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April 11th, 2018, 09:54 PM  #1 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 374 Thanks: 26 Math Focus: Number theory  Edgy cube's faces paths
How many unique paths can one start at each face of a cube and move square by square (only to unused squares of shared edges) until all six faces are included?

April 13th, 2018, 02:48 PM  #2 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 374 Thanks: 26 Math Focus: Number theory  How many ways can an exploded cube's 6 faces connect together along their edges?
How many ways can an exploded cube's 6 faces connect together one by one along their edges? Start with one of (6) six bottom faces. Next, connect it continuously with one of its (4) side faces. Third, having used two already, find (3) three faces of four remaining to the second, momentarily excluding the (1) side face opposite it. There are more potential mappings, the last one dependent on the original choice. Can you find the total number of paths? 

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cube, cubefaces, edgy, faces, paths 
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