Jared wrote:

Thanks Jaap! It's still a helpful result.

I do have one more question - if we use a variant set of pieces, identical except for each set of 5 same-colored tokens also being numbered from 1 to 5, and neither same-color or same-number pieces are allowed to be adjacent, how many solutions do we have there?

This has 11992 solutions (reduced by colour permutations, and number permutations). Reducing this by rotation/mirror symmetry, you get at least 1499 unique solutions. There is a further symmetry of swapping the colours with the numbers, which would reduce it by another factor of 2, approximately.

**Code:**

3,4

1,1 2,2 1,3

2,4 3,3 4,4 3,1 2,5

5,2 4,5 5,1 1,5 5,3 4,2 5,4

1,4 2,3 3,2 2,1 3,5

4,1 5,5 4,3

1,2

5,5

1,1 2,2 3,1

5,4 3,3 4,4 5,3 4,5

1,3 4,1 2,5 1,2 2,1 1,4 2,3

5,2 3,4 4,3 3,5 4,2

1,5 5,1 2,4

3,2