There is a 2 inch grid cube made up of 8 wire-frame cubes, each with wire where their edges should be and space in their middle and faces.

The quickest way to get from one vertex to the opposite vertex is 6 inches. How many such paths are there?

(In reply to Full Solution by Erik O.)

I think your middle 8 should be a 6. That would change other numbers around it, leaving you with...

1--1--1
|  |  |
1--2--3
|  |  |
1--3--6


 
        1---2---3
        |   }   }
        |   |   |
        2---6---12
        |   |   |
        |   |   |
        3---12--30
 
                    1-----3-----6
                    |     |     |
                    |     |     |
                    |     |     |
                    3-----12----30
                    |     |     |
                    |     |     |
                    |     |     |
                    6-----30----90

so that means e.g. was right.

Posted by Danny on 2004-06-08 08:44:07