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Problematic Pathways (Posted on 2004-06-08) |
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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?
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Submitted by Gamer
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Rating: 2.6667 (3 votes)
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Solution:
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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. |
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