[Guest]

this puzzle is loosely based on a true story.

there was this beautiful hotel i was in, that had a glass elevator that went to the top floor, 18 floors high.

i wanted to reach the top floor to see the view, but at various intervals people on the floor i was passing through would enter the elevator needing to go down a floor or two, and unless i was at the 17th floor, the elevator would favor them over me. it takes 15 seconds to go from one floor to another, 1 minute 30 seconds to load any people, and the same time to unload them. i ended up back at the first floor 2 times before finally reaching my goal of the 18th floor. i was able to reach it in roughly 60 minutes. how many times did the elevator likely stop to load people?

[bonanova]

Should we understand that, in a single 90-second stop, people could both load [enter] and unload [leave]?

[Guest]

yes. you should also understand that poeple entering are only going down.

[CaptainEd]

I get 5, each at the 16th floor (I gather that, if you could get to 17th, you would be able to get to 18th, so I assume that you never got to 17th until the very end).

Trips:

1-16, 16-1, 1-16, 16-1, 1-16, 16-2, 2-16, 16-2, 2-16, 16-2, 2-18

Counting the unload time at the end (but not the load time when you first got on the elevator), this takes 58 1/4 minutes, which is roughly 60 minutes.

If you want "roughly 60 minutes" to be rather exact, we need one more interruption, and shorten one of the trips.

[Guest]

58 and 1/4 minutes is god enough captain, but read the post again, most people aren't going more than 2 floor down.

[CaptainEd]

That must have been a very scenic elevator, or you have a LOT of patience!

13 downward trips:

1-3-1-3-1-15

then 11 trips down to 13 and back, last one goes straight up from 11 to 18.

57 min 3/4 minutes. We can get closer by adding a trip and shortening a few of them. Or we could waive the unloading operation at 18.

16 downward one-story trips, 60 1/4 minutes.

So you suffered between 13 and 16 interruptions on your way to the top.

Edited November 10, 2011 by CaptainEd

[Guest]

i think the lot of patience is really the answer though it was a scenic elevator! :-)