What are the odds?

I was "between gyms" for about a year. When I joined my current gym, I realized that I had completely forgotten the combination to my lock. I tried a few sequences, but couldn't recall the correct one. So rather than leave my stuff in the locker unlocked (you know there's a black market for white dress shirts, right?) I bought a new lock from the gym. As I was working out, I repeated the new combination to myself over and over, imprinting it on my brain. Then it occurred to me: I already knew this combination.

I went back to my locker, got out the old lock, tried the combination, and CLICK, it opened. My brand-new lock had exactly the same combination as my three year-old lock! I thought, what are the odds!? Then I thought, what are the odds?

The first and easiest answer may be 1-in-64,000. The combination has three numbers, each ranging zero to forty, so 64,000 is what I assumed initially. This made me feel very lucky. (Lucky doesn't seem like the right word...coincidence-stricken?) As nice as it would be to feel so luck-- er, coincidence-stricken -- I had a hunch there was more to it.

Both locks were manufactured by Master Locks, so I thought that perhaps the people at Master Locks must be so lazy that they actually only use ten different combinations in all of the locks that they sell! I like that theory, but I admit it's unlikely. So I went to the internet to put an end to the mystery once and for all, and what I found was nearly as shocking as the Lazy Master Lock Theory.

I won't bore you with the details. I'll let this guy bore you with the details, and I'll summarize: Because of the way they are made, there are only 100 possible correct sequences to single-dial combination locks. Think about that the next time you protect something valuable with one of these "locks".


kenny said...

Wow! I never realized how vulnerable my sweaty practice jersey and math books were in high school! If I knew then what I know now...

Kate said...

I kept my locker "set" just like 98% of kids at school - so I only had to turn it one notch and it would open. The problem with that was that Mr. Gaul, the Earth Science teacher, liked to teach the students a lesson by walking down the hall spinning our locks. There were so many kids who had no idea what their combination was!

alisa said...

i love hearing about all this mathy stuff. great post!

Carissa said...

See, these are quandries the Non-Math-Types, like me, never ever ever are troubled by. I ask Alisa, Beth, and Kat for backup here...These questions are "things beyond our ken". I remain utterly oblivious to such things, unaware of any statistical probability of any kind. It would absolutely never occur to me to think about the numbers in my world, how often they occur, the odds of anything, much less to actually know how to answer such horrific mathematical questions. I probably would have stopped at "dang, that's handy that I don't have to try to remember more numbers!"

You throbbing brain, you! So fun to read the various mental gymnastics of my brilliant friends!