It would be great to be able to start over.
It would be great to keep track of how many distinct solutions you have found.
It would be great to know how many solutions there are.
In a perfect world there would be just one solution per puzzle, agreed. But the pool of possible puzzles would be so much smaller.
> It would be great to be able to start over.
Agreed, I think I'll add a "reset" feature that puts all of the tiles back in their starting positions (and allows replay if the puzzle is already solved).
> It would be great to keep track of how many distinct solutions you have found. / It would be great to know how many solutions there are.
Something like "you've found X of Y possible solutions", perhaps? Not a bad idea.