An easier version of this puzzle is here.

A large panel needs to be moved through a corridor, the panel is tall as the corridor. The corridor is A feet wide before a right angle turn, after the turn, it is B feet wide. What is the maximum length of the panel that can pass through this corner.

Overhead view of the hallway:

+------------+---
|           /   |
|          /    |B ft
|         /     |
|        /+------
|       / |
|      /  |
|     /   |
|    /    |
|   /     |
|  /      |
| /       |
|/        |
+<-A ft-->|

I'm really with this 45 degree thing.

Consider a triangle, sides x and y with hypotenuse x^2 + y^2. The hypotenuse is clearly minimized when x = y and hence when the hyp' is at 45 degrees to the sides.
Place a series of 'points' on the hyp'. With enough points you can represent all the interior corners you need to move the panel round
(or, in real terms, all corridor width ratios)
To move the hypotenuse round any of these points would mean to make x and y unequal and hence make the hypotenuse longer.
The 'tightest' point is when the panel is on the 45 and this is the longest panel that will pass round any corridor corner.
So the longest panel would be
root 2 (a+b)
Empirically, I've moved a lot of things round a lot of corners and never got trapped when I'm more than halfway round.
Federico, feel free to debunk my ideas but could you use more pictures and make the font size bigger and preferably Arial?

Posted by Lee on 2004-05-27 00:39:42