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

+1 vote
1,074 views

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

+1 vote

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.

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).

The thief can be caught in 12 days.

–1 vote

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

Similar Puzzles
+1 vote

You have a flashlight that takes 2 working batteries. You have 8 batteries but only 4 of them work.

What is the fewest number of pairs you need to test to guarantee you can get the flashlight on?

You've got 27 coins, each of them is 10g, except for 1. The 1 different coin is 9g or 11g (heavier, or lighter by 1g). You should use balance scale that compares what's in the two pans. You can get the answer by just comparing groups of coins.
What is the minimum number weighings that can always guarantee to determine the different coin.

There are (n+1) people in a party, they might or might not know each others names.

There is one celebrity in the group(total n +1 people), celebrity does not know any of n peoples by name and all n people know celebrity by name.

You are given the list of people's names(n+1), You can ask only one question from the people. DO YOU KNOW THIS NAME ?

HOW MANY MINIMUM NUMBER OF QUESTIONS YOU NEED TO ASK TO KNOW THE CELEBRITY NAME?

NOTE: assume all names are unique.

+1 vote

You die and the devil says he'll let you go to heaven if you beat him in a game. The devil sits you down at a perfectly round table. He gives himself and you an infinite pile of quarters. He says, "OK, we'll take turns putting one quarter down, no overlapping allowed, and the quarters must rest flat on the table surface. The first guy who can't put a quarter down loses." You guys are about to start playing, and the devil says that he'll go first. However, at this point you immediately interject, and ask if you can go first instead. You make this interjection because you are very smart and can place quarters perfectly, and you know that if you go first, you can guarantee victory.
Explain how you can guarantee victory.