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Dodecahedron Chance Determination (Posted on 2016-10-20) Difficulty: 3 of 5
The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 are randomly written on the faces of a regular dodecahedron so that each face contains a different number.

Find the probability, in the form M/N, that no two consecutive numbers are written on faces that share an edge (10 and 1 are considered to be consecutive).

No Solution Yet Submitted by K Sengupta    
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re: clarification | Comment 2 of 6 |
(In reply to clarification by Daniel)

assuming it should be 1-12 instead of 1-10.

There are 12! possible ways of labeling the faces
Of these 660168 satisfy the requirement that not adjacent faces have adjacent values.

Thus the probability is

  Posted by Daniel on 2016-10-20 14:14:25
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