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:
++
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 / B ft
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 /+
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 / 
 / 
 / 
 / 
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/ 
+<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 20050317 03:51:16 