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?
1. Thief may or may not move to adjacent cave.
2. You can check any two caves, not necessarily be adjacent.
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Answer is 12 days.
Let’s assume the thief is in cave 1 and going clockwise and you start searching from cave 13 and 12 on your first day.
Cave 13 and 11 on second day,
Cave 13 and 10 on third day and so on till Cave 13 and 1 on 12th day.
So basically the idea is to check Cave no.13 everyday so that if thief tries to go anti clockwise you immediately catch it and if he goes clockwise you will catch him in maximum 12 days (including the case where he remains in Cave 1).