Crummy problem :( ----- (because random)
This is a permutation problem with a weak ordering requirement.
"shuffle" the grid indexes, about half the time always taking the first non-conflict from the array of empty indexes gives a valid order, if not, reshuffle till it works.
I am seeing on average slightly less than one reshuffle per grid solution over all the grids.
Processes all 361 grids in under 2 seconds total typically.
( slight cheat: All IMPOSSIBLEs are hard coded (HINT: there are very few) :)
It's not in final submit form because I wanted to test all grid sizes.
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