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I have been playing this obsessively the last few weeks without knowing about the implementation. I thought it expresses the known facts about the board configuration as a system of linear equations and uses one of the classic algorithms for solving these. Anyone know if that would be infeasible for some reason?

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I was thinking along the same lines when the systems of linear equations came up. The difficulty is that the variables are 0-1 while the equations are over the integers. So this is not quite as simple as solving a system over F_2, but is instead feasibility testing of an IP with 0-1 variables and a 0-1 matrix.

I wonder if solving the LP-relaxation might lead to a rounding based approach.

The variables would need to be constrained to be integers/booleans. And Integer Linear Programming is NP-complete.

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