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

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

posted May 8, 2014

## 4 Solutions

Lets assume the thief is in cave C1 and going clockwise and cops start searching from cave C13 and C12 on your first day.
Cave C13 and C11 on second day,
C13 and C10 on third day and so on till C13 and C1 on 12th day.
So basically the aim is to check C13 everyday so that if thief tries to go anti clockwise you immediately catch it and if goes clockwise cops will catch him in maximum 12 days (this include the case where he remains in Cave C1).

solution May 12, 2014

I agree with Hariom Sharma.
Since exchanging the cave will also catch the thief, moving both clockwise and anti-clockwise gets you the thief fastest.
So 7 days.

solution Jul 18, 2015 by

The thief can be caught in 12 days.

solution Aug 11
–1 vote

within 12 days we can catch him or it may require less than 12 days also.

solution Aug 11

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