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A pin tumbler lock has a series of pins, each of which must be positioned at the proper height to allow the lock to

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A pin tumbler lock has a series of pins, each of which must be positioned at the proper height to allow the lock to open. The security of the lock is determined by the number of pins in the lock, as well as the number of different possible lengths for the pins. Inserting the proper key in the lock aligns the pins properly and allows the interior of the lock to be turned. If a pin tumbler lock has eight pins, each of four different lengths, how many different keys should be tried in order to guarantee that the lock could open? To guarantee that the lock could open, keys should be tried.

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