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Problematic Pathways (Posted on 2004-06-08) Difficulty: 3 of 5
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?

  Submitted by Gamer    
Rating: 2.6667 (3 votes)
Solution: (Hide)
Think of going horizontally A, vertically B, and up/down C. Then this would be just finding how many different orders you could put AABBCC in. Starting with the letter A, there are 6!/(4!2!) ways to put it in. Then putting the letter B, there are 4!/(2!2!) places left to put it in. The letter C can only be placed in the remaining places, so it doesn't add any different possiblities. So, overall, there are (6!/(4!2!))(4!/(2!2!)) or 90 different possible ways to get there.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
AnswerK Sengupta2009-01-13 13:11:47
Nothing new but want to add 2 centsJer2004-06-08 12:18:29
re(2): Full SolutionErik O.2004-06-08 09:01:06
SolutionsolutionCharlie2004-06-08 08:55:16
Solutionre: Full Solution - oops!Danny2004-06-08 08:44:07
Some Thoughtsre: Full SolutionFederico Kereki2004-06-08 08:43:25
Full SolutionErik O.2004-06-08 08:22:02
SolutionSolutione.g.2004-06-08 07:50:43
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