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 four ​pins, each of five different​ lengths, how many different keys should be tried in order to guarantee that the lock could​ open?

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