13 Caves and a thief logic puzzle? [CLOSED]

Question

There are 13 caves arranged in a circle.
There is a thief hiding in one of the caves.
Each day the the thief can move to any one of of the caves that is adjacent to the cave in which he was staying the previous day.
And each day, you are allowed to enter any two caves of your choice.

What is the minimum number of days to guarantee in which you can catch the thief?

Note:
1. Thief may or may not move to adjacent cave.
2. You can check any two caves, not necessarily be adjacent.
3. If thief and you exchange your caves, you will surely cross at some point, and you can catch the thief immediately.

Answer 1

I think in 6 days the thief will be caught
Day 1: C2,C3.
Day 2: C1,C4.
Day 3: C13,C5.
Day 4: C12,C6.
Day 5: C11,C7.
Day 6: C10,C8
and if the thief in this case managed to stay hidden even on day 6, it's clear that the thief is in C9
and I will be able to catch him on day 6 itself.

P.S. => If there is a better answer please do post it below, I am curious to know if there is a better one.

Comments

Suppose on day 1 theif was at cave 1 and on day 2 he moves to cave 2 then?

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The solution will work only if we assume that the cop will come to know the thief's location
If the thief enters one of the caves the cop has already checked.
Otherwise if the thief just knows where the cop will check next he will never be found with any method

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The condition 3 on the notes of the question will prevent what you just said anyways.

Answer 2

in 12 days the thief can be caught