There's a castle with 17 bedrooms in a line, in which a princess sleeps.

Each night, she sleeps in a room that is adjacent to the room that she slept in the previous night.
A prince is allowed to knock on just one of the 17 rooms every morning.

To win the princess's heart, the prince must knock on the room where he could have found the princess yesterday.

What is the minimum number of days that the clever prince would require to guarantee that he can win the princess's heart?

Source: This question is inspired by another question from brilliant which required the prince to find the princess, meaning to knock on that room where he could find the princess on the day he knocks... In our version prince must knock on that room where he could have found the princess one day before the day he knocks...

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