Number of combinations

[zxretrosoft]

Number of possible combinations in the game is 3.55361255095E+28.

I hope I calculated it correctly:
(56+12+12+1)! / (56!*12!*12!*1!)

Interesting fact

[Jellby]

Looks alright, but can you prove that all of those are legally reachable positions? And how many are identical by symmetry/rotation?

[zxretrosoft]

Yes, they are all legally achievable.
But you are right about the symmetry. You could say that the positions are created symmetrically, so practically, i.e. from a game point of view, it is still divided by 4.

[a_trex]

What's the actual measure you're calculating? combinations of what?
If you're looking at something like "winning" positions, then the total number of *valid* combinations realistically would ONLY be where 1 or more tiles exist on D5, F5, E4, or E6. There is no way to win the game without an adjacent tile

[zxretrosoft]

It's what's technically called "state space".