### Find Minimum number of days to guarantee to catch the thief

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.

See Answers

Answer is 12 days.

Lets assume the thief is in cave C1 and going clockwise and you 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 idea is to check C13 everyday so that if thief tries to go anti clockwise you immediately catch it and if goes clockwise you will catch him in maximum 12 days(including the case where he remains in Cave C1).

**How?**Lets assume the thief is in cave C1 and going clockwise and you 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 idea is to check C13 everyday so that if thief tries to go anti clockwise you immediately catch it and if goes clockwise you will catch him in maximum 12 days(including the case where he remains in Cave C1).

Rupinder says

I think we are assuming that the Thief knows that there are cops searching the caves and that they can search 2 caves in a day.

It is not mentioned in the puzzle that the Thief is aware of this and hence there is no incentive for the Thief to move caves.

The cops should search 2 caves in sequence and at minimum on the 7th Day they would catch the Thief.

vinod says

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.

Manish K says

Never… Thief will remain in C1, Till Police comes to C2 and then thief moves to C2 when Thief checks C1 and this series continues. Thief can move clockwise and anticlockwise so thief may not wanted to cross C13, He can oscillates between C1-C12

divya says

@manish

if he tries to move to cave c1 when, the police will cross him while going from c2 to c1

MANISH says

Why cant the answer be 7.

DAY 1 C1 & C13

DAY 2 C2 & C12

DAY 3 C3 & C11

DAY 4 C4 & C10

DAY 5 C5 & C9

DAY 6 C6 & C8

DAY 7 C7

Nikunj says

cause if he is in cave 2 or cave 12 on the 1st day thn u r gonna miss him the next day onwards as he can either be in cave 1 o cave 13 respectively the next day..

which u will not chk for the rest of the 6 days

SOS says

if he goes to cave 2 he will be caught while crossing.

sos says

i too think it is 7.

Peeps says

Ya.. But what if he goes to c1 on day 2??

Read the question.. They r asking for minimum number of days….

anonymous says

solution is crooked as mentoned by sandeep…