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 Problematic Pathways (Posted on 2004-06-08)
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?

 See The Solution Submitted by Gamer Rating: 2.6667 (3 votes)

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 solution | Comment 5 of 8 |
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
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