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?
If you assume you are counting open as well as closed lockers, then your answer is the set of numbers 1 to 1000 that are relatively prime to 2, 3, 4, and 5. (i.e., 1,7,11,13,17... etc.) This equals 266 lockers. If you started opening with the first locker, then it is the same set +1 (i.e., 2,8, 12, 14, 18... etc.), also equal to 266 lockers.
If you count only *closed* lockers (not a valid assumption based on the wording), then the answer has been given 1000*1/2*1/3*1/4*1/5 (although it's not that simple due to rounding) = 201.
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