How Many Different Keys a Five-Pin Lock Really Has: Counting Usable Bitting Combinations Under an Adjacent-Cut Rule

A five-pin cylinder with six depth steps per pin is often described as offering 7,776 different keys, the value of six to the fifth power. That figure counts combinations a manufacturer cannot actually cut, because a working key must satisfy the maximum adjacent cut rule: neighbouring depths that differ too steeply produce a ramp the key cannot slide past the pins. This study enumerates all 7,776 combinations exactly and tests each against a stated adjacent-cut limit of three steps. Only 4034 combinations survive, so 48.1 percent of the advertised space is unusable, and two randomly keyed locks share a key with probability 0.0248 percent. Among 200 houses keyed at random from the usable set, the expected number of pairs sharing a key is 4.93. The figures argue for reading lock specifications by their usable combinations rather than their pin count, and for preferring six-pin cylinders or additional depth steps where key uniqueness across a street or a housing development actually matters. SIMULATED, NOT MEASURED.