Sunday, March 20, 2011

12-sided die

Instead of having 1, 2, ..., 12, on the faces of the die, a 12-sided die is created by engraving the numbers 1- 6 on the faces of a regular dodecahedron so that…

(1) Each number appears twice, and
(2) Each occurrence of each number is surrounded by all five other numbers.

In how many ways can this be done?
Two ways are considered the same if one can be rotated to become the other

Bonus question:

What shapes make the best dice,
(a) tetrahedron,
(b) hexahedron,
(c) octahedron,
(d) dodecahedron,
(e) icosahedron,
(f) other?

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