Summer
Institute For The GiftedClasses taught by Maureen L Greenbaum
Drew University
June 30 - July 20, 2002
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Summer
Institute For The Gifted Classes taught by Maureen L Greenbaum Drew University June 30 - July 20, 2002 |
At the Lincoln Park High School there are exactly 1000 lockers (numbered 1
through 1000). The student body at Lincoln Park High School numbers exactly 1000
students. On the opening day of class in September the students line up in front
of the school, single file. All 1000 are present. They conduct the following
procedure:
The first student enters the building and reverses each locker. (Reversing a
locker simply means that you close a locker that is open and you open a locker
that is closed).
When the first student is finished reversing each locker the second student
enters the building and reverses the lockers 2, 4, 6, 8, ...., Etc.
When student 2 is finished the third student enters the building and reverses
the lockers 3, 6, 9, 12, ......Etc.
When student 3 is finished the fourth student enters the building and reverses
the lockers 4, 8, 12, 16, Etc.
When student 4 is finished the fifth student enters the building and reverses
the lockers 5, 10, 15, 20, Etc.
In general, the n th student, upon his/her turn, enters the building and
reverses lockers numbered n, 2n, 3n, 4n, ......
The process continues right on through the one thousandth student. All the
lockers are closed prior to the first student entering the building. The problem
is how many lockers are open after the last student, student number 1000, has
finished the reversal process? This problem comes from Dr. Philip Zipse, the
Founder and Director of the Summer Institute For The Gifted. E-mail your answers
to him at: pzipse@cgp-sig.com
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