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        riddles >> hard >> CIRCULAR JAIL CELL
        
(Message started by: casual_kumar on Aug 7^th, 2006, 12:35am)

Title: CIRCULAR JAIL CELL
Post by casual_kumar on Aug 7^th, 2006, 12:35am

Its clear that the number of times a jail cell is accessed by the jailor is equal to the number of factors of that jail cell number.

For example: jail cell 10 will be accessed in 1st, 2nd, 5th and 10th rounds. i.e. 4 times

So, those cell numbers which have odd number of factors will remain open.

It is quiet interesting to note than most of the numbers have even number of factors, because for every x which is a factor of A, there exists a y such that x*y = A. Unless x=y, we will always have factors in pairs. Now for having odd number of factors, if x=y AND x*y = A, then A must be a perfect square.

So, 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100 will remain open.

Title: Re: CIRCULAR JAIL CELL
Post by casual_kumar on Aug 11^th, 2006, 1:01am

Come on guys, dont you people have any comments in this??

Title: Re: CIRCULAR JAIL CELL
Post by towr on Aug 11^th, 2006, 2:51am

Nope.. no comment.
The solution makes sense. I really couldn't think of anything to add.

Title: Re: CIRCULAR JAIL CELL
Post by casual_kumar on Aug 11^th, 2006, 4:05am

Sorry for being impatient, but can you people now promote me to something greater than newbie?? ;D

Title: Re: CIRCULAR JAIL CELL
Post by SMQ on Aug 11^th, 2006, 5:00am

Your "rank" (other than "moderator") is determined solely by the number of posts you have made. Keep participating in discussions and you'll advance fairly quickly. If you're interested, there's a thread (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_suggestions;action=display;num=1031563459) in the FAQ section which gives the number of posts needed for each level, but be sure to read all the way to the end...

--SMQ