>  (A sudoku problem only makes sense if it's unambiguous, iow. it can be
> solved unambiguously without trial-and-error, only by pure deduction.)

Isn't trial-and-error a form of deduction?  ie "If I put a 4 in here, that 
square will need to be 3, and then that doesn't work so it must be a 6 in 
the original square".  Of course there are more complicated chains of logic, 
but essentially you try one number and see if it gives a valid result.

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