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The faces of a cube are to be numbered with integers 1 through 6 in such a way that consecutive numbers are always on adjacent faces (not opposite ones). The face numbered 1 is on top and the face numbered 2 is toward the front. In how many different ways can the remaining faces be numbered?

 May 31, 2020
 #1
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There are 6 ways to number the remaining faces.

 May 31, 2020
 #2
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Actually, I got it. The right answer was 10. 

Coolio  Jun 1, 2020

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