The New Sudoku Players' Forum

[StrmCkr]

the argument/conditions seem to missed rjamil

the box formation as present {minimal er} to use my words
presents :

grouped interference between row & col {which i call ERI }
strong bi-local digits when viewed as a a box constraint.
note:
there is 2 eri locations in a minimal er row/col and col/row
and there is no eri cells active thus its a directional change row or col is true.

with a digit count >Minimal ER and then we have more stringent conditions attached to it
grouped interference between row & col {which i call ERI }
if the ERI Cell is
occupied - formation can only be a conditional weak structure ie R&C or R or C
empty - formation is a direction strong link between R or C

because of this distinction in formation a minimal ER
it has the ability to be classed as multiple different techniques based on which of the two link styles you are using: so really it comes down to personal preference which style of move set to use it with and both are correct.

most would use the minimal ER as the 2-string kite and very rarely as a skyscraper as the rows or cols used would land in the same band see below for what i mean

Code: Select all

|xxx /// xxx |
|xxx xxx xxx|
|xxx /// xxx |

its like evaluating this franken x-wing and realizing its also a 4x skyscraper with grouped nodes at all 4 points and also 4x finned x-wings

are you going to call it grouped skyscraper probably not but we could.

Code: Select all

|/x/ /// xxx |
|xxx xxx xxx|
|x// /// xxx |

Code: Select all

|/x/ /// /x/ |
|xxx xxx xxx|
|x// /// /x/ |

Code: Select all

|/x/ /// x// |
|xxx xxx xxx|
|x// /// /x/ |

Code: Select all

 this one should really show u the styles of links used clearly as it is 2 ER's but the rows  them selves are what cause the eliminations.
|/x/ /// xxx |
|/// xxx /x/|
|x// /// /x/ |

or how about the shashimi version

Code: Select all

|/xx /// xxx |
|xxx xxx xxx|
|xxx /// xxx |

[tarek]

I agree that we need to avoid ambiguity so I will refrain from using the term "Turbot" when we are discussing the grouped strong links in a box only without the added strong links.

For easiness in terminology:
(Simple) Strong link (in location using 1 value): is simply a conjugate pair
Grouped Strong link (in location using 1 value): when there are more than 2 candidates in the location.

In my opinion simpler techniques have to found 1st including box-line reductions and (Simple) Strong links before evaluating for a Grouped Strong link. This to me suggests that your minimal ER rjamil has to have 3 candidates (including at the intersection) to be called ER (but again this is a personal preference).

From a programming point of view:
There are 9 configurations of ER per box (based on the intersection cell). I refer to that cell as the "Heart cell". The remaining candidates in location occupy "Cross" cells and there is 1 set of "Cross" cells configuration per "Heart Cell". The empty cells occupy a "Rectangle" and there is 1 set of "Rectangle" cells per "Heart cell". The "Cross" is further divided into 2 "Blades" (Basically one is the mini-column and the other the mini-row). You need the "Rectangle" cells to be empty & each blade of the Cross cells to have at least 1 candidate to qualify as an "ER".

there are further 6 configurations for the grouped Strong link in a box that take into account 2 parallel mini-lines. 3 configurations are for mini-rows and the other 3 for mini-columns. The name for these final 6 groupings hasn't been formalized but they are not "ER"

Regarding naming the the 3 strong links patterns:
3-string Kite is when we get a mixture of Strong links in columns and rows (Yes my fault)
3 skyscrapers is when the strong links are parallel (again my fault)
3 (I have to be careful here) when there is a box strong link (I prefers others to be scalded for this)

tarek

[rjamil]

Hi SpAce, tarek and StrmCkr,

In my limited knowledge, if by replacing the last one's ERI cell with '/', the pattern will no longer be an ER and falls in to bilocal box wise strong link.

Well, it certainly is a "bilocal box-wise strong link" but it's also a minimal ER, as explained by StrmCkr here. Hodoku also counts it as an ER if you turn on the option "Allow ERs with two candidates" (and as far as I remember, that option is there because StrmCkr insisted). You don't have to trust me but I know you trust StrmCkr, so there should be no question about this. The minimal ER certainly functions like any other ER, except that it can act as two different ones. It's actually a double-hinge (*), in addition to being a hybrid linker, making it the most flexible ER of all.

(Btw, if you thought it couldn't be an ER without the ERI candidate, then you should have put an 'X' there instead of a dot, right?)

(*) I'm thinking, would it actually make more sense to call it "double-hinge" or "dual hinge" instead of "minimal hinge" like did in my diagrams? I know it definitely can't be called double-ER (or even less dual-ER) because they already mean something else.

Well, again find reference to my above mentioned quoted statement here as Exemplar 3 and 4. (I am accepting my old misinterpretation before pointing out by anyone else as usual.)

(Similarly, as far as checking ER patterns without either checking the ERI candidate or including the ERI cell is concern, see my test results here. "." means ERI cell is not included in ER pattern.) I request not to include the ERI cell in any ER pattern.

R. Jamil

[tarek]

Throwing another issue into the ER debate. With the strong link in a box where the link derives from 2 parallel mini-lines. You can argue that in there too there is an empty line pattern with up to six candidates mapped into 2 parallel mini-lines.

the reduced empty line (EL) pattern would have 1 of those mini lines restricted to 1 candidate (which resembles your reduced ER) and your minimal EL which is a conjugate pair (again your minimal ER appears here) …

The versatility of your reduced and minimal ER comes from the fact that they are also EL patterns. You may need to reduce your definition of ER pattern to " a set of 4-5 candidates in a block that can be mapped into 2 intersecting mini-lines" or "a set of 4-5 candidates in a block that can't be mapped into 2 parallel mini-lines only"

Code: Select all

+-------+
| X X . |
| X X . |
| / / / |
+-------+

I now have a name "The empty line" --- where are you Havard?

[rjamil]

Hi tarek and SpAce,

[Added as on 20191104] Below given pencilmark grid taken from tarek post:

Code: Select all

 +------------------+-------------+--------------------+
 | 9    1[3]   25   | 134  8  134 | 25     6      7    |
 | 8    (4)    [3]5 | 2    6  7   | [3]59  [3]59  (1)  |
 | 7    12[3]  6    | 13   5  9   | 8      4      2[3] |
 +------------------+-------------+--------------------+
 | 1    9      7    | 56   3  8   | 4      25     26   |
 | 36   5      4    | 7    9  2   | 1      8      [3]6 |
 | 236  2-3    8    | 456  1  45  | [3]57  [3]57  (9)  |
 +------------------+-------------+--------------------+
 | 23   7      9    | 8    4  13  | 6      123    5    |
 | 5    8      13   | 9    2  6   | 37     137    4    |
 | 4    6      123  | 135  7  135 | 239    139    8    |
 +------------------+-------------+--------------------+

My program detect three ERs with only one standard elimination as follows:
Grouped Empty Rectangle: ERI 3 @ b1r2c2 Link Column 9 between ERI 3 @ b3r2c9 and ERI 3 @ b6r6c9 => -3 @ r6c2; stte
(Here, grouped means an ER pattern is linked with two ER patterns.)
Imagine, if another ERI 3 @ b2r1c4 or ERI 3 @ b4r6c1 or ERI 3 @ b7r7c3 or ERI 3 @ b8r9c6 is/are added in to above technique, how much more eliminations may be possible?

However, I will let analyze all possibilities of reduced (and minimal as same) ER patterns' additional eliminations when used in various exemplars too.

R. Jamil

[SpAce]

Grouped Empty Rectangle: ERI 3 @ b1r2c2 Link Column 9 between ERI 3 @ b3r2c9 and ERI 3 @ b6r6c9 => -3 @ r6c2; stte
(Here, grouped means an ER pattern is linked with two ER patterns.)

So, you still insist on using the stupidest name there is, despite several requests to drop it -- in the middle of a discussion of grouped links and patterns (where grouped means something entirely different)? I pity any newbies who try to learn something from this discussion!

Do you understand that we're trying to find ways to get rid of the ambiguities plaguing the sudoku nomenclature? You're really not helping by once again bringing up the "Grouped Empty Rectangle" -- which is by far the most confusing name there is, especially in the context of this discussion. Don't you really understand what the huge problem with it is? I guess not, or you wouldn't be doing it.

Either way, I kind of warned you last time that I would eventually stop engaging in any discussions if you kept using it. I simply can't stand that term. It exemplifies everything that makes learning sudoku much harder than it should be.

[tarek]

rjamil,
At your Pencilmark position there are 5 different results possible using 3 strong links. Electronically I managed to count 11 different 3 strong link combinations that can achieve these different results. all of these 11 combinations will use at least 1 Grouped strong link of some description. I can only see another combination that achieves your exact result but with using a strong link in r5 instead of b6

[rjamil]

Hi SpAce,

Grouped Empty Rectangle: ERI 3 @ b1r2c2 Link Column 9 between ERI 3 @ b3r2c9 and ERI 3 @ b6r6c9 => -3 @ r6c2; stte
(Here, grouped means an ER pattern is linked with two ER patterns.)

So, you still insist on using the stupidest name there is, despite several requests to drop it -- in the middle of a discussion of grouped links and patterns (where grouped means something entirely different)? I pity any newbies who try to learn something from this discussion!

Do you understand that we're trying to find ways to get rid of the ambiguities plaguing the sudoku nomenclature? You're really not helping by once again bringing up the "Grouped Empty Rectangle" -- which is by far the most confusing name there is, especially in the context of this discussion. Don't you really understand what the huge problem with it is? I guess not, or you wouldn't be doing it.

Either way, I kind of warned you last time that I would eventually stop engaging in any discussions if you kept using it. I simply can't stand that term. It exemplifies everything that makes learning sudoku much harder than it should be.

I think, I have already regretted to do myself and accepted to change my wordings here.

If I missed any conclusion, presented by seniors/experts before, then accept my apology. I am unable to understand why you applying Marshall arts techniques, here and there, to me.

I am participating here because I am also go with what majority consensus finalize, but till then, continue using old nomenclatures, as I have not in a position and already apologize to do the same myself (alone).

Hope that you will continue remember me in your good book in future.

R. Jamil

[rjamil]

Hi tarek,

rjamil,
At your Pencilmark position there are 5 different results possible using 3 strong links. Electronically I managed to count 11 different 3 strong link combinations that can achieve these different results. all of these 11 combinations will use at least 1 Grouped strong link of some description. I can only see another combination that achieves your exact result but with using a strong link in r5 instead of b6

Thanks for sharing your findings.

Actually, I see Andrew Stuart wrote in Empty Rectangle techniques, "The solver normally returns just the first instance of an advanced strategy but in the case of Empty Rectangles it will return all instances."

R. Jamil

[tarek]

What Andrew Stuart chooses to do in his solver is up to him. Sukaku Explainer can apply all instances in a single step batch mode. This would guarantee the same outcome even if you are using an isomorphic version of the same puzzle and would eliminate the selection bias when confronted as with your pencilmark grid with 11 different ways to proceed. As some eliminations may influence an available pattern construction. Batch mode also eliminates this. This is possibly why Andrew Stuart decided to have all instances presented at once!

On a different matter here is an example with 2 different types of strong link groupings in a box:

Code: Select all

+-------------------+-------------------+-------------------+
| 6     9     5     | 237   1     278   | 2347  23478 2378  |
| 137   8     137   | 4    %237   9     | 6    %237   5     |
| 37    2     4     | 5     378   6     | 9     378   1     |
+-------------------+-------------------+-------------------+
| 13579 3456  1379  | 69   ^24578 ^24578| 2347  23478 23789 |
| 8     46    2     | 69    47    3     | 5     1     79    |
| 3579  345   379   | 1    ^24578 ^24578| 2347  6     23789 |
+-------------------+-------------------+-------------------+
| 2345  7     8     | 23    9     245   | 1    *235   6     |
| 2359  35    39    | 237   6     1     | 8    *2357  4     |
| 2345  1     6     | 8     23457 457-2 |*237   9    *237   |
+-------------------+-------------------+-------------------+
3 grouped strong links % ^ * r9c6<>2
Finned Franken Swordfish r2b59/c58b8 Fins r57c6, r9c79

[SpAce]

Hi rjamil,

I apologize if I'm sounding too harsh, but sometimes I get frustrated.

I think, I have already regretted to do myself and accepted to change my wordings here.

Thanks for that link. It provides some of the background for my frustration. To be honest, I also took a bit of an issue with this:

In that case, let's wait for an expert/senior opinion.

And now this again:

If I missed any conclusion, presented by seniors/experts before, then accept my apology.

So you still don't count me as a "senior/expert". That's an understandable position, considering my short time around, but it also represents a certain lack of judgment. Length of experience is not always an accurate way to estimate someone's skills and depth of understanding. The quality of one's arguments should be. Besides, my shorter experience makes me probably better at seeing problems that old-time veterans have become blind to.

I am unable to understand why you applying Marshall arts techniques, here and there, to me.

Sorry about that, but see above. I try not to take things personally, but sometimes it happens.

I am participating here because I am also go with what majority consensus finalize, but till then, continue using old nomenclatures, as I have not in a position and already apologize to do the same myself (alone).

I also wish to acquire a consensus, or at least a majority acceptance, because it's the only way anything can actually change. I just want to acquire the best possible consensus because I'm really bad at accepting and abiding by collective decisions that seem dumb to me. The majority is not always right, and neither are even "senior experts". The only thing that convinces me is a superior argument supported by facts and logic. I don't care at all who provides it.

Anyway, I'll try to argue one more time why the term "Grouped ER" should not be used. (If I remember correctly, I suggested some alternatives in that original discussion.)

The two most fundamental sudoku solving techniques are chaining and fishing. Both have well-established terminologies and notations. Everything else can be explained and replaced by those generalized bedrock techniques, including any ER pattern. That's why their chosen terms should have precedence over anything else. Any terms they use should be considered "reserved words" with no other competing meanings.

"Grouped" is one such word because it has a very clear meaning in chaining. Others are "strong", "weak", "link", etc. None of them should ever be overloaded to mean something else, or massive confusion is inevitable. Any already existing conflicting meanings should also be changed.

Now, I understand that it might sound a bit unfair, considering that those terms might have been used first with ERs, before chaining techniques and terms were fully developed. In other words, I'm not blaming StrmCkr or anyone else for that overlap. Nevertheless the overlap is detrimental and it should be removed. Those terms have now very different and widely accepted meanings, and pushing anything else only causes unnecessary confusion.

The only logical thing "Grouped ER" should mean is the opposite of "Minimal ER", i.e. a strong hinge with more than two candidates. For anyone not familiar with the peculiar ER terminology it's the only interpretation that makes sense or even comes to mind. Multiple interlinked ERs should clearly be called something else. For instance, I would call your example with the three ERs a Triple-ER. That's descriptive, more specific, and hard to confuse with anything else.

That's all. If you wish to disagree with any of that, I would like to see an actual counterargument that refutes what I just said.

Hope that you will continue remember me in your good book in future.

Don't worry, I will, and I hope you will the other way too. This is nothing personal. We just may have a rare opportunity to fix certain long-standing sources of confusion in the sudoku nomenclature. It's an issue close to my heart so I might take it a bit too seriously.

[SpAce]

Hi StrmCkr,

Just a couple of clarifications...

if the ERI Cell is
occupied - formation can only be a conditional weak structure ie R&C or R or C
empty - formation is a direction strong link between R or C

This is very confusing. In any normal use of an ER there's no functional difference at all whether the ERI cell is occupied or not. There's still a R or C strong link, just like without it. The only time the ERI cell occupancy matters is when the hinge is used as a weak link, but then it's not an ER at all (as far as I know, the term only applies to strong links). We've covered this before, and as far as I could tell, you accepted that as a fact.

most would use the minimal ER as the 2-string kite

No. When it's used as an ER, i.e. a strong hinge, it would be for a Turbot Crane or similar. When it's used for a 2-String Kite it acts as a weak hinge instead (which is possible with the minimal ER, because it's a strong-weak hinge, among other things), but then it's not an ER (as explained above).

and very rarely as a skyscraper as the rows or cols used would land in the same band see below for what i mean

"Rarely" should be "never" for any practical purposes (why would you when you can use simple pointing). Your examples are correct, but they're so theoretical that I'm not sure I see their point in this context.

[SpAce]

The versatility of your reduced and minimal ER comes from the fact that they are also EL patterns.

Exactly! That's what I meant with the "hybrid" linking possibility.

I now have a name "The empty line" --- where are you Havard?

Indeed! That's a perfectly logical partner to the "Empty Rectangle"! However, I thought you wanted to move away from the ER terminology...

What about the box-based weak links? The maximal pattern of a weak hinge has a single empty cell, and the maximal pattern of the weak [whatever corresponds with the EL] has none! How would you name those?

Code: Select all

+-------+
| / X X |
| X X X |  Grouped weak hinge : r1c23 - r23c1
| X X X |
+-------+

+-------+
| X X X | 
| X X X |  Grouped weak ???   : b1p123/456/789 - b1p123/456/789, b1p147/258/369 - b1p147/258/369
| X X X |
+-------+

An example of the latter:

Code: Select all

 1  1  1 | /   /   / | /   1-2  /
 1  1  1 | 1   1   1 | 1   1    1
 1  1  1 | /   12* / | /   2    /
 --------+-----------+-----------


Two different ways to get that elimination, the first one using the full weak link in box 1:

Grouped L2-Wing: (1)r1c8 = r1c123 - r3c123 = (1-2)r3c5 = (2)r3c8 => -2 r1c8

Grouped L2-Wing: (1)r1c8 = r2c789 - r2c456 = (1-2)r3c5 = (2)r3c8 => -2 r1c8

Notice that the latter uses the reduced ERs in b2 and b3, but not in the normal ER or even EL mode (cell-based weak links). Like I said, they're hybrids.

[SpAce]

Code: Select all

 +------------------+-------------+--------------------+
 | 9    1[3]   25   | 134  8  134 | 25     6      7    |
 | 8    (4)    [3]5 | 2    6  7   | [3]59  [3]59  (1)  |
 | 7    12[3]  6    | 13   5  9   | 8      4      2[3] |
 +------------------+-------------+--------------------+
 | 1    9      7    | 56   3  8   | 4      25     26   |
 | 36   5      4    | 7    9  2   | 1      8      [3]6 |
 | 236  2-3    8    | 456  1  45  | [3]57  [3]57  (9)  |
 +------------------+-------------+--------------------+
 | 23   7      9    | 8    4  13  | 6      123    5    |
 | 5    8      13   | 9    2  6   | 37     137    4    |
 | 4    6      123  | 135  7  135 | 239    139    8    |
 +------------------+-------------+--------------------+

My program detect three ERs with only one standard elimination as follows:
Grouped Triple Empty Rectangle: ERI 3 @ b1r2c2 Link Column 9 between ERI 3 @ b3r2c9 and ERI 3 @ b6r6c9 => -3 @ r6c2; stte

In other words:

Grouped L1-Wing: (3)r13c2 = r2c3 - r2c78 = r3c9 - r5c9 = (3)r6c78 => -3 r6c2
...or:
Mutant 3x4-Fish: (3)B136\r2c9[r6c2] => -3 r6c2

However, the third ER can and normally should be replaced with a simple bilocation strong link in r5:

Grouped L1-Wing: (3)r13c2 = r2c3 - r2c78 = r3c9 - r5c9 = (3)r5c1 => -3 r6c2
...or:
Mutant 3x4-Fish: (3)R5B13\r2c9[c2b4] => -3 r6c2

Btw, did you notice that those same hinges can be used weakly:

Code: Select all

.-----------------.-------------.-------------------.
| 9    b13    25  | 134  8  134 |  25    6      7   |
| 8     4    c35  | 2    6  7   | d359  d359    1   |
| 7    b123   6   | 13   5  9   |  8     4     e23  |
:-----------------+-------------+-------------------:
| 1     9     7   | 56   3  8   |  4     25     26  |
| 6-3   5     4   | 7    9  2   |  1     8    f(3)6 |
| 236  a2[3]  8   | 456  1  45  |  57-3  57-3   9   |
:-----------------+-------------+-------------------:
| 23    7     9   | 8    4  13  |  6     123    5   |
| 5     8     13  | 9    2  6   |  37    137    4   |
| 4     6     123 | 135  7  135 |  239   139    8   |
'-----------------'-------------'-------------------'

Grouped L1-Wing / Grouped 3-String Kite:

(3)r6c2 = r13c2 - r2c3 = r2c78 - r3c9 = (3)r5c9 => -3 r5c1,r6c78
...or:
Siamese Mutant 3x4-Fish: (3)R2C29\b13[r5b4|r6b6] => -3 r5c1,r6c78

Actually, I see Andrew Stuart wrote in Empty Rectangle techniques, "The solver normally returns just the first instance of an advanced strategy but in the case of Empty Rectangles it will return all instances."

That's an incredibly stupid and confusing practice. Makes no sense at all, especially with multiple digits.

[SpAce]

On a different matter here is an example with 2 different types of strong link groupings in a box:

Code: Select all

+-------------------+-------------------+-------------------+
| 6     9     5     | 237   1     278   | 2347  23478 2378  |
| 137   8     137   | 4    %237   9     | 6    %237   5     |
| 37    2     4     | 5     378   6     | 9     378   1     |
+-------------------+-------------------+-------------------+
| 13579 3456  1379  | 69   ^24578 ^24578| 2347  23478 23789 |
| 8     46    2     | 69    47    3     | 5     1     79    |
| 3579  345   379   | 1    ^24578 ^24578| 2347  6     23789 |
+-------------------+-------------------+-------------------+
| 2345  7     8     | 23    9     245   | 1    *235   6     |
| 2359  35    39    | 237   6     1     | 8    *2357  4     |
| 2345  1     6     | 8     23457 457-2 |*237   9    *237   |
+-------------------+-------------------+-------------------+
3 grouped strong links % ^ * r9c6<>2
Finned Franken Swordfish r2b59/c58b8 Fins r57c6, r9c79

Nice example!

In practice, I would rather use the two strong hinges in b3 and b9 and the grouped strong link in c4:

Code: Select all

.-------------------.-----------------------.------------------------.
| 6      9     5    |  e237  1        278   |  d2347  c23478  d2378  |
| 137    8     137  |   4    237      9     |   6     c237     5     |
| 37     2     4    |   5    378      6     |   9      378     1     |
:-------------------+-----------------------+------------------------:
| 13579  3456  1379 |   69   24578    24578 |   2347   23478   23789 |
| 8      46    2    |   69   47       3     |   5      1       79    |
| 3579   345   379  |   1    24578    24578 |   2347   6       23789 |
:-------------------+-----------------------+------------------------:
| 2345   7     8    | f(2)3   9       245   |   1     b235     6     |
| 2359   35    39   | f(2)37  6       1     |   8     b2357    4     |
| 2345   1     6    |   8     3457-2  457-2 | a[2]37   9     a[2]37  |
'-------------------'-----------------------'------------------------'

Grouped L1-Wing: (2)r9c79 = r78c8 - r12c8 = r1c79 - r1c4 = (2)r78c4 => -2 r9c56

Mutant 3x4-Fish: (2)C4B39\r1c8[r9b8] => -2 r9c56

--
Added. Hmm. Your fish seems interesting:

Finned Franken Swordfish r2b59/c58b8 Fins r46c6, r9c79

That's a neat trick to get only r9c6 like the chain (I'm assuming you're using so many fins for that reason), but did you notice that it's a headless fish (i.e. the body is a DP)? Isn't that against your own rules? I guess the normal variant would be:

Finned Franken Swordfish (2)R2B59\c568 f:r9c79 => -2 r9c56
...aka:
Franken 3x4-Fish: (2)R2B59\c8[c56r9] => -2 r9c56