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The last number of months I have been reading about numerous ways on how to solve Sudokus. So far I am familiar with obvious and hidden singles, obvious, hidden and pointing pairs, obvious, hidden and pointing triples, XY-wings and the swordfish-technique.

Any other tips on how to solve Sudokus linearly so that one solves a Sudoku more efficiently?

With the word 'linearly' I refer to the way of solving Sudokus from top to bottom and from left to right or vice versa.

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    $\begingroup$ For speed solving, you'll probably want to master the Forbidden Techniques (bifurcation, reasoning from uniqueness) first, they'll save you the most time, when they get you out of a rut. Then, learning fast scanning (I find scanning columns for missing digits to be significantly slower than scanning a row, which is still way slower than scanning a box) may make your solve look "linear", even though such a technique doesn't really exist: the deductions come from all directions, and their order cannot be significantly affected during the solve. $\endgroup$ Commented Oct 29 at 11:48
  • $\begingroup$ Thank you for the elaborate answer. $\endgroup$ Commented Oct 29 at 14:41
  • $\begingroup$ Brute force is "linear" but not efficient. $\endgroup$ Commented Oct 30 at 3:38

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What follows is a frame challenge.

You are asking for two fundamentally different things:

  • how to solve Sudokus "linearly"
  • how to solve Sudokus "efficiently"

A restriction on the order/manner in which cells are filled in will cause a decrease in efficiency. For any given Sudoku puzzle (really, for any given grid deduction puzzle), there will be one or more "natural" solution paths. These are sequences of deductions that naturally follow from each other.

Filling in a Sudoku cell will immediately eliminate other possibilities within that box, row, column, etc. with possible knock-on effects elsewhere. Once one cell is filled, some other cells will be easier to solve. So on and so forth. While it may be technically possible to make deductions which are off of this "natural" solution path, it would typically require more involved deductions with complex chains of reasoning.

There is no guarantee that the "natural" path will be "linear" as you define it. A setter may design a puzzle such that the "linear" solve is a natural one, similarly to how some Sudokus are purposely made such that filling in all 1s, then all 2s, then all 3s, etc. is a "natural", intended path. But if you're trying to solve Sudokus in general by forcing deductions to occur in a "linear" order, that will naturally lead to a decrease in efficiency.

Thus, there are no tips I can possibly give you that will increase "efficiency" by forcing deductions to occur "linearly".

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  • $\begingroup$ The way you have put it makes me understand that indeed solving sudokus linearly does decrease your efficiency when considering speed solving. Thank you for highlighting this distinction. $\endgroup$ Commented Oct 31 at 19:39

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