The janitor at Grand high school fixe the locks on all 1,000 lockers so that the

Question

The janitor at Grand high school fixe the locks on all 1,000 lockers so that they cannot be reopend after they are closed.

On the first day of school, all the lockers are open except locker #1.

The first student enters and walkd to the first open locker, Locker #2. He puts his book into this locker and leaves it open. But then he closes all multiples of his locker number ( 4,6,8,10,....).

The next student walks to the next open and unoccupied locker. She claims this locker, leaves it open, and closes all multiples of her locker number.

Students continue to enter one at a time, each one claiming the next open and unoccupied locker. They each leave their locker open but close all multiples of their locker number.

After all students have entered, which lockers are open and which are closed?

Explanation / Answer

Locker 1 is already closed.

Locker 2 is open and all multiples of 2 are closed.

Locker 3 is open and all multiple of 3 is closed.

So, next student goes to locker 5 (as 4 is multiple of 2, which is closed).

Next student goes to locker 7 (as 6 is a multiple of 2, which is already closed).

So, only lockers with prime numbers will be open and all other lockers will be closed.

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