Impossible Math Question

[TerranForces]

A trivia question about math was posted on another forum and I just can't figure it out. I've been at it for days. I am sure one of you guys can get it. I'll send a couple gmail invites to whoever can figure it out. Its really bothering me. Anyway, here it is:

"# 9 - I hate math...so today's is worth 2 points

How many (more or fewer) possibilities does a typical mechanical lock have versus a combo lock? Closest noted estimation wins. Don't forget to show your work.

*Hint: typical mechnical locks - used on vaults, masterlocks.... combo lock - they're usually 6 digits ranging from 0 - 9 + the # key."

Most of the other questions get answered in a couple hours, but this one is approaching a week. My guess was 11^6 - 40x39x39 = ~1.7 million
It was wrong of course. The closest answer was 39,916,800 according to the OP. I noticed that his answer was 11!=39,916,800.

 

[CycloWizard]

I'm not sure what you mean by 'mechanical lock.' If it's a masterlock (i.e. a keyed lock), then it's basically infinite, since it's an analog device (limited by the tumbler arrangement and so on). If you mean a dialing combination lock, then the answer is: it depends. How many numbers are on the lock is the deciding factor.

 

[Mark R]

What types of mecahnical lock, and what type of combination lock? There are loads of different types.

E.g. cheap lever mortice locks (commonly found on back doors and side doors) may have as few as 2 levers - giving anything from 15 - 30 different key combinations.
OTOH a high quality cylinder (as is often found in large buildings and office blocks) can be very complex
One lock system I looked at recently offered 30 billion different key combinations - if I opted for their high end model it would be 300 quadrillion.

Most domestic 'high-security' locks offer around 1000 different keys (lever locks) (4 cut depths, 5 levers = 4^5 combinations) or 30,000 different keys (cylinder locks) (6 cut depths, 6 pins = 6 ^ 6 minus a bit because neighbouring cuts can't always be independent - e.g. can't put a shallow cut next to a very deep cut).

For the combinationn lock - how many digits in the code, and on the key pad - and does the order matter? Most mechanical combo locks can have the code entered in any order.

The combo locks used around here use 5 out of 13 possible digits, entered in any order. This gives 1287 codes (13! / (13-5)!/5!)

Edit: Forgot about the any order bit