The New Sudoku Players' Forum

[richardm]

Thanks to all for your comments.

The approach I used didn't require PM as the opportunity to eliminate 6 from r9c5 seemed to be strongly suggested. And so I didn't look for the 3-fish.

As a non-PM solver I seem to find the forced net approach quicker to yield results.

Anyway, once again many thanks for your comments.

Richard

[richardm]

The Time super fiendish last Friday (6th March) ended up after simple elimination with R8 and R9 as follows:

Code: Select all

| x  x  68  | 628  x  x  |  x  x  62 |
| x  x  68  | x   62  x  | 628 x  x  |


This is amost an x-wing in 6 and 6 in R9C5 is eliminated

There is something there, but I see it as a W-wing. You've got two cells with (26) linked by the conjugate 6's in box 7. That means that any (2) that can see both the (26) cells can be eliminated, =>r8c4,r9c7<>2.

That leads to the eliminations you found. I don't think I see an almost X-wing yet, as I know it.

Why do you see this as a w-wing? I'm not saying anything about the possibilities for 2 in r789 other then the cells marked. In other words 2 hasn't been eliminated from r7 or those cells marked x. Does your w-wing argument still hold?

Richard

[Pat]

thanks, DonM, for the quote from SuDoPedia,
though i can't accept their claim that a "chain" requires a single stream of implications---

aran, my distinction of "chain" vs "net"
is based on my understanding of the definitions given by Jeff (2006)

[udosuk]

Why do you see this as a w-wing? I'm not saying anything about the possibilities for 2 in r789 other then the cells marked. In other words 2 hasn't been eliminated from r7 or those cells marked x. Does your w-wing argument still hold?

Richard, what you need is just a crash course on w-wings:

http://www.sudopedia.org/wiki/W-Wing
http://forum.enjoysudoku.com/viewtopic.php?p=63874#p63874

You only need 4 cells for the w-wing to hold: 2 cells with a strong link on digit A, and 2 cells holding [AB] only.

In your puzzle you have the strong link on digit 6 in r89c3, and 2 cells holding [62] only. That's enough to form the w-wing, allowing you to eliminate digit 2 from r8c456+r9c789.

[ronk]

richardm, hang in there. It's not usually this difficult to title a thread or establish the scenario for a question.

[aran]

thanks, DonM, for the quote from SuDoPedia,
though i can't accept their claim that a "chain" requires a single stream of implications---

aran, my distinction of "chain" vs "net"
is based on my understanding of the definitions given by Jeff (2006)

Pat thanks for the pointer.
I see nothing in Jeff's definitions that describes as a net the creature to which I refer, that is a chain with memory ie a chain which remembers earlier findings made within its own implication stream.
No merging implication streams here.
So I maintain
- Jeff's definitions do not encompass what we are talking about
- which is just as well, because it is sheer common sense...
To anyone who says "who cares ?", good point...
except that there are some out there who would wish to deny to the solving public (via the pejorative taunt of "net") this oh so simple bit of logic.

[ronk]

I see nothing in Jeff's definitions that describes as a net the creature to which I refer, that is a chain with memory ie a chain which remembers earlier findings made within its own implication stream.
No merging implication streams here.

"Memory" is just an alternate term for multiple inference, which is covered by Jeff's definitions.

Also covered by Jeff's definitions is an almost-locked-set, which provides a means to express some "multiple inferences" in the single inference style of a chain. For richardm's example ...

r9c5 -6- r9c3 -8- r8c3 -6- r8c9 -2- als:r9c37 -6- r9c5, ==> r9c5<>6

... which is a chain with endpoint overlap at r9c3.

[DonM]

IMO, there is a broad point, which I tried to point out in my last post, that a lot of the disagreement over sudoku terminology is due to the fact that some of these terms have never been really nailed down just as in the Sudopedia example I gave, where the term forcing net is given an aka as a generalized forcing chain.

More specifically, the term 'net' seems to mean different things to different people and some want to give it another name. Hopefully, over time some sort of standardization will occur. For the moment, I tend to disuade newer solvers from the technique used above where you start from a bivalue cell and test each value. To me, it's too broad a weapon and if one gets the headset that it's some sort of elegant technique then they'll be less likely to learn the truly elegant techniques. But that's just me.

On the other hand, the use of 'net-based' or 'memory-based' techniques at the higher levels of puzzle difficulty becomes more a matter of personal preference. Personally, I'll give in to them starting at somewhere around ER=8.4 to 8.5 puzzles, but that level continues to increase as I get better at what I consider more elegant techniques (again, a purely personal preference). One thing I do know is that based on the experience of several 'challenge' puzzles at Eureka, if someone presents a solution without anything resembling a 'net', it tends to get more appreciation than one that has what resembles a 'net' (and sometimes, I was the one using the 'net' ). Rightly or wrongly, it just is what it is.

[aran]

I see nothing in Jeff's definitions that describes as a net the creature to which I refer, that is a chain with memory ie a chain which remembers earlier findings made within its own implication stream.
No merging implication streams here.

"Memory" is just an alternate term for multiple inference, which is covered by Jeff's definitions.

Also covered by Jeff's definitions is an almost-locked-set, which provides a means to express some "multiple inferences" in the single inference style of a chain. For richardm's example ...

r9c5 -6- r9c3 -8- r8c3 -6- r8c9 -2- als:r9c37 -6- r9c5, ==> r9c5<>6

... which is a chain with endpoint overlap at r9c3.

Jeff's definitions :
Network - a collective term for forcing chain and forcing net.
Multiple Inference - a network is said to have a multiple inference when a node of an implication steam infers 2 or more nodes downstream. A multiple inference network is a net and should never be described as a chain.
So a network is a forcing thing, and multiple inference occurs within that forcing thing.
No application there to memory within a single chain.
Take a simple example :
r4c2=36
r6c2=369
r5c3=39.
Then 9r5c3=3r5c3-(3=6)r4c2-(36=9)r6c2.
You want to call that a network/net or whatever.
I just say its simple memory and common sense.
It's no more forcing than a=b is forcing in a bivalue ab.

[daj95376]

I see nothing in Jeff's definitions that describes as a net the creature to which I refer, that is a chain with memory ie a chain which remembers earlier findings made within its own implication stream.
No merging implication streams here.
So I maintain
- Jeff's definitions do not encompass what we are talking about
- which is just as well, because it is sheer common sense...
To anyone who says "who cares ?", good point...
except that there are some out there who would wish to deny to the solving public (via the pejorative taunt of "net") this oh so simple bit of logic.

Forcing Net - same as a forcing chain, except that in a forcing net, a node could infer 2 or more nodes downstream. Such inference is regarded as a multiple inference. (Refer definition of "multiple inference" below)

In richardm's chain ...

Code: Select all

r9c3=8 => r8c3=6 => r8c9=2 => r9c7=6 => r9c5=2


... r9c3=8 not only implies r8c3<>8 but it also implies r9c7<>8 for the logic to work. That's two downstream implications using my arithmetic!

[ronk]

IMO, there is a broad point, which I tried to point out in my last post, that a lot of the disagreement over sudoku terminology is due to the fact that some of these terms have never been really nailed down just as in the Sudopedia example I gave, where the term forcing net is given an aka as a generalized forcing chain.

I think your example using the "generalized forcing chain" term is a poor one. Why? Because no one, except you of course, has ever used that term on this forum.

And your reason for this example is false.

I mention this because what is really a forcing net is often defined/described as a forcing chain in tutorials. Just one example:

http://www.palmsudoku.com/pages/techniques-10.php

It's not a forcing net, but an xy-chain; a rather long chain, but still just a chain.

[DonM]

IMO, there is a broad point, which I tried to point out in my last post, that a lot of the disagreement over sudoku terminology is due to the fact that some of these terms have never been really nailed down just as in the Sudopedia example I gave, where the term forcing net is given an aka as a generalized forcing chain.

I think your example using the "generalized forcing chain" term is a poor one. Why? Because no one, except you of course, has ever used that term on this forum.

Perhaps in your mind that settles the matter, but someone put it in Sudopedia, many people read Sudopedia and many people will likely be confused by both it and the disagreement in this thread over terminology. That's where things stand. That is my point. Besides whether people on this forum have ever used a certain terminology or not doesn't de facto decide anything to a certainty anyway.

And your reason for this example is false.

I mention this because what is really a forcing net is often defined/described as a forcing chain in tutorials. Just one example:

http://www.palmsudoku.com/pages/techniques-10.php

It's not a forcing net, but an xy-chain; a rather long chain, but still just a chain.

Well, whether it's false or not is a matter of opinion and in this case, your opinion. Others can decide for themselves. In that example, it is titled 'Forcing Chain' and if you look down farther in the example, the person giving the example says 'Now start again, but this time instead of a 1, this time make the top cell a 2', which is hardly the routine used in an xy-chain. Whether the exclusion can be arrived at using a simple xy-chain is IMO beside the point- we aren't discussing alternative techniques in tutorials. Even if that doesn't convince you -which I'm sure it doesn't- then the title 'Forcing Chain' only reinforces my point about terminology differences & confusion.

[richardm]

Richard, what you need is just a crash course on w-wings:

http://www.sudopedia.org/wiki/W-Wing
http://forum.enjoysudoku.com/viewtopic.php?p=63874#p63874

You only need 4 cells for the w-wing to hold: 2 cells with a strong link on digit A, and 2 cells holding [AB] only.

In your puzzle you have the strong link on digit 6 in r89c3, and 2 cells holding [62] only. That's enough to form the w-wing, allowing you to eliminate digit 2 from r8c456+r9c789. :idea:

Yes I see that, but why isn't this simply a remote pair in 62 that happen to be placed nicely enough to eliminate more than just the 62 at their intersection? Or is that what a w-wing really is - a specialization of a remote pair?

Richard

[ronk]

Perhaps in your mind that settles the matter, but someone put it in Sudopedia, many people read Sudopedia and many people will likely be confused by both it and the disagreement in this thread over terminology. That's where things stand. That is my point.

As I understand it, anyone can author a sudopedia page and anyone can edit a sudopedia page. As a result, I take everything on sudopedia with a grain of salt, and advise you to do the same.

Besides whether people on this forum have ever used a certain terminology or not doesn't de facto decide anything to a certainty anyway.

Then perhaps you can provide a link or two to other sites that do use the "generalized forcing chain" terminology.

And your reason for this example is false.

I mention this because what is really a forcing net is often defined/described as a forcing chain in tutorials. Just one example:

http://www.palmsudoku.com/pages/techniques-10.php

It's not a forcing net, but an xy-chain; a rather long chain, but still just a chain.

Well, whether it's false or not is a matter of opinion and in this case, your opinion.
[...]
Whether the exclusion can be arrived at using a simple xy-chain is IMO beside the point- we aren't discussing alternative techniques in tutorials.

OK, let's get back my point, that your cited example is a forcing chain rather than a forcing net. Here are the pencilmarks and nice loop for your convenience.

Code: Select all

 4678  1267 I12    | 5     68   H27    |C14    3     9
 68    3     9     | 68    4     1     | 2     5     7
A47    127   5     | 27    3     9     | 6     8    B14
-------------------+-------------------+------------------
 5-7   9   JF14    | 3     2   KG47    |E18    6     158
 123   12    8     | 9     5     6     | 7     4     13
 567   67    34    | 47    1     8     | 9     2     35
-------------------+-------------------+------------------
 29    4     6     | 1     78    5     | 3     79    28
 23    8     7     | 246   9     234   | 5     1     246
 1239  5     123   | 2468  678   234   |D48    79    2468

 r4c1 -7- r3c1 -4- r3c9 -1- r1c7 -4- r9c7 -8- r4c7 -1- r4c3 -4- r4c6 -7- r1c6 -2- r1c3 -1- r4c3 -4- r4c6 -7- r4c1 ==> r4c1<>7

If there is a multiple inference, where is it If there is no multiple inference, how is it a matter of opinion

[DonM]

Perhaps in your mind that settles the matter, but someone put it in Sudopedia, many people read Sudopedia and many people will likely be confused by both it and the disagreement in this thread over terminology. That's where things stand. That is my point.

As I understand it, anyone can author a sudopedia page and anyone can edit a sudopedia page. As a result, I take everything on sudopedia with a grain of salt, and advise you to do the same.

You don't seem to be getting my point. Please go back and re-read my posts if necessary. My point is definitely not that the Sudopedia is accurate one way or the other; my point is that the use of the term Forcing Net with an aka of 'Generalized Forcing Chain' on a web page that people use as a reference is a good example of how terminology is being used that confuses people about these terms. With that in mind, there's no reason why I would want to bother finding a link to the term 'generalized forcing chain'.

As to the other: Anyway you slice it, IMO, the example I gave indicates the reason these terms are being used in a confusing way. If it makes you feel better, I agree that what ends up is an xy-chain, but the method being used to find it IMO described that more of a net ie. assign one value first and follow it, then assign the other value and follow it. In any event, one can be picky about what the definition of a tree is when calling into question one's view of a forest, but I choose not to be.