Weiser Permutations

assume (its too cold for me to go out in 10 degree weather and look..) there are as you say 10 depths.. 10 to the 5th.. that is TOTAL.. a more realistic number might be, say 80-85% of that number..

lets assume a MACS of 7.. first cut is a 0-the NEXT can be anything between 0 and 7.. and depending on THAT cut, the next might be any of 10 possible...

you eliminate (or should) all of same number.. 55555 for instance. ther are others that 'should not' be used as well..01010 and the like,, given the crappy key machines floating around everywhere, that might not be 'secure' under some circumstances

--Shiva--

If sure of depths, use the powers!

Using 5 pin: 10 X 5 then go to the 5th power

Newnsie

I think it is 7 but you might be able to strech it to 8 if you used Lab pins and didn't widen your cuts.

Prior to discarding the undesirable combinations (MACS violations, descending cuts level cuts etc.) there would be 100,000. Then it would be a matter of tossing combinations that wouldn't work.

The answer is probably "plenty"

Ok Christopher,

I see you are posting this everywhere you can think of :)

If there were no constraints it would be number-of-depths to the power of number-of-pin-chambers. That needs to be reduced not only to allow for MACS, but to reject combinations which are unacceptable for other reasons of practicality (eg, those which are excessively pickable or which tend to malfunction after the key has experienced some wear.)

The least-thought way to get this number is to simply ask the manufacturer. Next-least-thought is to write a program which counts through the possibilities, rejecting those which violate the constraints. ("Experimental mathematics" rather than theoretical.) A formula is possible but probably more ugly than you really want to deal with.

As do most keying programs. But if you have any programming knowledge it's not hard to write your own, especially if you aren't concerned about how quickly it produces the result.

Actually it's the only commercially available keying program that does what it does. In addition to working with the normal depth and MACS specifications you can tell it many other rules to follow. You can tell it how many positions can be the same, how many positions must be different, how many in a row the same, what maximum difference must be in every code, etc.

It is >

I'm sorta surprised those aren't more common features. Then again, if you had anything to do with its creation I'm not surprised it *does* have those features...

Interestingly I had brief access to a very old locksmithing book (must have been 1800's) and the author condemed the use of differs where cuts were at the same level. He argued that in a six lever lock if two cuts were at the same level, it was equivalent in security to a five lever lock, I do not recollect any explanation being given for this. This drastically reduces the number of differs available eg for a six lever lock with six depths this would reduce the number of differs from approx. 46,000 to 720, or even less eg if 123456 and

654321 were excluded. I think that Bramah may have respected that limitation at least in their earlier locks.

Each level was different in the 'parautoptic' lock. The user would assemble a number of loose bittings (each of a different depth) to make up the key, and turning the key to shoot the bolt would set the levers accordingly. I think there were 10 or more levers so there would have been a satisfactory number of differs despite the limitation imposed by the available loose bittings.

Lever locks could have a 'converse' of MACS limitations. A shallow cut between two deep cuts could result in a narrow 'stalk' that could be vulnrable to bending or breaking.