The New Sudoku Players' Forum

[ronk]

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'.

With double-talk like that, you would make a great politician ... IMO, of course.

[DonM]

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'.

With double-talk like that, you would make a great politician ... IMO, of course.

[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.
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!

daj
The key word is surely forcing.
How do you reckon that downstream implications whether they be two or several are forced whereas one downstream implication is unforced ?
That point has to be dealt with.
I say that the number of downstream implications is irrelevant to a "net".
The essence of a net as the very word suggests is branching and merging or converging. What is forced is the convergence. That is : at the point where a node splits, the separate implication streams, if they merge "force" whatever results from that merger.
No node splits in a single implication stream with memory.

[aran]

Don
Further to your exchange with Ronk :
in the example to which you refer, I would say that under existing Jeff terminology it is a forcing chain, since to qualify as a forcing net under his terminology there would have to be multiple inference within one or both of the streams.
My own view as already expressed is that multiple inference is normal practice, forces nothing, and having got mixed into the pioneering definitions of forcing nets of long ago, is regarded by some as sufficient for a net.
This is language got out of hand.
Personally I would remove "multiple inference" out of the definitions.
Which would have the great benefit of removing the need for two names : forcing chains, forcing nets. Forcing net would be the clear choice.
After all chains don't force anything, they just produce implications from which conclusions can be drawn.
The forcing chain in existing nomenclature consists of two chains exiting from the two and only two possibilities within a boolean eg bivalue. If those chains imply the same thing, then that joint implication leaves no choice and forces a conclusion.

So to conclude
1. forcing chain is a misnomer
2. forcing net would do very well for all that forcing business
3. multiple inference is a complete red herring in all of the above.

And very lastly in the example you quoted :

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


a good old hidden pair would deal with that much quicker
67r6c12=5r6c1-(5=3)r6c9-(3=1)r5c9-(1=4)r3c9-(4=7)r3c1 :=><7>r4c1.

[ronk]

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!

The key word is surely forcing.
How do you reckon that downstream implications whether they be two or several are forced whereas one downstream implication is unforced ?

Doubtful, but maybe a diagram will help.

Code: Select all

           ___ Inference #2
          V
   + ----------8---------- +
   |                       |
r9c3 -8- r8c3 -6- r8c9 -2- r9c7 -6- r9c5
      ^
      |___ Inference #1

Two or more inferences means multiple inference. Moreover, to say that r9c7=6 or r9c5<>6 is "forced" by the above is improper. "Forcing" occurs because the alternative to r9c3=8 (not shown) also has the outcome of r9c5<>6.

[daj95376]

daj
The key word is surely forcing.
How do you reckon that downstream implications whether they be two or several are forced whereas one downstream implication is unforced ?
That point has to be dealt with.
I say that the number of downstream implications is irrelevant to a "net".
The essence of a net as the very word suggests is branching and merging or converging. What is forced is the convergence. That is : at the point where a node splits, the separate implication streams, if they merge "force" whatever results from that merger.
No node splits in a single implication stream with memory. WRONG!

Thanks, you just supplied the counter argument to your position.

Just because richardm didn't write it as a forcing network doesn't mean that what he wrote is correct.

He should have written ...

Code: Select all

            r9c7<>8
          /                  \
r9c3=8 =>                      => r9c7=6 => r9c5=2
          \                  /
            r8c3=6 => r8c9=2


.. which splits and then merges!

Note: Jeff uses ...

Code: Select all

r9c3=8 (=> r9c7<>8) => r8c3=6 => r8c9=2 => r9c7=6 => r9c5=2


... to denote the split and merge of downstream implications on one line.

[Allan Barker]

maybe a diagram will help.

Code: Select all

           ___ Inference #2
          V
   + ----------8---------- +
   |                       |
r9c3 -8- r8c3 -6- r8c9 -2- r9c7 -6- r9c5
      ^
      |___ Inference #1

Two or more inferences means multiple inference. Moreover, to say that r9c7=6 or r9c5<>6 is "forced" by the above is improper. "Forcing" occurs because the alternative to r9c3=8 (not shown) also has the outcome of r9c5<>6.

Just to make sure that richard goes home with a full bag of answers.

Noting Ronk's omission of candidate 2r9c5, it's also true that 2r9c5 need not be part of the logic and it's sufficient to show that either r9c3=6 or r9c7=6 => r9c5<>6. In this case, the logic can also be represented as a small double loop as shown below, in addition to the various inference deductions.

Thumb

.
.

[DonM]

Don
Further to your exchange with Ronk :
in the example to which you refer, I would say that under existing Jeff terminology it is a forcing chain, since to qualify as a forcing net under his terminology there would have to be multiple inference within one or both of the streams.
My own view as already expressed is that multiple inference is normal practice, forces nothing, and having got mixed into the pioneering definitions of forcing nets of long ago, is regarded by some as sufficient for a net.
This is language got out of hand.
Personally I would remove "multiple inference" out of the definitions.
Which would have the great benefit of removing the need for two names : forcing chains, forcing nets. Forcing net would be the clear choice.
After all chains don't force anything, they just produce implications from which conclusions can be drawn.
The forcing chain in existing nomenclature consists of two chains exiting from the two and only two possibilities within a boolean eg bivalue. If those chains imply the same thing, then that joint implication leaves no choice and forces a conclusion.

So to conclude
1. forcing chain is a misnomer
2. forcing net would do very well for all that forcing business
3. multiple inference is a complete red herring in all of the above.

I hear what you're saying and you make a number of good points. I agree that the multiple inference issue is an unnecessary sidetrack to this discussion. Truth be told, considering the obvious disagreement on terminology among several individuals in this one thread, my main concern/issue is the fact that some of these sudoku terms are all over the map, the disagreement over what is a net and what isn't being a good example.

If I have any main issue it is with the specific terminology surrounding the term, forcing chain. Currently it is being used as both a broad generic term and specific term to describe a technique, not to mention the disagreements over what is a 'forcing chain' and what is a 'forcing net'. This must be very confusing to those new to sudoku. In the end, I'm a manual solver and I don't care enough about splitting hairs on terminology so much as I do about people finally agreeing on some sort of standard terminology for some of these 'definitions'. So if the concensus were to be that something was a 'net' vs a 'chain' or vice versa then I'd be fine with it. Since I am in this for the solving I don't really care that much.

[udosuk]

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.

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?

Again, you need another crash course on remote pairs:

http://www.sudopedia.org/wiki/Remote_Pairs

To qualify as a remote pair, you must have all 4 cells being [62]. But since r89c3 are [68] instead, it is NOT a remote pair. It is probably a semi remote pair as some likes to call, but IMO w-wing is much more universally recognised (and sweetly shorter ).

[ronk]

After all chains don't force anything, they just produce implications from which conclusions can be drawn.

I think you can thank the AIC/Eureka folks for creating that second and different definition of chain, a redefinition that has certainly contributed to today's confusion.

[DonM]

After all chains don't force anything, they just produce implications from which conclusions can be drawn.

I think you can thank the AIC/Eureka folks for creating that second and different definition of chain, a redefinition that has certainly contributed to today's confusion.

As if the AIC/Eureka folks were of one mind & all agreed on anything either, not to mention that you were/have been among those folks periodically.

[ronk]

I think you can thank the AIC/Eureka folks for creating that second and different definition of chain, a redefinition that has certainly contributed to today's confusion.

As if the AIC/Eureka folks were of one mind & all agreed on anything either, not to mention that you were/have been among those folks periodically.

As if I had anything to do with the definition of "chain" in alternating-inference-chain NOT

[edit: To be clear, I'm referring to the lopping off of the weak links, if any, from the ends of a forcing chain.]

[DonM]

I think you can thank the AIC/Eureka folks for creating that second and different definition of chain, a redefinition that has certainly contributed to today's confusion.

As if the AIC/Eureka folks were of one mind & all agreed on anything either, not to mention that you were/have been among those folks periodically.

As if I had anything to do with the definition of "chain" in alternating-inference-chain NOT

[edit: To be clear, I'm referring to the lopping off of the weak links, if any, from the ends of a forcing chain.]

Yes, good idea to be clear. I'm still wondering specifically who those 'AIC/Eureka folks' are who did anything other than follow standard AIC notation. Don't remember any 'lopping off of weak links' controversy raised by anyone. Of course, I might have missed it.

[daj95376]

I think you can thank the AIC/Eureka folks for creating that second and different definition of chain, a redefinition that has certainly contributed to today's confusion.

As if the AIC/Eureka folks were of one mind & all agreed on anything either, not to mention that you were/have been among those folks periodically.

As if I had anything to do with the definition of "chain" in alternating-inference-chain NOT

[edit: To be clear, I'm referring to the lopping off of the weak links, if any, from the ends of a forcing chain.]

Yes, good idea to be clear. I'm still wondering specifically who those 'AIC/Eureka folks' are who did anything other than follow standard AIC notation. Don't remember any 'lopping off of weak links' controversy raised by anyone. Of course, I might have missed it.

Well, this part of the discussion is about a month too late for me because I've been banging heads with Asellus in the DailySudoku forum over his insisting that AICs contained initial and trailer weak links. Damn!

[DonM]

I think you can thank the AIC/Eureka folks for creating that second and different definition of chain, a redefinition that has certainly contributed to today's confusion.

As if the AIC/Eureka folks were of one mind & all agreed on anything either, not to mention that you were/have been among those folks periodically.

As if I had anything to do with the definition of "chain" in alternating-inference-chain NOT

[edit: To be clear, I'm referring to the lopping off of the weak links, if any, from the ends of a forcing chain.]

Yes, good idea to be clear. I'm still wondering specifically who those 'AIC/Eureka folks' are who did anything other than follow standard AIC notation. Don't remember any 'lopping off of weak links' controversy raised by anyone. Of course, I might have missed it.

Well, this part of the discussion is about a month too late for me because I've been banging heads with Asellus in the DailySudoku forum over his insisting that AICs contained initial and trailer weak links. Damn!

Stay tuned. In addition to the above & Eureka being an alleged den of squabbling, I have it on good authority that it is responsible for Jimmy Hoffa's disappearance!