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One Hundred Locks

A lot of people commented on how easy this puzzle was. The answer which you could either arrive at experimentally or through deduction, was that the locks 1,4,9,16,25,36,49,64,81 and 100 needed to be turned. The rest could be left alone.

An officer turns a lock only if his number is a divisor of the locks number, e.g., Officer #7 turns locks 7,14,21,etc. But for every divisor of a number, there is a second number which complements it. The only exceptions are those numbers who have a divisor which, when multiplied by itself equals the number. And those would be the perfect squares.

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