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Topic: CIRCULAR JAIL CELL (Read 1752 times) |
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casual_kumar
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CIRCULAR JAIL CELL
« on: Aug 7th, 2006, 12:35am » |
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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.
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| « Last Edit: Aug 8th, 2006, 3:04am by casual_kumar » |
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casual_kumar
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Re: CIRCULAR JAIL CELL
« Reply #1 on: Aug 11th, 2006, 1:01am » |
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Come on guys, dont you people have any comments in this??
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towr
wu::riddles Moderator
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Some people are average, some are just mean.
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Re: CIRCULAR JAIL CELL
« Reply #2 on: Aug 11th, 2006, 2:51am » |
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Nope.. no comment.
The solution makes sense. I really couldn't think of anything to add.
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Wikipedia, Google, Mathworld, Integer sequence DB
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casual_kumar
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Re: CIRCULAR JAIL CELL
« Reply #3 on: Aug 11th, 2006, 4:05am » |
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Sorry for being impatient, but can you people now promote me to something greater than newbie?? 
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SMQ
wu::riddles Moderator
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Re: CIRCULAR JAIL CELL
« Reply #4 on: Aug 11th, 2006, 5:00am » |
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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 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
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--SMQ
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