Locker Problem

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?



  • Manually open or close a locker by clicking on the locker.
  • Click on the buttons <--- or ---> to scroll the lockers.
  • Animate the problem starting with Student 1 opening every locker, press the PLAY button. NOTE: If you have open lockers press RESTART before pressing PLAY. Press PAUSE to suspend the animation and PLAY to continue.
  • Select the FAST option to speed up the animation.
  • Enter a number n in the box and press the RETURN or ENTER key to switch every n-th locker.
© 2006 Connected Mathematics Project, Michigan State University

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