SOLUTION: A new high school has just been opened, with an enrollment of 1000 students. The school has 1000 lockers, numbered 1 to 1000, to accommodate them. On the first day of school, all

Question 369226: A new high school has just been opened, with an enrollment
of 1000 students. The school has 1000 lockers, numbered 1 to
1000, to accommodate them. On the first day of school, all
1000 lockers are closed and all 1000 students are outside
waiting to be let into the building. The first student enters and
opens all of the lockers. The second student follows and
closes every second locker, beginning with the second locker.
The third student enters the school and reverses every third
locker beginning with locker 3 (e.g., if the locker is closed it is
opened and vice versa). This procedure is continued until all
1000 students have passed by all the lockers. When they
finish, which lockers will be open?
Answer by acalgebra(30) (Show Source): You can put this solution on YOUR website!
The square numbered lockers (1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, and 961).
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