Calling ATOT statisticians...

[bignateyk]

I just bought a combination lock box that has 10 keys (1-10).

You have to pick a 4 digit combo, but I found out that it doesn't matter what order you enter your combo in for it to work, so lets say my combo is 3456.

I can enter 3456 and it will open.

Or I can enter 6354 and it will open, etc...

This obviously makes it much easier for someone to guess the correct combination, but how many times would they have to randomly guess to get it right?

I'm thinking it involves combinations and permutations somehow, but I haven't used my statistics in about 5 years, so I'm having trouble remembering.

 

[DCal430]

can you use the same number twice?

 

[blackdogdeek]

(10*9*8*7) / (4*3*2*1) = 210

 

[bignateyk]

can you use the same number twice?

No, you have to use each of the 4 numbers.

 

[bignateyk]

(10*9*8*7) / (4*3*2*1) = 210

Can you explain that? Why isn't there a *6*5 on the numerator?

 

[dank69]

No, you have to use each of the 4 numbers.

Communication isn't your strong suit, is it?

 

[bignateyk]

Communication isn't your strong suit, is it?

I thought he was asking if you could repeat numbers within your 4 digit combo to get it to open.

But no, you have to pick 4 unique numbers. You basically turn a dial on the inside of the lock box under each number you want to use.

http://www.amazon.com/AccessPoint-Or...4799561&sr=8-1

 

[dank69]

Can you explain that? Why isn't there a *6*5 on the numerator?

10*9*8*7 is the number of unique 4 digit combinations when sequence matters. 4*3*2*1 removes the duplicate combinations since sequence does not matter.

 

[Schfifty Five]

I thought he was asking if you could repeat numbers within your 4 digit combo to get it to open.

But no, you have to pick 4 unique numbers. You basically turn a dial on the inside of the lock box under each number you want to use.

http://www.amazon.com/AccessPoint-Or...4799561&sr=8-1

You said "you have to use each of the 4 numbers". There are 10 different numbers, so what you said technically doesn't match your OP.

I know you meant you have to use a unique number in each spot, but just pointing out that what you said earlier didn't match that. And that's why Danka69 said communication isn't your strong point.

 

[DrPizza]

I've never heard of a combination lock like this before. You guys been had! You just did his homework for him. I always tell my students "a locker combination is really a permutation, because the order you put in the numbers matters." This seems like a very contrived combination homework problem.

dank69 explained it; I'll try to add a little to it:
10*9*8*7 is the counting principle. Think of it as a tree diagram. There are 10 different numbers you can pick first, and for any of those numbers, there are 9 remaining to choose from for the second pick. So, 1 has 9 choices for a second pick, 2 has 9 choices for a second pick, etc. - each of ten digits has 9 choices of second digits, resulting in 90 groups of two numbers. Now, each of these 90 groups has 8 choices for a 3rd digit: 90*8 = 720. Then each of those 720 groups of 3 digits has 7 choices for a 4th digit: 720*7 = 5040

So, if the order mattered, there are 5040 choices for your "combination." But, the order doesn't matter. So pick any of those 5040 choices and see how many ways you can rearrange it? Of the 4 digits, you choose 1 to be first (4 ways), then there are 3 left to choose from for the 2nd, then 2 left to choose for the third, then only one choice for the fourth: 4*3*2*1 ways to rearrange any four digits. Thus in that 5040, each combination where order doesn't matter is counted 4*3*2*1 different ways. 5040 divided by 24 = 210

Of course, it's a lot easier to carry out this calculation without multiplying things first:
10*9*8*7
------------
4*3*2*1

The 8 cancels with the 4 and 2, the nine cancels with the 3, leaving you with 10*3*7 = 210.


OR, you can just use the combination button on your calculator. Since HP has now pulled out of the calculator market (bastards; now TI will really rape people for profits) I'll give you TI instructions for a graphing calculator (83 or 84):
type in 10, hit the math button, scroll across the menu; I believe it'll say PRB at the top, select nCr from the menu, type in 4, hit enter.

 

[bignateyk]

I've never heard of a combination lock like this before. You guys been had! You just did his homework for him. I always tell my students "a locker combination is really a permutation, because the order you put in the numbers matters." This seems like a very contrived combination homework problem.

http://detonator.dynamitedata.com/cgi-bin/redirect.pl?user=u00000687&url=http%3A%2F%2Fwww.amazon.com%2FAccessPoint-Original-Permanent-Pushbutton-Titanium%2Fdp%2FB000CER1BA%2Fref%3Dsr_1_1%3Fie%3DUTF8%26qid%3D1314799561%26sr%3D8-1

From the first review, if mine isn't enough for you:

This lockbox has 10 buttons to set the combination, but it's an unordered combination - that is, 1234 is the same as 4213. If you use all 10 buttons, there is a 100% chance that someone pressing all 10 buttons will open it. That said, someone without the combination does indeed have over 1000 possible combinations to try (1023), which is better than a four-digit combination lock.

Also, this is the same box that the local fire departments use for getting a key into businesses and homes where the owner has requested it, though the fire box uses a tubular key. A very, very solid box with a great reputation.

 

[DrPizza]

Oh, and another note: your teacher who made up that contrived problem is an idiot. If you have to choose from 1 - 10 for a key, you can't make a 4 digit number using 10 and 3 other keys. It should have been "choose a digit from 0 to 9."

 

[DrPizza]

Wow, how about that! I forgot all about those things.



YOU need to look more carefully, not some teacher - it's a 0, not a 10 at the bottom right.


**I wonder how much I could find one of those on ebay, used, for? It'd be awesome to have in class to give kids something more concrete to think about.

 

[bignateyk]

Wow, how about that! I forgot all about those things.



YOU need to look more carefully, not some teacher - it's a 0, not a 10 at the bottom right.


**I wonder how much I could find one of those on ebay, used, for? It'd be awesome to have in class to give kids something more concrete to think about.

I was going from memory :awe:. I got it because my wife is always paranoid when I am on travel for work and she locks every door and window in the house and always manages to lock herself out.

I always tell her if someone wants in they'll just smash the sliding glass door. I just leave everything unlocked when I'm home.

I figure if the 2 german shepherds don't scare them away, the 12 guage will.

 

[edro]

That's a standard realtor lockbox. I have one.

Thanks for the PRB button info, Pizza. I have no idea what that did.

 

[torpid]

I always tell her if someone wants in they'll just smash the sliding glass door. I just leave everything unlocked when I'm home.

I'm not so sure about this line of reasoning. True, if someone specifically wants to target your house and really wants to get in, they could smash a sliding door. However, also possible is that they just go around the neighborhood checking for open/unlocked windows/doors, and move on if encountering a house with locked windows/doors.

 

[arkcom]

I'm not so sure about this line of reasoning. True, if someone specifically wants to target your house and really wants to get in, they could smash a sliding door. However, also possible is that they just go around the neighborhood checking for open/unlocked windows/doors, and move on if encountering a house with locked windows/doors.

Not to mention, if there are no signs of forced entry, you're screwed as far as insurance goes.

 

[edro]

Not to mention, if there are no signs of forced entry, you're screwed as far as insurance goes.

So you kick the door in yourself...

 

[DrPizza]

That's a standard realtor lockbox. I have one.

Thanks for the PRB button info, Pizza. I have no idea what that did.

The realtor that had our house had a regular combination box with the key in it. I threw it out with the key in it. Never had a key for the front door. They wanted to put up a "sold" sign. The best they were going to get was a "do not do business with" above the realtor's name.

 

[Lithium381]

The realtor that had our house had a regular combination box with the key in it. I threw it out with the key in it. Never had a key for the front door. They wanted to put up a "sold" sign. The best they were going to get was a "do not do business with" above the realtor's name.

wut? you threw away the key and then didn't want to do business with them..?

 

[Fayd]

10c4 = 210.

 

[sjwaste]

ok, lame joke

 

[DrPizza]

wut? you threw away the key and then didn't want to do business with them..?

The house was a foreclosure. The day after we put in a purchase offer, the account switched from one realtor to another. The second realtor did everything they possibly could to sabotage the sale - telling our lawyer that it wouldn't work out (he chewed them a new asshole), telling our broker to forget it, telling our realtor to forget it, and telling the bank who owned the property to drop us. Reason: the offer was put in through the previous realtor on the last day - that meant they didn't get the commission; and they had already had a cash offer the day after they listed it (but just after the bank accepted our offer and deposit.) So, when we moved in, the box disappeared immediately. All contents on the property belonged to me.