and the next day in that room.

One day a prince arrives at the castle. The King tells him of the princess' sleeping patterns and informs him that each morning he may knock on one of the outside doors. If the princess happens to be behind that door, she will open it and consent to marry him. The prince must return to his kingdom in 30 days, so he can make at most 30 attempts. Can the prince win the hand of the princess and if so, what is his strategy?

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