Indeed, if you count the two polarized domino orientations [there's a mouthful] as different results, and I don't see why one wouldn't. However, Magnetic Field isn't my design, and I wanted to make a design with that feature. As it turns out, there's no theoretical limit to Seeking Syren's order of determination, although the largest I've yet made - and probably will ever make, since more than four colors strikes me as wasteful given the four-color theorem - is senary.

There's probably some level of fractal reduction that can be made on these orders of determination based on the rules of each puzzle; for example, none of the dynasty puzzles can have 50% or more "black", so two-to-the-power-of-the-number-of-grid-cells will always be too high a value for the actual number of possible solutions, no matter what the givens are. I leave this task as an exercise for the insane. - ZM