Locker

In front of you are 100 closed lockers numbered 1 to 100 belonging to an eccentric billionaire. The billionaire tells you that she will leave her entire estate to you, if you can solve the following riddle:

She is going to walk past the lockers 100 times. The first pass, she will open every locker. The second pass, she will close every other locker. The third pass, she will go to every third locker and close it if it is already open or open it if it is currently closed. The fourth pass, she will go to every fourth locker and close it if it is already open or open it if it is currently closed. This pattern continues for every pass after the fourth pass until she completes her hundredth pass. At that point, no other lockers will be opened or closed.

Which lockers will be open after she finishes all her passes?

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