Before tackling this one, take a look at this one.

     +-------------D
    /|            /|
   / |           / |
  /  |          /  |
 /   |         /   |
C-------------+    |
|    |        |    |
|    B--------|----+
|   /         |   /
|  /          |  /
| /           | /
|/            |/
+-------------A

A, B, C and D are non-adjacent vertices of a cube. There is a point P in space such that PA=3, PB=5, PC=7, and PD=6. Find the distance from P to the other four vertices and find the length of the edge of the cube.
There are two answers, one with P outside the cube and one with P inside the cube.

(In reply to Heuristic computer solution for modified problem by Charlie)

If PD is reduced to 6, we seem to be able to get an internal point:

x     y     z       size       
2.881 4.065 0.421;  5.4880  3.0000  5.0000  7.0000  6.0000

as well as an external point

x     y     z        size
1.787 3.891 -2.581;  3.0898  3.0003  5.0000  7.0000  6.0000

(The choice of internal or external point can be influenced by the choice of initial randomization limits.)

Posted by Charlie on 2004-07-18 20:18:01