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As the author mentioned, it cannot solve any boards where all unfilled cells have more than one possible value within the cell's domain. More information about the algorithm here:

https://en.wikipedia.org/wiki/AC-3_algorithm

You would need to implement something like forward checking or backtracking algorithm to solve all possible boards with higher cost.

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Here is one in Swift I did a few years ago that does:

https://github.com/isaksky/sudoku-swift/blob/master/Sudoku-S...

This one solves all 50 from Euler: https://projecteuler.net/problem=96

And here is a classic one in Python from Norvig:

http://norvig.com/sudoku.html

Shameless plug, my OCaml implementation: https://github.com/eprochasson/norvig-ocaml

So this can't solve anything more than the most trivial boards? :/

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