There's a point of view where this transforms it from a game into a task. Execute the algorithm as quickly as possible.
(There are many exceptions that do use die/dice, but for those that have not played board games invented after Monopoly, the idea of a board game that does not have die-introduced randomness may be quite foreign.)
They are usually sitting right in the middle between entirely abstract games like backgammon and "simulation" games like Risk or Monopoly. There is usually some theme, but gameplay considerations (mostly revolving around keeping the game interesting for those not on an obvious path to victory and balancing luck vs skill, hence the mention in this thread) are far more important in the design than adhering to that theme. Sometimes it even seems as if the theme was not serving as inspiration for the rules but it's only a skin pasted over the bare rules after the gameplay had been tweaked to perfection.
And using trivial deductions (based on the numbers in the column, row, and square there is only one possibility) is not sufficient to be better than me (and I don't consider myself to be good).
Many years ago I used to be quite addicted. The unconscious pattern matching went far enough to detect unknowable situations and do even the switch back and forth between guessing and solving without spending a conscious thought. The goal was not to solve as many boards as possible with a timeframe, but to get the best time so there was a kind of triage going on between trying to solve possible solvable large scale situations and failing fast. The strategic level was finding the right cutoff.