What is the longest
pole I can swing around the 90° corner of a hallway of unit width?
For the simplicity of this problem, the pole must be kept exactly horizontal, while maneuvering it.
(In reply to and if...
I think you knew you were in trouble when you said you could probably jam it into place.
Picture the pole already in place at 45 degrees, touching both walls. To get out of there the far end would have to turn inwards towards the center of the hall, which means that the near end would have to turn outwards away from the center (remembering that the pivot is right in the center of the pole). Since the pole is already up against the wall, it can't do this. And, like you said (but the other way round), if it can't get out of that position, it couldn't have gotten into that position.
As for the real answer. Well, I'll leave that to someone with more time on their hands...
Posted by Sam
on 2004-03-13 17:02:09