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?

Does the first person open all the even lockers, or all the odd ones? (There is a slight difference as the problem progresses to the later persons.)

Assuming that it is the even ones, are the second person's first two lockers 3 and 9 (the first two odd numbered lockers divisible by 3) or 5 and 11 (the third and sixth of those still closed)?*

The related questions concerning the third and fourth persons' "every fourth" and "every fifth"

*If the first person opens the odd lockers, the first part of the question becomes 4 and 10, and the second part becomes 2 and 8.

Posted by TomM on 2002-12-06 21:29:26