Prime Time

Locker Problem

Instructions

There are 1,000 lockers in the long hall of Westfalls High. In preparation for the beginning of school, the janitor cleans the lockers and paints fresh numbers on the locker doors. The lockers are numbered from 1 to 1,000. When the 1,000 Westfalls High students return from summer vacation, they decide to celebrate the beginning of the school year by working off some energy.

  • Student 1 opens every locker.
  • Student 2 either opens or closes every other locker.
  • Student 3 opens or closes every third locker. And so on, ...

Which locker doors are open when every student finishes?

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© 2006 Applet written by S. Keller, Department of Mathematics, Michigan State University

 
© 2006 Connected Mathematics Project, Michigan State University and Pearson
Education, Inc. publishing as Pearson Prentice Hall