A Yahoo! answers user suggested that there are 5^5 possible unique configuration

Question

A Yahoo! answers user suggested that there are 5^5 possible unique configurations for a physical key, but the answer wasn't sourced. I wondered if anyone had similar numbers for how many possible key combinations there are. I ask because, it seems impossible that there can be a unique key for every lock in the world, and I'd like to know how many different key configurations a thief would have to try to have a certainty of cracking the lock (if the thief didn't want to force the lock in another way.)

How many unique house keys can possibly exist?

Explanation / Answer

There's actually a mathematical paper on the subject available to read at jstor.org and the answer isn't quite as simple as {the number of cuts}^{possible cut depths} because there are cases where on cut will remove the possibility of an adjacent depth and so forth. The paper is ingeniously named "How Many Different Keys?" and is by a bloke called something Coulson. It does get complicated though! There are so many different factors to take into account that it's likely each lock/key combo is pretty unique although some cheap padlocks could have the same shape if the manufacturer is cutting corners.

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