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# The continuous Elevator question

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Posted 05 February 2014 - 03:07 AM

Mr. Smith works on the 13th ﬂoor of a 15 ﬂoor building. The only elevator moves continuously through ﬂoors 1, 2, . . . , 15, 14, . . . , 2, 1, 2, . . . , except that it stops on a ﬂoor on which the button has been pressed. Assume that time spent loading and unloading passengers is very small compared to the travelling time.

Mr. Smith complains that at 5 pm, when he wants to go home, the elevator almost always goes up when it stops on his ﬂoor. What is the explanation?

Now assume that the building has n elevators, which move independently. Compute the proportion of time the ﬁrst elevator on Mr. Smith’s ﬂoor moves up.

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### #2 Sairakan

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Posted 05 February 2014 - 05:45 AM

Spoiler for

I'm not sure at the moment how exactly to tackle the generalization, although I have the feeling it is likely the same answer as for the first part.

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Posted 06 February 2014 - 03:33 PM

good start.

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### #4 dgreening

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Posted 06 February 2014 - 10:12 PM

Spoiler for

I'm not sure at the moment how exactly to tackle the generalization, although I have the feeling it is likely the same answer as for the first part.

Edited by dgreening, 06 February 2014 - 10:15 PM.

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### #5 dgreening

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Posted 07 February 2014 - 09:46 PM

A few observations

the 5 PM reference is just a red herring! the odds are the same all day

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### #6 bonanova

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Posted 08 February 2014 - 01:52 PM

Spoiler for My take

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #7 plasmid

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Posted 08 February 2014 - 06:03 PM

Spoiler for I don't think that the probability of catching an elevator going down is independent of the number of elevators in the system.

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### #8 bonanova

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Posted 09 February 2014 - 10:44 AM

Spoiler for I don't think that the probability of catching an elevator going down is independent of the number of elevators in the system.

Spoiler for You changed my mind - EDITED. here is the real n-elevator solution

Edited by bonanova, 11 February 2014 - 03:52 AM.
Include the n-elevator solution

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

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