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5/30/07 10:16 PM
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mikeblak
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Edited: 30-May-07
Member Since: 01/01/2001
Posts: 3919
 
I have a problem I have to solve and give 2 ways of explaining the problem to middle school students due tomorrow. Any ideas or assistance would be greatly appreciated. I'll paraphrase to keep it as brief as possible: There are 1000 open lockers and 1000 kids. The 1st kid runs by and slams all the lockers shut. The 2nd kid goes and opens every 2nd locker starting with his number in line (2). The 3rd kid starts at his number in line (3) and changes every 3rd locker's position (if it was open, close it, if it was closed, open it). That pattern continues until all 1000 kids did their thing. 4th in line changes position of every 4th locker, 5th in line changes the position of every 5th locker, etc... At the end of the process, what locker doors would be closed?
7/15/07 6:02 PM
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AlbertEinstein
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Edited: 15-Jul-07
Member Since: 06/15/2007
Posts: 61
1. Every locker whose number is a perfect square will be shut. The rest will be open. 2. Equivalently every number that has an odd number of integral factors will be shut. P.s. you can google this problem I'm sure and find more ways.
7/17/07 5:01 PM
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Jonwell
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Edited: 17-Jul-07
Member Since: 01/01/2001
Posts: 48502
Moot point I think, he needed it May 31st ;)

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