There is a wall with 1000 closed lockers on it. A person walks down the hall opening every other locker. Then the next person opens every 3rd locker. The next opens every fourth locker. The next every fifth locker.

Once this has been done, how many lockers are still closed?

I'm assuming that the people that come after the first open every 3rd, 4th, etc. locker that is still open.

The first person opens 500 of them. The second person opens every 3rd one that's still open (166 of them so 334 left). The next person opens every 4th that's still open (83 of them so 251 left). The last person opens every 5th that's still open (50 of them). Therefore, only 201 are still closed.

Posted by np_rt on 2002-12-07 14:04:59