Puzzle about elevators....
 

Got bombarded with a bunch of puzzles during an interview for an investment bank.

Good thing they ask these general questions, because I don't know a thing about finance. I'll willing to learn of course, and I'm prepared for the 70hour weeks.......

anyway... here goes..

Say that you have a an elevator that stops at 5 floors. It goes in sequential order, up and down. (1-2-3-4-5-4-3-2-1-2-3-4-5-4-....) and stops at each floor for 15 minutes. Assume it takes no time to go between floors.

Say you just arrived at the 4th floor. What is the probability that the next elevator at the 4th floor is going up? The elevator may or may not be there when you arrive.

3/4

There are 8 positions that elevator can be in when you get to the 4th floor. It's equally likely that it will be in any one of those 8 positions.
It's headed down in 2 of those positions (5 headed down, and 4 headed down). In the other 6, it will be headed up next time it gets to the 4th floor. Hence the chance is 6/8 = 3/4.

Maybe Im interpreting the question wrong but wouldnt it be 1/2. The elevator goes sequentially up and then down and then up again. If the elevator is going up this time then it will go down next time and vice-versa. The elevator only goes 2 ways. we dont know which way its going this time. The options for the next time the elevator hits floor 4 is it is going up or down. 2 options of which we dont have enough information to make a judgment which. Thus 1/2 probability that it will be going up next time it hits floor 4. Maybe I interpreted the question wrong though...

That was my first thought, it's either going up or it's going down, right?? I figured all those other details were thrown in just to try and confuse the situation....


EDIT: I guess it would depend on how you just arrived, if you arrived in the elevator, and whether it was going up or down to get you there. The way it was described then, i.e. *always* as <1-2-3-4-5-4-3-2-1-2-3-4-5-4-....>, the *next* elavator would have 100% probability that it would be travelling in the opposite direction.

But if you came at some random time and waited for the elevator, without any prior knowledge of the direction of travel, I'd still say there's just a 1/2 chance that it will be going up or down. Anyone else agree/disagree??

TIO is correct.

When you arrive at the 4th floor, the elevator can be in 1 of 8 positions.

First floor -UP
2nd Floor - UP/DOWN
3rd - Up/Down
4th-up/down
5th-down

if the elevator is on 1st 2nd 3rd floors, it will either be going up, in which case we are done, or going down, only to come up again. so there are 5 states that will result in the next elevator on the 4th floor that goes up.

Then there is also 1 state (4th floor -UP) that gives you the desired result.

so 6 states out of 8. 3/4.
I'm pretty sure of the answer. Both through my own logic and also coz several math professionals confirm it....

The guy who gave this to me was a math professor at Northwestern before he went into finance. I passed this along to my prof, who 'collects' puzzles. i'm pretty sure its correct.

not that a lot of people agreeing makes things correct.. but....

Fascinating question....I think I see TIO's explanation now!! :) and now I think i agree.

The fact that you're on the 4th floor on the building is what matters, isn't it?? If you were on the middle floor, I think it would be 50/50, but since you're above the mid-point it does indeed sound like it makes a difference. For example, if you're on the top (5th) floor, there's zero chance that it's going up....

I'm glad you were up for this job. I don't know that I would have gotten the question.

I don't know that I would have bothered, really.

thats a pretty cool question for a job interview

15 minutes! Who's got time for that?

well... there's more..... especially since there were 6 interviews in a row.. with around 2 puzzles per interview... among other things.........

perhaps i'll start more puzzle threads.... they're fun anyway....

maybe i'm thinking too simplisticly here, but... i think it's 100% certain that it is going down next to floor 3, because...

<i>It goes in sequential order, up and down.</i>

but there is a non-zero chance that the elevator might be going UP. since it does have to get to the 5th floor at some point....

In the future, everyone will be stuck in an elevator for 15 minutes...

Mr Mephisto

/me takes the stairs & fergets all about it ;)