Things I want to know about Sudoku!

  • Is there an initial configuration of the board which looks sensible, but has a logical inconsistency so there aren’t actually any solutions.
  • In the puzzles posed by newspapers (at least the easy ones I have done), there is normally always a fully constrained position for every next move. Is this always the case?
  • If there isn’t a fully constrained position for every next move, are all subtrees except one blind alleys, or not?
  • How does one generate a puzzle where one knows that there are always enough constraints to make a reasonably unambiguous decision?
  • In the case of underconstrained configurations how large is the state space?
  • In the case of no initial constraints (no numbers at all), how large is the state space of all possible solutions?

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