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?

The easiest way of figuring that the answer is 6!/2^3 = 90, is that each dimension (x, y and z) must be changed twice, by 1 each time. So you need the number of rearrangements of xxyyzz, which is 6!/(2^3).

Posted by Charlie on 2004-06-08 08:55:16