Puzzle:
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Suppose there is a school with an infinity of lockers, numbered 1, 2, 3, ....
Initially all lockers are closed.
Definition: A locker is "switched" if it is changed from shut to open, or vice versa.
At 1/2 minute to noon, every 2nd locker 2, 4, 6, ... is switched.
at 1/3 minute to noon, every 3rd locker 3, 6, 9, ... is switched.
Or in general: For each positive integer n >= 2:
* At 1/n of a minute to noon, every nth locker n, 2n, 3n, ... is switched.
No other changes are made to the lockers.
Question:
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Which lockers are open at noon?
—Dan
