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The janitor has all the lockers closed

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School is about to begin. The janitor has all the lockers closed. All 1000 of them.

Student #1 comes along and opens ALL of the lockers.

Student #2 comes along and closes doors 2, 4, 6, 8, 10, etc....

Student #3 comes along and changes the state of every 3rd locker ( 3, 6, 9, 12, 15).

Student #4 comes along and changes the state of every 4th locker (4, 8, 12, 16).

Student #5 comes along and changes the state of every 5th locker (5, 10, 15, 20)

Student #6 comes along and changes the state of every 6th locker (6, 12,18. 24)

It keeps going until all 1000 students go through. What lockers are closed?

Reference no: EM13957355

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