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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+<A ft>
(In reply to
Agreement with F.K. by Jer)
I'll rewrite this now. The formatting buttons seem to have really gone haywire.
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
Sqrt(x^2 + y^2) becomes (x/(x1))Sqrt((x1)^2  R^2)
[I wish I had thought to ignore the square root like Fredeico did.]
The derivative eventually reduces to (x1)^3 R^2 and is equal to zero when x= R^(2/3)+1
Sqrt(x^2 + y^2) becomes (R^(2/3) + 1)^(3/2)
This is equal to 2Sqrt(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 45degrees when R=1
Jer

Posted by Jer
on 20040528 08:59:28 