## XY-Chain Specifics

Advanced methods and approaches for solving Sudoku puzzles

### XY-Chain Specifics

I'm sorry for the Eureka notation in this forum, but a discussion elsewhere leads me to get an opinion here.

I was recently told that the following discontinuous AIC loop, with two weak links, is the proper way to view a specific XY-Chain elimination. I was under the impression that the AIC is all that's necessary to justify the elimination.

Code: Select all
`(9)r2c1 - (9=1)r2c9 - (1=4)r2c6 - (4=3)r8c6 - (3=9)r8c1 - (9)r2c1; r2c1<>9          (9=1)r2c9 - (1=4)r2c6 - (4=3)r8c6 - (3=9)r8c1          ; r2c1<>9`

Am I mistaken? I shudder at extending the first format for an XY-Chain with six eliminations!
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

Danny,
#1... you may want to at least provide a URL for the discussion that you are referring to.

#2... you may want to at least post the puzzle so that the viewers have some background to the chain you posted.

#3... you may want to read up on AIC rules at this link...
http://forum.enjoysudoku.com/viewtopic.php?t=3865

I believe the first example in Myth's first posting answers your questions.
furthermore, this quote from his "deductions" says a lot.

"Quite simply, at least one or the other (possibly both) of the two endpoint candidates (or candidate premises) of an AIC is true. Any deductions that you can make based on that are valid. This tends to produce the best results if the endpoints either share a group, or if the endpoints involve the same candidate. When your chain endpoints satisfy one of those conditions, it is time to check for any deductions"
storm_norm

Posts: 85
Joined: 27 February 2008

### Re: XY-Chain Specifics

daj95376 wrote:I'm sorry for the Eureka notation in this forum, but a discussion elsewhere leads me to get an opinion here.

I was recently told that the following discontinuous AIC loop, with two weak links, is the proper way to view a specific XY-Chain elimination. I was under the impression that the AIC is all that's necessary to justify the elimination.

Code: Select all
`(9)r2c1 - (9=1)r2c9 - (1=4)r2c6 - (4=3)r8c6 - (3=9)r8c1 - (9)r2c1; r2c1<>9          (9=1)r2c9 - (1=4)r2c6 - (4=3)r8c6 - (3=9)r8c1          ; r2c1<>9`

Am I mistaken? I shudder at extending the first format for an XY-Chain with six eliminations!

Perhaps the person meant 'view' as in perception, otherwise when it comes to actually presenting the chain, starting and ending with the strong links is correct (2nd chain). Also, there should be no reason to apologize for using the Eureka notation. FWIW: The name was assigned simply because it originated at Eureka, but based on the extensive advanced solving of complete puzzles using AICs w/Eureka notation that has occurred there and the fact that Myth seems to have accepted it as the AIC notation, it would seem to me that the Eureka notation is now the standard notation for AICs so it should be acceptable for that purpose anywhere.
DonM
2013 Supporter

Posts: 475
Joined: 13 January 2008

### Re: XY-Chain Specifics

daj95376 wrote:I'm sorry for the Eureka notation in this forum, but a discussion elsewhere leads me to get an opinion here.

I was recently told that the following discontinuous AIC loop, with two weak links, is the proper way to view a specific XY-Chain elimination. I was under the impression that the AIC is all that's necessary to justify the elimination.

Code: Select all
`(9)r2c1 - (9=1)r2c9 - (1=4)r2c6 - (4=3)r8c6 - (3=9)r8c1 - (9)r2c1; r2c1<>9          (9=1)r2c9 - (1=4)r2c6 - (4=3)r8c6 - (3=9)r8c1          ; r2c1<>9`

Am I mistaken? I shudder at extending the first format for an XY-Chain with six eliminations!

What you were told is not true.
It may be the teller's preferred method.
The AIC which you present is fine, simpler, shorter and equally effective.
aran

Posts: 334
Joined: 02 March 2007

Further to what Don writes
The name was assigned simply because it originated at Eureka, but based on the extensive advanced solving of complete puzzles using AICs w/Eureka notation that has occurred there and the fact that Myth seems to have accepted it as the AIC notation, it would seem to me that the Eureka notation is now the standard notation for AICs so it should be acceptable for that purpose anywhere

I didn't even know that there may have been an unwritten rule regarding which notation to use on which forum.
And hope that my exclusive use of "eureka" notation isn't out of order.

A personal view on a related general point :
taking this quote from Sudopedia

In a discontinuous loop, the first/last cell is referred to as the discontinuity. Discontinuous loops are more frequent, but they only have an effect on the discontinuity. This effect depends on the type of links it has to the adjacent nodes.

* When the discontinuity has 2 links with weak inference for a single digit, this digit can be eliminated from the discontinuity.
* When the discontinuity has 2 links with strong inference for a single digit, this digit can be placed in the discontinuity.
* When the discontinuity has 2 links with different inference for 2 different digits, the digit providing the weak inference can be eliminated from the discontinuity

I would put it like this :
once the logic of alternating link deductions is understood, there is no need for the above rules, and until it is understood, mechanically applying them without understanding why they work could be either confusing or unsatisfying or both.
aran

Posts: 334
Joined: 02 March 2007

aran wrote:I didn't even know that there may have been an unwritten rule regarding which notation to use on which forum.
And hope that my exclusive use of "eureka" notation isn't out of order.

IMO there is ... and it is.

Out of general courtesy and to support everyone's efforts on Eureka! to encourage Bill Richter to use a common notation, Mike Barker and I (and probably others I've forgotten) learned and used AIC notaton when posting on Eureka!

Other than some posts by DonM using both notations, I've not seen a similar courtesy extended by the Eureka! crowd posting here.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

ronk wrote:
aran wrote:I didn't even know that there may have been an unwritten rule regarding which notation to use on which forum.
And hope that my exclusive use of "eureka" notation isn't out of order.

IMO there is ... and it is.

Out of general courtesy and to support everyone's efforts on Eureka! to encourage Bill Richter to use a common notation, Mike Barker and I (and probably others I've forgotten) learned and used AIC notaton when posting on Eureka!

Other than some posts by DonM using both notations, I've not seen a similar courtesy extended by the Eureka! crowd posting in this forum.

English or French in Quebec but only NL on the Player's forum ?
Why not take the bilingual approach to the two major languages, whilst perhaps not encouraging little-spoken dialects ?
aran

Posts: 334
Joined: 02 March 2007

Since my original question seems to be answered, I'd like to join in the tangent topic of notation.

I spent a lot of time learning strong/weak inference/links and fundamental NL notation -- no embedded ALS/UR/etc. When I first reviewed Eureka notation, I had a hard time accepting that a second form of notation was necessary.

After reviewing several examples of fundamental Eureka notation in another forum, it finally hit me that I could more easily follow AICs in Eureka notation -- especially because the links within cells stood out better (for me).

Don't get me wrong, I still tend to think in terms of NL notation segments, but I will sometimes convert it to Eureka notation as a final way of expressing my thoughts.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

### Re: XY-Chain Specifics

DonM wrote:Perhaps the person meant 'view' as in perception, ...

No, the other person was adamant that the first perspective was the only correct perspective.

ALL XY Chains that perform eliminations are (discontinuous) loops. If there happen to be multiple victims, they are included at the discontinuity. It is still a loop, regardless. In general:
Victim A|Victim B|Victim C|etc - AIC - Victim A|Victim B|Victim C|etc; A,B and C, etc., are false

I don't find fault with his reasoning, only a disagreement that it is the only way to interpret an XY-Chain.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

aran wrote:
ronk wrote:
aran wrote:I didn't even know that there may have been an unwritten rule regarding which notation to use on which forum.
And hope that my exclusive use of "eureka" notation isn't out of order.

IMO there is ... and it is.

Out of general courtesy and to support everyone's efforts on Eureka! to encourage Bill Richter to use a common notation, Mike Barker and I (and probably others I've forgotten) learned and used AIC notaton when posting on Eureka!

Other than some posts by DonM using both notations, I've not seen a similar courtesy extended by the Eureka! crowd posting in this forum.

English or French in Quebec but only NL on the Player's forum ?
Why not take the bilingual approach to the two major languages, whilst perhaps not encouraging little-spoken dialects ?

I think it would be unfortunate for the message to be spread that the Eureka/AIC notation be unacceptable or discourteous on the Player's forum as if NL notation is 'the' de facto language here. Sudoku as discussed in the two main forums is still evolving and there is room for two concepts/notations.

There was a reason why people coming over to Eureka had to adapt to the AIC/Eureka notation beyond simple courtesy. It was because there developed, for the first time, the complete solving of puzzles using increasingly advanced methods, some of them pushing the envelope and there were some really interesting associated threads. These involved a fair number of people known at Player's as well- Myth, Steven K, Ruud, as mentioned- Mike B and Ronk, etc. Everyone simply had to be speaking the same language.

As to how the two formats can exist in peace over here, I think that's yet to be determined and personally, I think it's in the best interest of the Sudoku hobby to have the door open to both of them. There's no doubt that most people are using NL notation and so whenever possible and when it seems the right thing to do, I try to post chains in both formats. However, I don't see much in the way of the complete solution of advanced puzzles in NL format. It seems to be mostly used in discussions of isolated parts of puzzles. I hear questions here about things such as AHSs and the like, but I've seen little use of them expressed in NL format while they are commonplace at Eureka. So the question is raised- if someone like ttt or myself were to post an entire solution to an advanced puzzle where the format of the methods we've become accustomed to has been made fairly clear in Eureka/AIC format, but not necessarily in NL notation, are we obligated to translate to NL format? Also, not to forget that the AIC concept did originate here albeit using a different notation.

I may not be putting this to well, but that's the best I can do at the moment.
DonM
2013 Supporter

Posts: 475
Joined: 13 January 2008

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