13 Caves And A Thief Logic Puzzle

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: 2 Policemen

As the Caves are arranged in a circle, Start Searching in 2 adjacent Caves on 1st day
Then on next day, 1 person moves Clockwise and another moves anticlockwise.
So it would take a maximum (minimum guarantee) of 7 days to catch the thief.

1 Policeman

The answer is 12

For example: lets say police checks c1 & c13 on 1st day. Now every day keep checking c2, c3, c4 & so on…and also check c13.
1st Day; c1 & c13
2nd day: c2 & c13
3rd Day: c3 & c13
..
.. 12th Day: c12 & c13
so on max 12th day police can catch the thief.