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Moving Day (Posted on 2004-05-26) Difficulty: 3 of 5
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-->|

See The Solution Submitted by Brian Smith    
Rating: 3.8333 (6 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Agreement with F.K. | Comment 14 of 31 |

I decided to simplify things by scaling A and B by dividing A.

This creates new widths of 1 and B/A.  Let R=B/A

My steps are much the same.  The function to be minimized 

(x+y) becomes (x/(x-1))((x-1)-R)

[I wish I had thought to ignore the square root like Fredeico did.]

The derivative eventually reduces to (x-1)-R and is equal to zero when x= R^(2/3)+1

(x+y) becomes (R^(2/3)+1)^(3/2)

This is equal to 2(2) when R=1

In terms of the original A and B the solution is:

A((B/A)^(2/3)+1)^(3/2)

The angle at the tightest fit is Arctan((R+R^(1/3))/(R^(2/3)+1)) which is only 45 when R=1

-Jer

 


  Posted by Jer on 2004-05-27 10:16:11
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