How many possible combinations are there?

[bobbybeatbilly]

Math has never really been my strong suit. If I am dealing with a 5 pin lock that has 5 factory depths. How many different possible lock combinations are there and why. Obviously there won't be a key cut to 1:1:1:1:1 so how would you calculate the amount of possible combinations.

[macgng]

5 cuts with 5 depths is 5^5 = 3125, minus combos that don't conform to MACS. I'm sure someone with more lockie knowledge can explain.

[mdc5150]

Math has never really been my strong suit. If I am dealing with a 5 pin lock that has 5 factory depths. How many different possible lock combinations are there and why. Obviously there won't be a key cut to 1:1:1:1:1 so how would you calculate the amount of possible combinations.

Here is a nifty little tool to help you figure that all out. http://www.lockcodes.com/combcoun/

[bobbybeatbilly]

Thanks guys. You never disappoint.

[clearmoon247]

Ya know, mac, thats pretty close to spot on, but there are others that just wont happen, e.g. 1-1-1-1-1 or 5-5-5-5-5, so you can remove another 5 combo's bringing it down 3120, if it has that few of combos, id guess it has a MAC of 4, but for sake of argument, lets say 3 is the MAC, so correct me if im wrong, but that would mean you could not have a bitting of 1-5, but 1-4 is possible, so you can eliminate another 29, bringing the count down to 3099. If you were looking for realism, its possible to build a chart of all combo's, eliminate the 34 based on MAC or "zero bitting" then all non-practical bittings, you can get a much smaller scope, but as far as brute force combo's are concerned, it wouldn't cover ever possible combination

[Farmerfreak]

I've seen factory Schlage keys cut and factory stamped 55555.. So yes it does happen even though it shouldn't. I've also seen lots of people use locks that are still zero or one bitted..

[MBI]

I've seen factory Schlage keys cut and factory stamped 55555.. So yes it does happen even though it shouldn't. I've also seen lots of people use locks that are still zero or one bitted..

That's funny. I'd love to find a lock like that for my collection. Factory pinned with factory punched keys to a bitting like 55555 or something like that.

[rai]

I used to have a schlage C cut to a bitting of 99989 or something like that, it was factory the numbers were stamped on it. a natural bump key.
Why do schlage and american lock co's stamp the bitting on keys? this means that anyone could make a copy if they have seen the key. its basically insecure.
GM used to stamp the code or bitting on a knockout from the keybow with a hole in it so you could save that number without it being attached to the key, that was much better thought out.

[rai]

there are many combinations that should not be used,
55555 is a bitting that can be picked easily with a straight piece of wire, and anyone who has seen the key could do it.
further, if this key is copied, and copied again, by the third generation or so, the little peaks between the pins start to get smaller with each generation and they disappear, this leaves a straight key and such a key can easily be pulled out of the lock without resetting it to top dead center, meaning it can be pulled out leaving the plug picked.
I once had an apartment key that had a step down bitting and one day I came home and saw that the lock was picked, however it was picked in the direction for locking, I got suspicious until I realized that as I was locking up and leaving I was simultaneously pulling out the key while turning away from the door, and simply pulled the key out without locking the plug.

[blate]

Adding to rai's comments...

Any bitting that allows the removal of the key without the plug at top dead center (or equivalent) is generally considered improper. For example, numbering bow to tip, a 54321 should be disallowed but a 54323 is OK. I don't recall the combanitorics (sp?) to work out all such illegal codes, but it substantially reduces the key space.

Most sound keying systems will also have rules about how many adjacent cuts may be at the same height -- e.g., 53335 may be disallowed because there are three 3's in a row.

In some systems, there are also rules about where and/or how many very deep cuts may be placed on the key -- the concern being weakening of the key.

You can see how having a high MACS, more depths, and more pins can make a huge difference in the size of the key space.

Tobias has a very detailed section about this subject in LSS; other good sources are available, too, if you want to learn more.

[easy-e]

I've seen factory Schlage keys cut and factory stamped 55555.. So yes it does happen even though it shouldn't. I've also seen lots of people use locks that are still zero or one bitted..

When I was younger all of the new portable classrooms that were trucked into my schools all used blank keys. From what I remember there was no milling at all. The schools locksmith would come by sometime before the school year started and re-pin them. A few different summers I came in to setup computers and other stuff otherwise I never would have known. My thought always was that the manufacturer probably does it for convenience of not having to keep track of the keys when all of their customers are going to re-pin them anyways.