Naked Singles in SudoRules

This post reveals how naked singles are produced, in Berthier’s rule hierarchy of increasing logical complexity,  by single rule that is a member of the set of rules for every resolution method. This explains why number scanning candidates, and maintaining multiple grid spaces, clearly impractical in human solving, is justified in The Hidden Logic of Sudoku as logically elegant and computationally feasible.

royle-17-3-numscanHere is the number scanned version of the grid, immediately after the 25 hidden single steps of Denis Berthier’s trace on p. 85 of THLS. This was much less work than number scanning the original puzzle. Now imagine the condition of your paper puzzle at this point, after erasing all the candidates removed for the sin of seeing the  hidden single clues added so far.

On this grid, another hidden single c6hs1 is available, but the first naked single to emerge, SEns9 has precedence.

royle-17-3-naked-s-trWith your number scanned grid, you can now follow the sequence of naked singles, as each one removes candidates to produce one or more new naked singles, as traced at left. The run ends when the naked singles are use up, and a box hidden single is retrieved from the reserve list.

royle-17-3-after-ns-runAfter this run, the grid is much clearer and your paper puzzle, more tattered.






But now, Berthier’s trace in 2-D descends sharply into collapse:

royle-17-3-final-singles-trNaked singles are detected by the simplest ECP rule, applied with every candidate elimination. The rule promotes a candidate to a clue when it is the only one one left in the cell  That makes ECP 1 a member of every set of rules. It always overrides all other rules.

Berthier labels the ECP rules, plus the hidden singles rules, as L1_0.


THLS introduces the hidden logic grids next, to show how they transform hidden singles in lines to naked singles in lines. These transformations multiply the data the computer solver carries along, to be updated with every new clue. In THLS, addition of all this work is not considered to increase the logical complexity of a set of rules.

After the homework, you have very different opinion of the added computational complexity, I’m sure. But number scanning is a small part of it.


About Sudent

I'm John Welch, a retired engineering professor, father of 3 wonderful daughters and granddad to 7 fabulous grandchildren. Sudoku analysis and illustration is a great hobby and a healthy mental challenge.
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