Notes for Locker Problem

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“The locker problem”:
A school has 1,000 students and 1,000 locker. On the first day, all the lockers are open. 
  • student #1 closes each locker
  • student #2 opens each 2nd locker
  • student #3 changes each 3rd locker
  • student #4 changes each 4th locker
  • student #5 ……………….5th locker

After all 1,000 are done, which lockers are open/closed?why?

















Answer:
Every door with a square number within 1000 (2^2 th, 3^2 th ....... 31^2 th, except 1^2) is closed, and others are open.

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