The New Sudoku Players' Forum

[Gee]

I had solved this puzzle and then ran it through a "solver" and got this far. At this point, the solver said:

" X_cycle on 8 (Discontinuous Alternating Nice Loop, length 6:
8[b4]-8[f4]=8[f7]-8[c7=8[b8]-8[b4]-

Discontinuity is two weak links joined at b4, 8 can be removed from that cell"
Cells in question are the 5 cells with an "X".

First, I know that 8 can be excluded from c7 using multiple colors Also, I would think of this as a Turbo where 8 can be placed in b8. What my question is simply. It looks to me as if there is a strong from b8 to b4 so I don't understand why the solver said two weak links were joined at b4.

All help appreciated.

Code: Select all

 *-----------------------------------------------------------*
 | 379   79    8     | 23    249   6     | 1     49    5     |
 | 139   19    6     | 38x   49    5     | 7     489x  2     |
 | 2     4     5     | 189   7     18    | 89x   6     3     |
 |-------------------+-------------------+-------------------|
 | 578   3     2     | 189   6     18    | 589   17    4     |
 | 58    6     1     | 7     259   4     | 3     2589  89    |
 | 4     57    9     | 128x  25    3     | 258x  17    6     |
 |-------------------+-------------------+-------------------|
 | 159   8     47    | 6     3     79    | 245   259   179   |
 | 6     2     3     | 45    1     79    | 458   589   789   |
 | 159   159   47    | 45    8     2     | 6     3     179   |
 *-----------------------------------------------------------*


[storm_norm]

First, I know that 8 can be excluded from c7 using multiple colors Also

Gee,
you are letting yourself fall prey to the confusion caused by many many different ways to say the same thing.
(sometimes you want to name each tree in the forest when all you want to do is name the forest.)
the solver (by definition of its predetermined algorithm) might find the cycle in a different manner than what you did.
you chose multi-coloring to determine which 8 can be eliminated. and if you are comfortable seeing that way then I wouldn't worry about the other 3 or 4 ways to describe it.

your use of multi-coloring is a good way to look at the candidate 8.

other terms to describe the candidate 8 might include:
skyscraper
kite
cycle

but...
it isn't the name of the technique that is important here.
its the concept behind the technique name that is pertinent and will hopefully and eventually fill in all those gaps and spike the learning curve which I have no doubt I fall short in regards to the geniuses on this site

Norm

[hobiwan]

It looks to me as if there is a strong from b8 to b4 so I don't understand why the solver said two weak links were joined at b4.

Any strong link can be used as weak link if necessary and thats what happened here. You are right of course that r2c48 form a strong link on candidate 8, but since r2c8 was reached via a strong link is has to be left via a weak link (on the same digit).

[Luke]

hobiwan covered this whilst I wrote the following, but here it is anyway.

I've spent the last three months trying to figure out the answers to questions like yours. Here's my take on it, and if I'm fuzzy on it, someone will set me straight and we'll both learn something.

By definition, if a strong inference exists in a link, a weak one does also. The link you cite is indeed strong, in that the two candidates can't both be false. It also meets the criteria for a weak link, in that the two premises can't both be true. In other words, any strong inference can be used as a weak link or a strong link, but a weak inference can only be used as a weak link.

If your loop begins and ends on a weak link, that is a discontinuity in the rules of propagation, and the candidate involved can be eliminated from that cell.

For more on this nomenclature, check
Paul's Nice Loop paper or Myth Jellie's AIC article.

BTW, the solver I think you are using has a toggle to switch its output to the row/column format (like r2c4) that folks like to use around here.

[DonM]

I would add that I think it is counterproductive to the learning process to try to decipher the 'explanatory' part of most computer solver output when it comes to these chains. Sometimes I've seen people even cite the output of Sudoku Explainer as some sort of explanation for an elimination when that solver wasn't updated much past 2006. Overall, I think it's better to use the information that's already available to understand this relationships such as Luke's references above. The Paul Stephen's tutorial is an excellent starting point.

Just to make the above general explanations of weak & strong links complete (though not as important to comprehend yet as the above concepts): In a continuous loop (ie. where there are no discontinuities), all weak links are proved strong.

[daj95376]

I had solved this puzzle and then ran it through a "solver" and got this far. At this point, the solver said:

" X_cycle on 8 (Discontinuous Alternating Nice Loop, length 6:
8[b4]-8[f4]=8[f7]-8[c7=8[b8]-8[b4]-

Discontinuity is two weak inferences joined at b4, 8 can be removed from that cell"
Cells in question are the 5 cells with an "X".

First, I know that 8 can be excluded from c7 using multiple colors Also, I would think of this as a Turbo where 8 can be placed in b8. What my question is simply. It looks to me as if there is a strong from b8 to b4 so I don't understand why the solver said two weak links were joined at b4.

All help appreciated.

The problem appears to be the terminology. In Sudopedia, continuous and discontinuous nice loops are described in terms of strong/weak inference. I corrected the message above to match what I believe it should have said. As I'm sure you know, a weak inference can be represented by a strong link ... as in [row 2]. That said ...

The X_Cycle is overkill and distracting. You have a turbot fish in the form of a simple Empty Rectangle for that elimination.

Code: Select all

 (8) [r6c4]=[r6c7]-[r3c7]=[r2c8]; => [r2c4]<>8
 +--------------------------------------------------------------+
 |  379   79    8     |  23    249   6     |  1     49    5     |
 |  139   19    6     |  3-8   49    5     |  7    *489   2     |
 |  2     4     5     |  189   7     18    | *89    6     3     |
 |--------------------+--------------------+--------------------|
 |  578   3     2     |  189   6     18    |  589   17    4     |
 |  58    6     1     |  7     259   4     |  3     2589  89    |
 |  4     57    9     | *128   25    3     | *258   17    6     |
 |--------------------+--------------------+--------------------|
 |  159   8     47    |  6     3     79    |  245   259   179   |
 |  6     2     3     |  45    1     79    |  458   589   789   |
 |  159   159   47    |  45    8     2     |  6     3     179   |
 +--------------------------------------------------------------+
 # 66 eliminations remain


There are other eliminations in <8> as well. (Annotated results from my solver.)

Code: Select all

2-Fish r6b3\c47                 fF 101\020  <> 8  [r2c4]   Empty Rectangle

2-Fish r6b2\c47                 fF 101\020  <> 8  [r3c7]   Empty Rectangle

2-Fish r6c6\r3b5                fm 110\101  <> 8  [r3c7]   2-String Kite
2-Fish r6c6\c7b5                fm 110\011  <> 8  [r3c7]   "   "     "

2-Fish r26\c47                  Sk 200\020  <> 8  [r3c7]   Skyscraper elim [box 3]
2-Fish r26\c48                  Sk 200\020  <> 8  [r5c8]       "       "   [box 6]


[aran]

I've never seen the distinction between "link" and "inference" as useful and only ever use the terms strong link/weak link/conjugate link
Strong link between a and b means : at least one must be true, or equivalently both cannot be false, and both may be true.
Weak link between a and b means : at most one can be true, and both may be false.
Conjugate link between a and b : exactly one of a and b is true is also very useful.
The fact that a conjugate link satisfies definitions of both strong link and weak link is irrelevant.
I regard anything else as superfluous.
On loop terminology, I don't see any need to think in terms of discontinuities or the nature of links at such a point or whatever.
If the solver spent some time learning some straightforward basics, he could dispense with all of that.

Examples :
a loop from cell C starts : "not a"/"a false"/"a=" (all of which are equivalent) and ends back at cell c with "a"/"a true"/"=a" (all of which are equivalent) :
no need to look at what links are hanging around the discontinuity : you just reason : the loop shows : if a is false, it is true, and clearly if it is true, it is true. Conclusion : a must be true.
a loop from cell C starts : "a"/"a true"/"a-" (all of which are equivalent) and ends back at cell c with "not a"/"a false"/"-a" (all of which are equivalent) :
then there is no need to look at what links are hanging around : you just reason : the loop shows : if a is true, it is false, and clearly if it is false, it is false. Conclusion : a must be false.
a loop from cell C starts : "not a"/"a false"/"a=" (all of which are equivalent) and ends back at cell c with "not b"/"b false"/"-b" (all of which are equivalent) :
no need to look at what links are hanging around the discontinuity : you just reason : the loop shows : if a is false, b is false and clearly if a is true, b is false. Conclusion : b must be false
and so on.

I'm sure no one will disagree...

[Luke]

Gee had a simple question. He was asking why the solving program saw two weak links when what he saw was a weak and a strong. I think the answer lies in the combination of terminology and concept, and both are important in reaching conclusions. I have no problem with the idea that it’s better to arrive at an understanding of the terminology from an understanding of the concepts, rather than the other way around. Speaking of concepts.....

Strong link between a and b means : at least one must be true, or equivalently both cannot be false, and both may be true.

aran, I’m curious about the last part there, “and both may be true.” I never noticed until now that “both cannot be false” leaves the door open to “both may be true.” I see you differentiate between a strong link and a conjugate link. Obviously conjugate candidates can’t both be false, so there must be a link of which I’m unaware that’s strong and yet not weak.

[Pat]

I've never seen the distinction between "link" and "inference" as useful

and only ever use the terms

• strong link
• weak link
• conjugate link

aran, you may wish to review this discussion --

The terms strong inference and weak inference were coined by Jeff precisely because the term strong link meant different things to different people. Personally, I've avoided the term strong link ever since.

[ronk]

Obviously conjugate candidates can’t both be false, so there must be a link of which I’m unaware that’s strong and yet not weak.

Any two candidate values of an ALS ... and two "extra" non-UR candidates of a UR are examples.

[Gee]

I want to thank everybody for their replies.

2-Fish r6b3\c47 fF 101\020 <> 8 [r2c4] Empty Rectangle

2-Fish r6b2\c47 fF 101\020 <> 8 [r3c7] Empty Rectangle

2-Fish r6c6\r3b5 fm 110\101 <> 8 [r3c7] 2-String Kite
2-Fish r6c6\c7b5 fm 110\011 <> 8 [r3c7] " " "

2-Fish r26\c47 Sk 200\020 <> 8 [r3c7] Skyscraper elim [box 3]
2-Fish r26\c48 Sk 200\020 <> 8 [r5c8] " " [box 6

I am confused with the above. take the first line which reads, "2-fish r6b3\c47"". I don't understand what the "b" represents in "r6b2". Can anybody help me with that? The solver I used was Scanraids and I wonder which solver daj95376 used and if it is more comprehensible than Scanraids.

I must admit I don't see the empty rectangle alluded to in the above.

many thanks.

[aran]

Speaking of concepts.....

Strong link between a and b means : at least one must be true, or equivalently both cannot be false, and both may be true.

aran, I’m curious about the last part there, “and both may be true.” I never noticed until now that “both cannot be false” leaves the door open to “both may be true.” I see you differentiate between a strong link and a conjugate link. Obviously conjugate candidates can’t both be false, so there must be a link of which I’m unaware that’s strong and yet not weak.

Strong link : "and both may be true" : this is a strictly logical statement of no practical use.
Obviously both could not be true if located in the same unit/constraint (ie : column, row, box, or indeed cell).
However if a chain starts in cell C and finishes in cell D, where C and D do not share a unit, then there is no logical reason why both might not be true ie for a chain xcellC=..........=xcellD (C, D in separate units) then both xs may be true.

When strong links lie within same unit, then in effect a strong link is a conjugate link (at least one is true/both can't be true=>exactly one is true). So those strong links could indeed be called conjugate links.
Nevertheless I prefer to refer them as strong links and tend to reserve "conjugate" for the one circumstance where it is a useful concept ie in nice loops where "weak links" are transformed into conjugates and acquire new powers.

[aran]

I've never seen the distinction between "link" and "inference" as useful

and only ever use the terms

• strong link
• weak link
• conjugate link

aran, you may wish to review this discussion --

The terms strong inference and weak inference were coined by Jeff precisely because the term strong link meant different things to different people. Personally, I've avoided the term strong link ever since.

Pat, thanks for the pointer.
I would say that I have taken a precisely opposite view and dismissed from my lexicon "strong/weak inference" (not that I ever employed the term).
I don't see any useful nuance which makes it important to keep both (inference/link).
I would go so far as to say that the artificial distinction kept alive is off-putting to many.

[Pat]

2-Fish r6b3\c47 fF 101\020 <> 8 [r2c4] Empty Rectangle
2-Fish r6b2\c47 fF 101\020 <> 8 [r3c7] Empty Rectangle

I am confused with the above. take the first line which reads, "2-fish r6b3\c47"". I don't understand what the "b" represents in "r6b2".

these are advanced types of fish

b = box

[ttt]

Strong link between a and b means : at least one must be true, or equivalently both cannot be false, and both may be true.

I never see: "strong link" that is both may be true...
Perhaps, you meant SIS (Strong I... Sets)

ttt