Locker Problem Activity

Imagine you are at a school that still has student lockers. There are 1000 lockers, all shut and unlocked, and 1000 students.

  1. Suppose the first student goes along and opens every locker.
  2. The second student goes along and shuts every other locker beginning with number 2.
  3. The third student then goes along and changes the state of every third locker beginning with number 3. (If the locker is open, the student shuts it and if the locker is closed, the student opens it.)
  4. The fourth student changes the state of every fourth locker beginning with number 4.
If this continues until all 1000 students have followed the pattern with these lockers, which lockers will be open and which will be shut at the end? Why?

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