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Topic:  Locker Problem 
Related Item:  http://mathforum.org/mathtools/tool/43/ 
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Subject:  Locker Problem 
Author:  Michael McKelvey 
Date:  Apr 21 2004 
This is another one of those tools whose validity I questioned at first. I
didn't really understand what the heck it was designed to do, until I looked at
the lessons that were designed to make use of it. Then it all fell into place
and it grew on me immmensely. The applet's not too exciting, but it
accomplishes its task and seems to complement the lessons very nicely.
While poking around, I came upon the Middle School Problem of the Week for March
913, 1998:
http://mathforum.org/midpow/solutions/19980309.midpow.html
The 3part question extended the scope of the Locker Problem, also including
the questions "Which locker was switched the most times?" and "Which lockers
were touched exactly twice?" Now, I'm in a number theory class (Math 353), and
the solutions to these 3 problems involve some of the stuff we've been studying
recently, yet I was stymied at firstI had no problem with the "exactly
twice" questionthose are primes, of course, but I wasn't really seeing why
all the open lockers would be perfect squares. I was astounded when I read Jay
Gill's rather detailed solutions to these problems (about a quarter of the way
down the page). He even went so far as to prove why there couldn't be more than
12 factors of any number less than or equal to one hundred! When he explained
the reason for the perfect squares lockers remaining open it suddenly clicked
and I understood it. It just goes to show you that a first year Master's
student can still learn from an 8th grader. It was a very humbling experience,
I must admit.
Michael

Posted for George Reese's C&I 336 class, Spring 2004
http://www.mste.uiuc.edu/courses/ci336sp04
 
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