You are asked to help design a Three Lock Box. Your job is to decide the locations of the three locks. The door is a unit square. To operate properly, each lock must be the same distance from the nearest door edge and also that same distance from each of the other two locks.

(In reply to solution by Charlie)

Charlie: "The triangle could be tilted a little and made a little larger and brought down a little, and such a scheme would also work, until it was tilted so much that one vertex would be closer to the bottom edge than to the top."

Considering the locks at the circumference of a circle, what rotation would be allowed (and the relocation of the triangle centre) to achieve the maximum TriangleSide-TriangleToEdge distance? 

I'd contemplated the more obvious, which you've described, and considered the 'tilt'.  What is the extent of that tilt?

Posted by brianjn on 2010-07-20 05:17:04