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).

(In reply to re(2): clarification by Charlie)

For the denominator to be the full 12!, the solution count in the numerator should have all orientations of the found solutions. That includes a choice of 12 faces to be on top and 5 rotations of each, so it should be a multiple of 5.

Posted by Charlie on 2016-10-20 16:48:08