XY-wing pincers as a strong link

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XY-wing pincers as a strong link

Postby keith » Sat Dec 17, 2016 9:51 pm

As we have known for a long time, two strong links form the basis of the Turbot Fish pattern, which includes Skyscrapers and Kites. Ten years ago, Havard wrote an excellent explanation:

strong links for beginners

Now, the pincers of an XY-wing are a strong link. Even if the XY-wing itself does not make an elimination, it may be supplemented by another strong link to make a two-link elimination.

This idea has been around for a long time, but I have never seen it implemented, nor used much in discussions. I have seen an XY-wing that has no eliminations called "useless" or "flightless", and the addition of another link called with "coloring" or "transport".

It seems to me that this extension of an XY-wing is not too difficult to grasp if one understands the two-strong link patterns. I have used it effectively for a long time, perhaps because it is a technique that does not figure in the arsenal of puzzle creators when they decide the difficulty of their puzzles.

I'd appreciate any references to further discussions of the topic. Are there solvers that implement this?

Keith
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Re: XY-wing pincers as a strong link

Postby champagne » Sun Dec 18, 2016 6:17 am

keith wrote:
I'd appreciate any references to further discussions of the topic. Are there solvers that implement this?

Keith


In fact, an XY-Wing is a piece of an XY chain (in the sense that the conflict if any is not shown) and as such, can be part of longer XY chain. I see no interest for a solver to use it as "shortcut" to show a simpler chain. This does not prevent any manual solver to do so.

I used some "simple logical or" as strong link in AICs, but coming out of UR threats or ALS(s) .
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Re: XY-wing pincers as a strong link

Postby StrmCkr » Sun Dec 18, 2016 6:44 am

http://www.dailysudoku.com/

is the only site Ive seen where the users use the "transport" concept.

i did manage to manually use "patterns" of any type combined with other techniques to make deductions via logic: but some called it "kraken" logic

http://forum.enjoysudoku.com/strong-links-within-fish-patterns-t30392.html
Some do, some teach, the rest look it up.
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Re: XY-wing pincers as a strong link

Postby keith » Sun Dec 18, 2016 11:31 pm

In fact, an XY-Wing is a piece of an XY chain

So, what?

http://www.dailysudoku.com/
is the only site I've seen where the users use the "transport" concept.

I am guilty as charged.

In a couple of weeks we will look at some examples. Then we can decide whether this is just a rephrasing of some other pattern

I think what will prove to be powerful is that the pincers of an XY-wing are a strong link between two cells that do not "see" each other.

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Re: XY-wing pincers as a strong link

Postby champagne » Mon Dec 19, 2016 9:27 am

keith wrote:
In fact, an XY-Wing is a piece of an XY chain

So, what?
Keith


So if a solver looks for AIC's or xy chains, if I got correctly your point, any elimination that you would produce using XYwing in an AIC would come in a longer AIC of the solver. I don't see here a strong incentive to add code to make it shorter.
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Re: XY-wing pincers as a strong link

Postby keith » Tue Dec 20, 2016 2:31 am

Here's an example of what I mean. It just happens to be a Friday Detroit Free Press Puzzle I have been staring at all day.

Remember, this is pencil & paper:

Code: Select all
+-------+-------+-------+
| 5 . . | 6 . . | . . 9 |
| . . 4 | . 7 3 | 5 . . |
| 1 . . | 9 . . | 6 . . |
+-------+-------+-------+
| . . 6 | . . 9 | . . . |
| 2 . 9 | . . . | 1 . 6 |
| . . . | . . . | 8 . . |
+-------+-------+-------+
| . . 2 | . . 5 | . . 4 |
| . . 7 | 3 8 . | 9 . . |
| 6 . . | . . 2 | . . 1 |
+-------+-------+-------+


After basics:

Code: Select all
+-------------------+-------------------+-------------------+
| 5     7     8     | 6     24    1     | 24    3     9     |
| 9     6     4     | 28    7     3     | 5     1     28    |
| 1     2     3     | 9     5     48    | 6     47    78    |
+-------------------+-------------------+-------------------+
| 378   3458  6     | 12458 1234  9     | 24    2457  2357  |
| 2     3458  9     | 458   34    478   | 1     457   6     |
| 37    345   1     | 245   6     47    | 8     9     2357  |
+-------------------+-------------------+-------------------+
| 38    389   2     | 17    19    5     | 37    6     4     |
| 4     1     7     | 3     8     6     | 9     25    25    |
| 6     39    5     | 47    49    2     | 37    8     1     |
+-------------------+-------------------+-------------------+

And after an X-wing and a couple of XY-wings:

Code: Select all
+----------------+----------------+----------------+
| 5    7    8    | 6    24   1    | 24   3    9    |
| 9    6    4    | 28   7    3    | 5    1    28   |
| 1    2    3    | 9    5    48   | 6    47   78#  |
+----------------+----------------+----------------+
| 378* 3458 6    | 1458 124  9    | 24   457  3-7  |
| 2    458  9    | 458  3    478  | 1    457  6    |
| 37*  345  1    | 245  6    47#  | 8    9    23   |
+----------------+----------------+----------------+
| 38   389  2    | 17   19   5    | 37   6    4    |
| 4    1    7    | 3    8    6    | 9    2    5    |
| 6    39   5    | 47   49   2    | 37   8    1    |
+----------------+----------------+----------------+


There is a useless (or spent) XY-wing 4-78 in R3C6. The link on 7 is in C1, taking out 7 in R4C9, solving the puzzle.

# and * are two strong links on 7, making the elimination. Please note that the strong link on 7 that happens to exist
in R6 is absolutely not required for this logic.

This one just happened to show up today, more examples are to follow.

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Re: XY-wing pincers as a strong link

Postby JasonLion » Tue Dec 20, 2016 4:51 am

I would call that an AIC. From my point of view you simply used the fact that you had already recognized the XY-Wing to save time in discovering it.

Giving this technique it's own name isn't completely unprecedented, but I would argue against it. XY-Wing warrants it's own name because it is the shortest possible XY-Chain. Once the chain gets longer it is difficult to justify giving it an individual name apart from the chain technique it is an example of.
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Re: XY-wing pincers as a strong link

Postby keith » Tue Dec 20, 2016 6:37 am

JasonLion wrote:I would call that an AIC. From my point of view you simply used the fact that you had already recognized the XY-Wing to save time in discovering it.

Giving this technique it's own name isn't completely unprecedented, but I would argue against it. XY-Wing warrants it's own name because it is the shortest possible XY-Chain. Once the chain gets longer it is difficult to justify giving it an individual name apart from the chain technique it is an example of.

So, Jason,

Naming rights was furthest from my mind. But, you would rather just call kites and skyscrapers as AICs? How about W- and M-wings?

Giving names is an aid to language and communication.

Let me rather ask, how would you have solved this puzzle or found this elimination?

Keith
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Re: XY-wing pincers as a strong link

Postby champagne » Tue Dec 20, 2016 7:03 am

keith wrote:And after an X-wing and a couple of XY-wings:

Code: Select all
+----------------+----------------+----------------+
| 5    7    8    | 6    24   1    | 24   3    9    |
| 9    6    4    | 28   7    3    | 5    1    28   |
| 1    2    3    | 9    5    48   | 6    47   78#  |
+----------------+----------------+----------------+
| 378* 3458 6    | 1458 124  9    | 24   457  3-7  |
| 2    458  9    | 458  3    478  | 1    457  6    |
| 37*  345  1    | 245  6    47#  | 8    9    23   |
+----------------+----------------+----------------+
| 38   389  2    | 17   19   5    | 37   6    4    |
| 4    1    7    | 3    8    6    | 9    2    5    |
| 6    39   5    | 47   49   2    | 37   8    1    |
+----------------+----------------+----------------+


There is a useless (or spent) XY-wing 4-78 in R3C6. The link on 7 is in C1, taking out 7 in R4C9, solving the puzzle.

Keith


So I think that I got your point,

The corresponding entire AIC

7r3c9 - 7r2c9 = 8r2c9 - 8r2c6 = 4r2c6 - 4r6c6 = 7r6r6 - 7r6c1 = 3r6c1 - 7r6c1 = 7r3c1 -7r3c9

containing the XYwing chain

7r2c9 = 8r2c9 - 8r2c6 = 4r2c6 - 4r6c6 = 7r6r6

giving at the end

7r3c9 - 7r2c9 = 7r6r6 - 7r6c1 = 3r6c1 - 7r6c1 = 7r3c1 -7r3c9

EDIT
BTW I started using a full coloring technique (that I called full tagging) where all bi values where solved and reduced to a"tag". The final effect was "similar" to that one (in the sense that AICs where shortened). I gave up mainly because skill manual solver don't work in that way.

Edit typo adjusted (I hope so) after eleven remark
Last edited by champagne on Tue Dec 20, 2016 6:03 pm, edited 1 time in total.
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Re: XY-wing pincers as a strong link

Postby eleven » Tue Dec 20, 2016 5:14 pm

Hi Keith,

there are not much manual solvers left here (sometimes i see Marty posting a solution).
Most of the solvers are using programs, and those who manually find the solution, are trained to find AIC chains including ALS's (the puzzles in the "Puzzles" section are biased to such solutions).

So don't wonder, that there is little interest in extensions to typical newspaper techniques.

Don't be confused by champagne's notation, there are typos. In the Puzzles thread it would be written something like
(7=8)r3c9-(8=4)r3c6-(4=7)r6c6-r6c1=7r4c1 => -7r6c9,-7r4c9
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Re: XY-wing pincers as a strong link

Postby keith » Wed Dec 21, 2016 5:38 am

eleven wrote:Hi Keith,

there are not much manual solvers left here (sometimes i see Marty posting a solution).
Most of the solvers are using programs, and those who manually find the solution, are trained to find AIC chains including ALS's (the puzzles in the "Puzzles" section are biased to such solutions).

So don't wonder, that there is little interest in extensions to typical newspaper techniques.

Don't be confused by champagne's notation, there are typos. In the Puzzles thread it would be written something like
(7=8)r3c9-(8=4)r3c6-(4=7)r6c6-r6c1=7r4c1 => -7r6c9,-7r4c9

eleven,

Thank you.

I do find your note a little depressing, in that it implies an arms race in terms of software. To me, the point is to solve interesting puzzles in interesting ways, not to write software that solves puzzles.

Having a piece of software that throws up all the links, so the problem becomes one of connecting the dots, is not of interest to me.

But, I've had years of fun solving puzzles of a certain difficulty on paper, and I will continue to do so.

Happy holidays!

Keith
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Re: XY-wing pincers as a strong link

Postby JasonLion » Wed Dec 21, 2016 6:26 am

keith wrote:Let me rather ask, how would you have solved this puzzle or found this elimination?

By looking for AIC that could advance the puzzle. I never look specifically for XY-Wings anymore. They are found anyway when searching for AIC, and are not usually productive enough on their own to be worth a dedicated search. That is my experience anyway. It can vary depending on where you get your puzzles (which can dramatically influence the percentage of puzzles where an XY-Wing is found) and how much practice you have searching for one kind of thing relative to another.
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Re: XY-wing pincers as a strong link

Postby keith » Tue Dec 27, 2016 6:47 pm

Are AICs bi-directional?

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Re: XY-wing pincers as a strong link

Postby JasonLion » Tue Dec 27, 2016 6:54 pm

Yes, AIC are reversible.
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Re: XY-wing pincers as a strong link

Postby keith » Tue Dec 27, 2016 8:13 pm

JasonLion wrote:Yes, AIC are reversible.

So, if an inference is not reversible, it's not an AIC?

Thank you,

Keith
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