Three Questions

Advanced methods and approaches for solving Sudoku puzzles

Three Questions

Postby andre43 » Sat Jun 16, 2007 3:30 pm

I have two questions for all guys of the forum, and above all, for the “advanced” guys, that is for all these great minds in the forum, who share their thoughts and inventions with us, for which we are all of us grateful (no need to say names-we all know them by now!!).
1) How much useful are, at the very end, all these “new wave” fishing methods which have been analysed in the forum lately (I mean in the “Ultimate FISH Guide”), such as Kraken Fish, Mutant Fish etc.? How many times, dear friends, may someone spot them in a sudoku puzzle?
2) Why we are discussing (still) about X-Wing and (all these different types of) Swordfish? For those who didn’t’ realise it, owing to the Nice Loops rules (and, namely, the continuous Nice Loops), we don’t need any longer to hunt for these two (and I don’t know which others) types of fishing!!! In two words, going through Nice Loops we will meet and deal with X-Wings and Swordfish, and (in my opinion) in a more convenient way!
3) I’d like to hear from you, if there is any thread in the forum about the ALS Chains. And, one last remark: I note that it’s by far easier for me to use the ALS (mainly in extreme level of course) in chains rather than to search for two individual ALS groups which I ‘d need to effectuate the xz-rule. Am I right, or what? Thanks!
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Postby Myth Jellies » Sat Jun 16, 2007 4:02 pm

1) I use the simpler fish groups and constraint groups in AICs all the time. It is a nice way to keep what is effectively an expanding and then collapsing net linear. To use them in this way, you have to know what they are.

2) Once you have more than 2 candidates involved in each line, you have to resort to networks in nice loops. Many people see a finned X-wing or swordfish more easily as a pattern rather than constructing a network.

3) I see ALS components as a simple part of an AIC. As a locked set with an extra digit "fin". Also as a complement to a Weak ALS / Almost Hidden Set. Others see them in other ways. There is an advantage in being able to see deductions in multiple ways. Sometimes understanding how it works in another method provides markers that you can search for while using your favored method.
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Postby RW » Sat Jun 16, 2007 4:15 pm

1) For manual solvers, not very useful. It's usually a lot easier to spot the forcing chain/nishio version of the elimination. I think the extreme fish patterns are mostly useful for programmers who only want to implement pattern based techniques and for manual solvers who feel better when they find a pattern based explanation to their eliminations. However, studying and inventing new fish is always useful, even though manual solvers may never spot them. The more patterns and implications we find and understand, the better we understand the grid.

2) You are right. If you use nice loops, then there is no need to use techniques like fishes, subsets or locked candidates... It's just that some techniques are easier to spot than others. When I solve manually I often spot X-wing eliminations as chains instead of as patterns and I'm okay with that. If you rather use nice loops than fishes, then feel free to do so.

3) I've probably never spotted an ALS xz-rule by spotting the two groups and so on. I always see the elimination as a chain.

All of the above depend very much on your solving methods. If you use a program like Simple Sudoku with candidate highlighting, then fishes are very easy to see. If you are solving on paper without pencilmarks, then most patterns are extremely hard to see, it's easier to find chains.

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Postby Mike Barker » Sun Jun 17, 2007 12:22 am

1) I agree with RW, I doubt very much people will think, "I should look for a Kraken Fish now." The purpose of techniques such as Kraken fish are to explain how others have solved difficult puzzles and to provide suggestions of how to approach a puzzle if the occasion arises. Such descriptions also help to provide a qualitative assessment of how difficult a puzzle is and to allow people to exchange ideas. Their usefulness comes about because there are puzzles which cannot be solved with nice loops, but which can only be solved with networks (Jeff's Multiple Inference Nice Loops, Kraken techniques, etc). Many techniques may fall by the wayside (Turbot fish are often replaced by Skyscrapers now days) and these may, but we keep exploring what is possible hoping to find something better than what we have. Check out Steve K's solution to Unsolvable #23 for an example of how useful they can be. Note that his original post doesn't discuss Kraken fish or Kraken Columns and doesn't need to, but formulating the eliminations in these terms can help others to understand what he did (sure wish I could figure out how he did it!)

2) For puzzles which can be solved with nice loops we don't need to look for fish or other pattern techniques, however, uniqueness tests can still be very useful and are not covered by nice loops. For someone starting out I think things like X-wings and XY-wings still provide a valuable stepping stone to nice loops especially if one knows in advance the level of difficulty of the puzzle. On a less practical level I think names like X-wing, Mutant fish and the like add color and clarity to our discussions which a discussion of just nice loop eliminations does not.

3) Bennys' and Bob Hanson's original posts deal with ALS chains. ALS chains are also part of grouped nice loops and here's my shot at a description. Note that the requirement that the ALS be disjoint is overly restrictive. They can share cells if the cells do not contain the linking digit.
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Postby andre43 » Sun Jun 17, 2007 3:21 pm

One first reaction to your answers, Myth, RW and Mike Barker (and many thanks for your time): For (1): Yes, RW, I’m exclusively a manual solver. Anyway, I agree with you that, “The more patterns and implications we find and understand, the better we understand the grid.”. Also, I agree with Mike, expressing similar ideas about the motivation of so many fish patterns analysis. (2):Mike, I didn’t speak of Uniqueness Tests! Needless to say that I very often resort to them (I also don’t forget their aid in Nice Loops / AICs, usually involving AUR!). Otherwise I agree with you for those who starting out…And Myth, yes, at the very end, our methods of solving it’s a matter of taste of the solver, of course! (3) Myth, I don’t understand you saying that you see ALS components “as a complement to a Weak ALS / Almost Hidden Set.” What do you mean?
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Postby Myth Jellies » Mon Jun 18, 2007 9:21 am

If you have an AHS/Weak ALS then you have N - 1 digits locked in N cells. In the remaining unsolved cells of the house you will have M + 1 digits in M cells (an ALS) where M + N equals the number of unsolved cells and also the number of unsolved digits in the house. This can be an easier way to find larger ALSs.
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