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 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
¡î(x©÷+y©÷) becomes (x/(x1))¡î((x1)©÷R©÷)
[I wish I had thought to ignore the square root like Fredeico did.]
The derivative eventually reduces to (x1)©øR©÷ and is equal to zero when x= R^(2/3)+1
¡î(x©÷+y©÷) becomes (R^(2/3)+1)^(3/2)
This is equal to 2¡î(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 20040527 10:16:11 