Problem solving: 1000 lockers and 1000 students

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melimarti12

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Jul 14, 2008
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I have this problem:
Pascal High School has exactly 1000 lockers and exactly 1000 students. On the first day of school, the students meet outside the building and agree on the following plan. The first student will enter the school and open all the lockers. The second student will then enter the school and close every locker with an even number. The third student will then “reverse” every third locker. That is, if the locker is closed, the student will open it. If the locker is open, the student will close it. The fourth student will reverse every fourth locker, and so on, until all 1000 students have entered the building and reversed the proper lockers. Which lockers will finally remain open?

I tried solving it by squaring each locker until i got to 31 and I got 961, but i'm not sure if that is right. can someone help me?
 
melimarti12 said:
I tried solving it by squaring each locker until i got to 31....
Click to expand...
What was your reasoning for this?

Please be complete. Thank you! :D

Eliz.
 
Pascal High School has exactly 1000 lockers and exactly 1000 students. On the first day of school, the students meet outside the building and agree on the following plan. The first student will enter the school and open all the lockers. The second student will then enter the school and close every locker with an even number. The third student will then “reverse” every third locker. That is, if the locker is closed, the student will open it. If the locker is open, the student will close it. The fourth student will reverse every fourth locker, and so on, until all 1000 students have entered the building and reversed the proper lockers. Which lockers will finally remain open?
Click to expand...
For each locker number, find all of the exact divisors including 1 and the number itself. If the number of divisors is odd, then the number of people who reversed the locker is odd, and the locker is open. If the number of divisors is even, then the number of people who reversed the locker is even, and it is closed. The only numbers with an odd number of divisors are the perfect squares. Therefore, the lockers that remain open are those identified by the perfect squares.
 
Are there any drawbacks to installing a Detroit Locker in the front differential? I will be installing a Detroit Locker in the rear diff. of my Excursion for better traction off road. I would really like to have true 4x4 and don't like the air lockers, cable operated lockers, etc. as much as the Detroit Lockers. The simplicity of the unit attracts me. How bad will be the on road performance with a front unit installed? Thank you in advance for any advice!
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Don't ya know that girls DO NOT install Detroit Lockers ?
 
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