From the brilliant(?) minds at vat19.com, I present to you, the IcoSoKu:

Just thousands, that’s it?

In my list of mathematical strengths probability does not appear, but there are: 12 unique numbers (vertices of an icosahedron), so 12! = 479,001,600 ways to arrange them. But because of the symmetry involved in a icosahedron, there are 12 ways to arrange a single icosahedron. So 12! / 12 = 11! = 39,916,800 ways to arrange the vertices. If each setup of vertices only has one solution, then that’s it, but I’m not sure if each solution is unique. If each tile is unique, then there are 20! ways to arrange the tiles, but I don’t think that comes into play for the number of challenges.

Am I missing anything? Is this interesting? Keep delving?

Anyway, interesting use of Platonic solids. BTW, bought it and it’s in the mail.