## Nishio Forcing Chain vs Empty Rectangle

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### Nishio Forcing Chain vs Empty Rectangle

Starting with the puzzle:
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`.5...9...4.9..6...2....7.3....4.2...5...1.....4...329....2....7...6.14..67..843..`

I have run it through Sudoku Explainer using Solve Step until I reach:
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`.5..49.264.9.26...2...57934...492...592718643.4.56329.9.4235.67.2.6714.967.9843.2`

At which point Sudoku Explainer recommends using a Nishio Forcing Chain to eliminate the 1 in r2c2 (starting with reset potential values it takes a few steps to get there, but it still gets there).

Looking at the accompanying Nishio Forcing Chain description it is describing the Block 3 vs Row 7 Empty Rectangle elimination from the point of view of the (only in this case) elimination cell. Does this mean that Empty Rectangles have an equivalent Rating of 7.6, or does it vary case by case?

(Incidentally, exactly the same set set of cells also produce a Nishio / Empty Rectangle elimination of 8 in r2c2, which comes up later in the Solve Step Sequence).
civiliza

Posts: 64
Joined: 25 October 2010

### Re: Nishio Forcing Chain vs Empty Rectangle

Sudoku Explainer has no "group" handling, so an empty rectangle elimination should always appear as a Nishio step.

The rating 7.6 is linked to the number of candidates contributing to the contradiction. As an empty rectangle is a short sequence, 7.6 should be a very common rating in that case;

But it could be that Sudoku Explainer uses other chains (XY chains) with a lower rating.

So at the end, the answer is linked to your own priority in the use of the rules.
champagne
2017 Supporter

Posts: 6939
Joined: 02 August 2007
Location: France Brittany