User Abigail comments on the titling of "Do sudoku answers always have a single minimal clue set?" :

I'd be surprised if there were a Sudoku which doesn't have at least 2 disjoint clue-sets.

Well then, is there a Sudoku answer that has only a single minimal clue set?

  • $\begingroup$ I think the definition of minimal is important here, you mean minimum number of clues, right? $\endgroup$ – hexomino Jun 25 '19 at 13:14
  • $\begingroup$ @hexomino, Yes. This avoids the large number of container clue-sets that might be made by adding more clues. $\endgroup$ – agc Jun 25 '19 at 13:21
  • $\begingroup$ Also, we could have disjoint clue-sets which are "minimal" in a set-theoretic sense (because they contain no subsets which provide unique solutions) but have different numbers of clues. $\endgroup$ – hexomino Jun 25 '19 at 13:23
  • $\begingroup$ @hexomino, It sounds like that would be departing from the question, since the term disjoint implies two of something. $\endgroup$ – agc Jun 25 '19 at 13:32
  • $\begingroup$ But basically, if you have two disjoint sets of clues which give the same unique solution and one has 18 clues and the other has 17, the one with 17 is minimal and the one with 18 is not (even if no subset of the 18 gives rise to a unique solution), that's correct? $\endgroup$ – hexomino Jun 25 '19 at 13:41

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