## Identical Pair Forcing Pattern

Advanced methods and approaches for solving Sudoku puzzles
Myth Jellies wrote:Once again, Denis, your statement is blatantly incorrect.

Myth, I know that logic isn't your cup of tea and that you are easily upset when a discussion becomes too precise, but is it a reason for becoming rude?

Knowing that r1c456 does not contain x does imply that r23c456 must contain x. BUT it doesn't imply that both of r2c456 and r3c456 must contain it.

Myth Jellies wrote:Therefore ANY division of those six cells containing x must form a valid strong inference set and that includes (x)r2c456=(x)r3c456.

I'm speaking of patterns, i.e. sets of conditions on candidates on a grid - factual conditions. I'm not speaking of inferences.

This is one of the typical problems I've often mentioned with your "inference level" and your subsequent vague definition of AICs.
You are now extending this definition to include ghost candidates.
But would any reasonable player use an AIC if x is not present in both of r2c456 and r3c456 and when a much simpler rule is available?
denis_berthier
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Denis, long ago I proved that any deduction pattern of unsolved candidates cannot depend on the existence of a particular candidate. Do you know what that means? Let me enlighten you. That means that a pattern is completely specified by the grid-factual conditions of where various candidates cannot be placed. I'll give you an example so that we are clear. A naked triple is not defined by the existence of generic candidates 123 in three cells in the same house. Instead it is completely defined by the lack of candidates 4 through 9 in those same cells. You may complain that there might be naked singles and pairs in those cells, but that is immaterial. The naked triple exists and its results can be applied regardless.

Likewise, the strong inference subpattern, (x)r2c456 = (x)r3c456, is completely specified by the grid-factual absence of candidate x in r1c456. Adding anything more to the definition is extraneous. If you want to be pedantic and complain that simpler patterns could possibly exist in those six cells then fine; but, similar to the naked triple above, it is misleading and just flat out wrong to claim that in those cases the subpattern and the AIC would cease to exist.

Denis wrote:Then you don't have a clear notion of clearness.

No more time to waste with such Eureka-style remarks, with no technical content.

That's exactly what I said in a more correct way in the previous post.

Myth, I know that logic isn't your cup of tea and that you are easily upset when a discussion becomes too precise, but is it a reason for becoming rude?

Hmm, well I know that you think your crap smells like roses, but is that really a valid reason for claiming that everyone who disagrees with you is absent in logic or in some way unworthy of an opinion?
Myth Jellies

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Myth

I can see you persevere in your typical agressive style to justify your vague definitions.

You couldn't choose a better example than NT! According to you, "a Naked Single is a Naked Triplet." That's exactly the kind of "scrap", to use your elegant terms, I don't accept. This can only lead to generalised confusion.

In my book, I've given precise conditions for an NT to be a real, i.e. non degenerate, NT, without being limited to the trivial and very rare case of exactly 3 numbers in 3 cells (you seem to ignore that there are other possible and better definitions). I've repeated these conditions several times in this forum. My analysis works similarly for Quads, and for the hidden and super-hidden versions of all subsets.
Moreover, this precise approach shows how close subset rules are to nrczt-chain rules, but why they can't be reduced to them.
I've also proven that deleting any left- or right- linking candidate in a (h)xy(z)(t) or nrc(z)(t) chain results in a shorter (and simpler) chain allowing the same eliminations. (Deleting z- or t-candidates doesn't change the length, it only makes the type simpler.) Obviously, after one year, you haven't yet assimilated this.
Similar things can easily be proven for AICs with ALSs - not only for the special case under discussion here.

What I'm saying (and it was already the message of my first post) is that taking inexistent candidates into consideration in AICs leads to an unnatural and unnecessarily complex definition of AICs with no real added generality, it isn't that it leads to false eliminations. It can only induce players and programmers into error.

If you don't agree, instead of turning to insults, could you show me an existing exemple, from a real player, where such an AIC based on non-existent candidates has been used to solve a real puzzle?

As for your "proof", I'd like to see it at work on BUGs.
denis_berthier
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denis_berthier wrote:No more time to waste with such Eureka-style remarks, with no technical content.

AFAIAC udosuk had the correct w-wing answer in the third post of this thread, so my "technical content" would have been redundant.

Since his post, there's been a lot of "noise" posted here ... in my opinion, of course.
Last edited by ronk on Fri Sep 05, 2008 4:17 am, edited 1 time in total.
ronk
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Any possible doubt as to Bud's starting conditions was clearly removed in the grid that udosuk posted prior to expounding on the w-wing.

Myth's response encapsulated that in a perfectly valid Nice loop form as requested.

As for the later postings can we cool things down both here and in other threads, this is not Eureka.
Glyn

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Glyn wrote:Myth's response encapsulated that in a perfectly valid Nice loop form as requested.

Myth Jellies wrote:(y=x)r2c9 - (x)r2c456 = (x)r3c456 - (x=y)r3c3 => r2c123, r3c789 <> y

To clarify: Myth posted a chain rather than a loop ... and used AIC notation rather than NL notation.
ronk
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Thanks ronk In my zeal to slap wrists I invoked a wrist slapping from you. Of course you are correct.
Glyn

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Glyn:

Asking a real example from a real player on a real grid of an AIC using non existent candidates: is this also too much for this forum?
denis_berthier
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Myth Jellies wrote:
Code: Select all
`Example of non-chute case. |---------------+---------------+---------------|  |   xy  .   .   |   .   .   .   |   .   .  -y   |  |   .   .   .   |   .   .   .   |   .   .   .   |  |   .   .   .   |   .   .   .   |   .   .   .   |  |---------------+---------------+---------------|  |   .   .   .   |   .   .   .   |   .   .   .   |  |   .   .   .   |   .   .   .   |   .   .   .   |  |   .   .   .   |   .   .   .   |   .   .   .   |  |---------------+---------------+---------------|  |   .  ~x  ~x   |   .   .   .   |   .   .   .   |  |   .  ~x  ~x   |   .   .   .   |   .   .   .   |  |  -y   .   .   |   .   .   .   |   .   .   xy  |  |---------------+---------------+---------------| (y=x)r1c1 - (x)r789c1 = (x)r9c123 - (x=y)r9c9 => r1c9, r9c1 <> ya Kraken/AAIC case (note strong link for z between r7c3 and r9c1) |---------------+---------------+---------------|  |   xy  .   .   |   .   .   .   |   .   .   .   |  |   .   .   .   |   .   .   .   |   .   .   .   |  |   .   .   .   |   .   .   .   |   .   .   .   |  |---------------+---------------+---------------|  |   .   .   .   |   .   .   .   |   .   .   .   |  |   .   .   .   |   .   .   .   |   .   .   .   |  |   .   .   .   |   .   .   .   |   .   .   .   |  |---------------+---------------+---------------|  |  ~z  ~xz  .   |   .   .   .   |   .   .   .   |  |  ~z  ~xz ~xz  |   .   .   .   |   .   .   .   |  |  -y  ~z  ~z   |   .   .   .   |   .   .   xy  |  |---------------+---------------+---------------| (y=x)r1c1 - (x)r789c1             ||            (x)r9c123 - (x=y)r9c9             ||            (x-z)r7c3 = (z)r9c1  ==> r9c1 <> y`

Thanks for the interesting examples. They surely are valid members of the W-wing family.

Here are my "verbal" interpretations of the techniques:

1. x @ b7 locked @ r78c1+r9c1+r9c23

If r78c1 contain x => r1c1=y => r1c9, r9c1<>y
If r9c1=x => r1c1=r9c9=y => r1c9, r9c1<>y
If r9c23 contain x => r9c9=y => r1c9, r9c1<>y

Therefore r1c9, r9c1<>y.

2. x @ b7 locked @ r78c1+r9c1+r9c23+r7c3
z @ b7 locked @ r7c3+r9c1

If r78c1 contain x => r1c1=y => r9c1<>y
If r9c1=x => r9c1<>y
If r9c23 contain x => r9c9=y => r9c1<>y
If r7c3=x => r9c1=z => r9c1<>y

Therefore r9c1<>y.

Also thanks for the AIC chain you posted. It's not the Nice Loop I requested but I guess it's explanatory enough.
udosuk

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I never was that fluent in NL, but I think it would look something like...

[r2c123|r3c789] -y- [r2c9] -x- [r2c456] =x= [r3c456] -x- [r3c3] -y- [r2c123|r3c789]
Myth Jellies

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Denis wrote:You couldn't choose a better example than NT! According to you, "a Naked Single is a Naked Triplet."

No, Denis. There is no way that anyone can logically make that statement based on what I said. My comments imply that a Naked Triple might possibly be made up of a Naked Pair and a Naked Single, or three Naked Singles; but in no way does any of that imply that "a Naked Single is a Naked Triplet."

...taking inexistent candidates into consideration in AICs leads to....If you don't agree, instead of turning to insults, could you show me an existing exemple, from a real player, where such an AIC based on non-existent candidates has been used to solve a real puzzle?

I don't agree. Find any puzzle where someone has solved it using a Sashimi X-Wing and you have your example. As for the insults, you reap what you sow.

As for your "proof", I'd like to see it at work on BUGs.

The theorem works perfectly fine on any BUG. It also works on URs ("you can't destroy a UR"), BUG-Lites, and MUGs.
Myth Jellies

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Myth Jellies wrote:My comments imply that a Naked Triple might possibly be made up of a Naked Pair and a Naked Single, or three Naked Singles; but in no way does any of that imply that "a Naked Single is a Naked Triplet."

OK, but even this is not acceptable for me. For me, a Triplet is not degenerate. If it is degenerate, it's two patterns, not one. That's all what this discussion is about: aggregating two patterns into a degenerate more complex one has no practical interest - except making things more complex for human players and for programmers of solvers and making it harder to see what's really new when a "new" pattern is proposed - as in this thread.

Find any puzzle where someone has solved it using a Sashimi X-Wing and you have your example.

This still doesn't give me the required concrete example. A non-degenerate sashimi X-wing has a compulsory candidate in the block where things happen; this allows one to see it as a standard AIC with no inexistent candidates.
If you give me a concrete example of an AIC using inexistent candidates, I'll show you simpler ones doing the same eliminations (indeed I've no doubt that you can find them by yourself) - as I did for the first pattern in this thread and as can be done for udosuk's re-writing of it. You may choose whatever you think is the hardest case.
denis_berthier
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Denis wrote:OK, but even this is not acceptable for me. For me, a Triplet is not degenerate....

The minimal amount of restrictions on the candidate grid candidates which guarantees a naked triplet deduction is one that allows degenerate cases. In my book, the simplicity is directly correlated to the amount of restrictions you have. In order for you eliminate the degenerate cases you have to add additional restrictions to my minimal set. What does this extra complexity buy anyone? Probably nothing and certainly not any extra guarantee that the triplet deduction is valid. I think your manual solver scoffs at the idea that they would ever be confused by a degenerate naked set and would more likely be confused to learn that two naked pairs in the same house could not also combine to form a naked quad.

This still doesn't give me the required concrete example....

A sashimi x-wing uses a deduction based on a degenerate x-wing group in combination with a fin. Yes the entire pattern is not degenerate, but one of the components is, and the deduction is based on spotting and using that degenerate subpattern component. You can rewrite sashimi finned fish into AICs, grouped AICs, and kraken AICs, but they would involve more strong links and so it would be quite debatable whether the new AIC was simpler. That is a decision that is really up to the end user. Also it's noteworthy that from a degenerate fish concept, frankenfish and other patterns would spin off. So it doesn't much matter to me if you find the concept useful, as I have and I believe others have as well.
Myth Jellies

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Myth Jellies wrote:
Denis wrote:OK, but even this is not acceptable for me. For me, a Triplet is not degenerate....

The minimal amount of restrictions on the candidate grid candidates which guarantees a naked triplet deduction is one that allows degenerate cases. In my book, the simplicity is directly correlated to the amount of restrictions you have. In order for you eliminate the degenerate cases you have to add additional restrictions to my minimal set. What does this extra complexity buy anyone? Probably nothing and certainly not any extra guarantee that the triplet deduction is valid. I think your manual solver scoffs at the idea that they would ever be confused by a degenerate naked set and would more likely be confused to learn that two naked pairs in the same house could not also combine to form a naked quad.

Opinions.
We obviously don't have the same idea of simplicity.
My book is not based on the shortest but on the most precise and least ambiguous definitions.
I'd like to see a manual solver invoke a quad when he can be done with 2 pairs.

Myth Jellies wrote:
Denis wrote:This still doesn't give me the required concrete example....

A sashimi x-wing uses a deduction based on a degenerate x-wing group in combination with a fin. Yes the entire pattern is not degenerate, but one of the components is, and the deduction is based on spotting and using that degenerate subpattern component. You can rewrite sashimi finned fish into AICs, grouped AICs, and kraken AICs, but they would involve more strong links and so it would be quite debatable whether the new AIC was simpler. That is a decision that is really up to the end user. Also it's noteworthy that from a degenerate fish concept, frankenfish and other patterns would spin off. So it doesn't much matter to me if you find the concept useful, as I have and I believe others have as well.

Still opinions and no concrete example.
Modified fish patterns don't have to spin off degenerate fish, they are modifications of normal fish: whenever a candidate that is compulsory in a normal non degenerate fish is made optional, another candidate in another place is made compulsory.
It is very instructive to have a look at the discussions about nomenclature in the fish thread and how they are plagued by vocabulary problems related to degenerate cases.
Finally, I can say the same thing as you: it doesn't much matter to me if you don't find ghost candidates useless, as it is obviously useless and misleading to me and to many others.
With each of our conclusions, I can't see any point in continuing this discussion. So this will really be final for me - unless you come up with a real AIC example from a real player on a real puzzle.
denis_berthier
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### re: degenarate

denis_berthier wrote:We obviously don't have the same idea of simplicity.
My book is not based on the shortest but on the most precise and least ambiguous definitions.
I'd like to see a manual solver invoke a quad when he can be done with 2 pairs.

It is very instructive to have a look at the discussions about nomenclature in the fish thread and how they are plagued by vocabulary problems related to degenerate cases.

the simplest definition of a quartet
will be so simple that it does allow degenerate case
-- e.g. two duos.

personally, i like those simple definitions.
(not that i would ever take 2 duos and use them as a quartet.)

others have shown a preference for complicating the definitions
in order to exclude degenerate cases.
(yes, those discussions in The Ultimate FISH Guide -- i never understood why bother with those complicated definitions, but i was clearly in the minority.)

Pat

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