The image below shows the seven pieces of a TANGRAM game.
There are a lot of possibilities to arrange these pieces.
One example is shown in the second picture. Overlapping of
pieces is not allowed and all pieces must lie flat on the
ground (two dimensional problem).
The distance between the farthest points in this case is
approximately 5.1 units. Your job is now to rearrange the
pieces so that the distance between the farthest points
becomes a minimum.
What is the minimum distance?
Correct answer: 3.49 units
Explanation:
The best idea is to fit all the pieces into a circle since a circle has the best area/width ratio for this problem.
When I created this problem I was convinced that the "house" solution in the image below with a maximum distance of about 3.61 units (sqrt(13)) is the best possible solution.
But this solution is wrong!
The correct solution is about 3.49 units (exactly: Sqrt[123/2+36*Sqrt[2]-6*Sqrt[61+48*Sqrt[2]]-2*Sqrt[2*(61+48*Sqrt[2])]]), see image below. The yellow arrows in this solution all have this minimum distance.
