Imagine a set of lockers, labelled 1 to x, that are closed. The janitor opens every 1st locker, making them all open. Then the janitor opens every 2nd locker, making then half open and half closed, and so on until the janitor is unable to open or close any more lockers. What state will the lockers be in? The answer is that every number with an odd number of factors, including 1 and itself, which has to be square numbers, will be open. Turbo mode is recommended.
The problem came from a Great Courses lecture about mathematical problem solving.
