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-->|

Maximun Length = sqrt((A+(B^2*A)^(1/3))^2 + (B+(A^2*B)^(1/3))^2)

Which also goes to 2sqrt(2)*A if A = B.

The solution can be expressed more simply in terms of the angle (c) that the right side of the panel forms with the positive x axis when it touches both of the outer walls and the inner corner,

tan c = (B/A)^(1/3)

Which also gives 45 degrees if A = B.

I have not checked my answer though, so it could be wrong.

Posted by ajosin on 2005-03-17 03:51:16