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It's trivial to know that it has more than one possible solution since less than 8 of the possible numbers are on the initial board meaning any valid solution that is found has a mirrored solution with all of one number swapped for all of another number.

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Sure. My solver is designed to return the first solution it finds (it doesn't check for solution uniqueness, just that there is one). However currently my solver is saying that it can't find _any_ solution at all.

Theoretically a board with multiple solutions should be easier to find a solution for though, right?

Theoretically a board with multiple solutions isn't a sudoku.

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