The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |1..|8..|...|
 |.2.|.3.|...|
 |3.7|...|.46|
 |---+---+---|
 |...|..2|..4|
 |8.9|574|2.1|
 |4..|6..|...|
 |---+---+---|
 |91.|...|4.8|
 |...|.4.|.6.|
 |...|..1|..7|
 *-----------*


Play/Print this puzzle online

[Ngisa]

Code: Select all

+--------------------+--------------------+--------------------+
|  1     459    456  | 8      569    5679 | 3       579     2  |
|  56    2      568  | 4      3      5679 | 5789    1       59 |
|  3     589    7    | 1      2      59   | 589     4       6  |
+--------------------+--------------------+--------------------+
|  57    357    1    | 39     89     2    | 6       5789    4  |
|  8     6      9    | 5      7      4    | 2       3       1  |
|  4     357    2    | 6      1      389  | 579     5789    59 |
+--------------------+--------------------+--------------------+
|  9     1     b356  | 7      56     356  | 4       2       8  |
|  257   578    58   | 29     4      589  | 1       6       3  |
|da26    348  ca3468 | d23    8-6    1    | 59      59      7  |
+--------------------+--------------------+--------------------+


(6)r9c13 = (6-3)r7c3 = r9c3 - (3=26)r9c14 => - 6r9c5; stte

Clement

[SCLT]

Code: Select all

+------------------+------------------+------------------+
|  1    459  456   |  8    569  5679  |  3     579   2   |
|  56   2    568   |  4    3    5679  |  5789  1     59  |
|  3    589  7     |  1    2    59    |  589   4     6   |
+------------------+------------------+------------------+
|  57   357  1     |  3-9 d89   2     |  6     5789  4   |
|  8    6    9     |  5    7    4     |  2     3     1   |
|  4    357  2     |  6    1    389   |  579   5789  59  |
+------------------+------------------+------------------+
|  9    1    356   |  7    56   356   |  4     2     8   |
|  257  578  58    | a29   4   b589   |  1     6     3   |
|  26   48   3468  |  23  c68   1     |  59    59    7   |
+------------------+------------------+------------------+


M-Wing: 9r8c4 = (9-8)r8c6 = r9c5 - (8=9)r4c5 => -9r4c4 ; stte

[Cenoman]

Code: Select all

 +---------------------+--------------------+---------------------+
 |  1     459   456    |  8    569   5679   |  3      579    2    |
 |  56    2     568    |  4    3     5679   |  5789   1      59   |
 |  3     589   7      |  1    2     59     |  589    4      6    |
 +---------------------+--------------------+---------------------+
 |  57*  a357*  1      | b39   89    2      |  6      5789   4    |
 |  8     6     9      |  5    7     4      |  2      3      1    |
 |  4     357   2      |  6    1     389    |  579    5789   59   |
 +---------------------+--------------------+---------------------+
 |  9     1     356    |  7    56    356    |  4      2      8    |
 | A257* z578*  58     | c29   4    d59-8   |  1      6      3    |
 | B26    48    3468   |  23  B68    1      |  59     59     7    |
 +---------------------+--------------------+---------------------+

UR(57)r48c12 using internals
(3)r4c2 - (3=9)r4c4 - r8c4 = (9)r8c6
(2)r8c1 - (2=68)r9c15
(8)r8c2
=> -8 r8c6; ste

[SteveG48]

Code: Select all

 *-----------------------------------------------------------*
 | 1     459   456   | 8     569   5679  | 3     579   2     |
 | 56    2     568   | 4     3     5679  | 5789  1     59    |
 | 3     589   7     | 1     2     59    | 589   4     6     |
 *-------------------+-------------------+-------------------|
 | 57    357   1     |b39   b89    2     | 6     5789  4     |
 | 8     6     9     | 5     7     4     | 2     3     1     |
 | 4     357   2     | 6     1     389   | 579   5789  59    |
 *-------------------+-------------------+-------------------|
 | 9     1     356   | 7    a56   a356   | 4     2     8     |
 | 257   578   58    | 29    4     589   | 1     6     3     |
 | 26    48    3468  | 2-3  a68    1     | 59    59    7     |
 *-----------------------------------------------------------*


(3=568)b8p238 - (8=93)r4c45 => -3 r9c4 ; stte

[rjamil]

Hi SCLT,

M-Wing: 9r8c4 = (9-8)r8c6 = r9c5 - (8=9)r4c5 => -9r4c4 ; stte

I am having difficulty identifying your M-Wing OTP solution.

In your OTP solution, bivalue cell should be 29r8c4. As per StrmCkr beautiful and straightforward explanation mentioned here, what I learned about M-Wings and M-Rings is that, each strong link must use separate digit from bivalue. But, I don't see the rule applied in your solution. (Maybe, it is due to my limited knowledge about M-Wings and M-Rings.)

Will you please point me the exact type of M-Wing (from Type 1 to 7, A and B) that you apply in your post. Or, is there any other types available that are not mentioned in this post?

R. Jamil

[SpAce]

Hi rjamil,

SCLT's solution is clearly an M-Wing, having one bivalue and two bilocal strong links with two digits, i.e. this pattern (reversed):

M-Wing: (a=b) - b = (b-a) = a => -a (any cell that sees both start and end cell)

Btw, H2-Wing has the same link structure but it uses three digits instead of two and has a different elimination logic:

H2-Wing: (a=b) - b = (b-c) = c => -c (start cell), -a (end cell)

Your question exemplifies the problem I have with the catalogs of zillion types and subtypes of various patterns. If you rely on them without understanding the underlying rule that unifies them all, you'll miss qualifying patterns that aren't listed, and it's a totally unnecessary strain on memory anyway. I don't know or care if SCLT's pattern is listed or not because I don't even want to look at such lists. Nevertheless I do know without doubt that it's an M-Wing.

IMHO, the best single post about various wing types is this. If you understand that, it's all you need to know to be able to identify any wing type correctly, including their grouped extensions etc. It's really that simple.

[rjamil]

Hi SpAce,

Let me conclude your stridulous reply that there are more patterns of M-Wings and M-Rings formed in terms of digit placement. However, I still can't see any other than the cell placement formations mentioned in given links. However, they are overlapping with some other moves.

Please note that I am always open to learning new things within my limited capacity. Currently, I can only understand what is available in patterns/exemplars form and can't digest eureka notations.

Let me apply the rules as what I imagined in SCLT solution as follows:

- start with bivalue cell 29r8c4;
- first strong link 9r8c46 in either b8 or r8; (wrong)
- secondfirst strong link 8r8c6,r9c5; is it strong link or weak link?
- thirdsecond strong link 8r94c5;
- 9 may be excluded from cell that sees both endpoints 9r8c4,r4c5 => -9r4c4. (But, 9 may also be excluded from r56c4,r78c5 if exist.)

R. Jamil

[SCLT]

Let me apply the rules as what I imagined in SCLT solution as follows:

- start with bivalue cell 29r8c4;
- first strong link 8r8c6,r9c5; is it strong link or weak link?
- second strong link 8r94c5;
- 9 may be excluded from cell that sees both endpoints 9r8c4,r4c5 => -9r4c4. (But, 9 may also be excluded from r56c4,r78c5 if exist.)

I'm afraid this is not remotely correct, even with your corrections included.

The two strong links are 9r8c4 = 9r8c6 and 8r8c6 = 8r9c5. These have a cell in common (r8c6), which is crucial for an M-Wing. In addition, there is a bivalue cell 89r4c5 which can see the "loose" end r9c5 of the strong link on 8's. That completes the pattern. The result is that 9 can be eliminated from any cell in sight of both the bivalue cell and the "loose" end (r8c4) of the strong link on 9's.

[SpAce]

Please note that I am always open to learning new things within my limited capacity. Currently, I can only understand what is available in patterns/exemplars form and can't digest eureka notations.

I understand that, but as before, I would highly recommend learning it. Don't you agree that it's much more efficient to describe every possible M-Wing pattern with that short line I wrote? Eureka is really not that hard, and learning it would multiply your skills immediately.

Let me apply the rules as what I imagined in SCLT solution as follows:

- start with bivalue cell 29r8c4;

Yes, that cell is one of the two start/end points of the pattern. If read from left to right, it can be considered the start cell because SCLT chose to write it that way, but it makes no difference, because every AIC can be read either way. Perhaps the more conventional way to write an M-Wing chain is to start with the cell that has to be bivalue in the pattern (in this case 89r4c5), but it really doesn't matter at all. In other words, these two are equivalent chains:

(a=b) - b = (b-a) = a

a = (a-b) = b - (b=a)

The latter orientation corresponds with SCLT's chain, where a=9 and b=8. In that orientation 9r8c4 is the start node, and it's totally inconsequential that it happens to be in a bivalue cell. That, or the candidate 2 in that cell, play no part in this M-Wing pattern. That cell could have any number of candidates. The only thing that matters is the 9 and its bilocation strong link with 9r8c6.

- first strong link 9r8c46 in either b8 or r8; (wrong)

Not wrong. That is indeed the first (bilocation) strong link:

a = (a-b) = b - (b=a)

After that we have the first weak link (9-8) in cell r8c6:

a = (a-b) = b - (b=a)

- secondfirst strong link 8r8c6,r9c5; is it strong link or weak link?

Not first but second (bilocation) strong link (i.e. your first version was correct):

a = (a-b) = b - (b=a)

- thirdsecond strong link 8r94c5;

No. That is the second weak link, or more accurately, weak inference (the link itself happens to be strong too, but it's used as a weak inference -- a subtle point that confuses many). Remember that "AIC" is Alternating Inference Chain. It means that strong and weak inferences must alternate. It (usually) starts and ends with a strong inference, but between them all the other inferences alternate. There can never be two adjacent strong or weak inferences in the chain. Native strong links can always be used for weak inferences as well (but not vice versa).

a = (a-b) = b - (b=a)

The last link is again strong, but this time it's a bivalue strong link, i.e. cell 89r4c5:

a = (a-b) = b - (b=a)

- 9 may be excluded from cell that sees both endpoints 9r8c4,r4c5 => -9r4c4. (But, 9 may also be excluded from r56c4,r78c5 if exist.)

Exactly. The chain proves that at least one of the end points must hold 9, or in the generic form 'a'.

[SpAce]

The two strong links are 9r8c4 = 9r8c6 and 8r8c6 = 8r9c5. These have a cell in common (r8c6), which is crucial for an M-Wing. In addition, there is a bivalue cell 89r4c5 which can see the "loose" end r9c5 of the strong link on 8's.

That's a bit misleading. All one-letter wings have exactly three strong links which can be either bilocation or bivalue types. The wing type depends on how many of each link types there are and in which order and how many digits are used. I think it's very confusing for AIC beginners if only bilocation links are called strong links. Bivalue cells are strong links as well, and there's no difference whatsoever.

The M-Wing strong-link configuration is VLL (V=biValue, L=biLocation), which is the same for H2-Wing (the difference is the number of digits). Thinking in those terms it's very easy to remember and describe each wing because there can be only six distinct configurations:

Code: Select all

VVV : Y-Wing
VVL : H3-Wing
VLV : W-Wing
VLL : M-Wing/Ring (2 digits) / H2-Wing (3 digits)
LVL : S-Wing/Ring (S-Ring <-> M-Ring)
LLL : L-Wings ((L1), L2, L3)

Those configurations are also valid for extensions, where L can be a bilocation group link or an AHS, and V can be an ALS. For example, ALS-XY-Wing has the same VVV configuration as Y-Wing, but each V is an ALS node (of course, bivalue is an ALS too, so Y-Wing is actually a special case of ALS-XY-Wing).

[rjamil]

Hi SCLT and SpAce,

Yes, that cell is one of the two start/end points of the pattern. If read from left to right, it can be considered the start cell because SCLT chose to write it that way, but it makes no difference, because every AIC can be read either way. Perhaps the more conventional way to write an M-Wing chain is to start with the cell that has to be bivalue in the pattern (in this case 89r4c5), but it really doesn't matter at all.

Well, if the start bivalue cell is 89r4c5, i/o 29r8c4, then it falls under M-Wing Type 2C (but with simultaneously a transposed Type 2A and a Type 2B):

Code: Select all

Type 2C:                             Or:
 .  .  .  | .  .  .  | .  .  .       -b  .  .  | .  .  .  | .  .  .
 . ab  .  | .  . -b  | .  .  .       -b ab  .  | .  .  .  | .  .  .
 .  .  .  | .  .  .  | .  .  .       -b  .  .  | .  .  .  | .  .  .
----------+----------+---------      ----------+----------+---------
 .  .  .  | /  /  /  | .  .  .        / /-b /  | .  .  .  | .  .  .
 /  a  /  | / ab+ /  | /  /  /        b  / ab+ | /  /  /  | /  /  /
 . -b  .  | /  /  b  | .  .  .        / a-b /  | .  .  .  | .  .  .
----------+----------+---------      ----------+----------+---------
 .  .  .  | .  .  .  | .  .  .        .  .  .  | .  .  .  | .  .  .
 .  .  .  | .  .  .  | .  .  .        .  .  .  | .  .  .  | .  .  .
 .  .  .  | .  .  .  | .  .  .        .  .  .  | .  .  .  | .  .  .

R. Jamil

[SpAce]

Well, if the start bivalue cell is 89r4c5, i/o 29r8c4, then it falls under M-Wing Type 2C (but with simultaneously a transposed Type 2A and a Type 2B):

So, your real problem with identifying the M-Wing was that it was written "backwards"? Well, now you know that it's still the same pattern because every AIC is bidirectional. Out of the six possible three-strong-link configurations only two even have this "problem" because they're asymmetrical: VVL <-> LVV (H3-Wing) and VLL <-> LLV (M-Wing / H2-Wing). That also explains why we only have six and not eight (2^3) distinct configurations. All the others are symmetrical so their links look the same no matter how you write or read them.

[rjamil]

Hi SpAce,

So, your real problem with identifying the M-Wing was that it was written "backwards"? Well, now you know that it's still the same pattern because every AIC is bidirectional. Out of the six possible three-strong-link configurations only two even have this "problem" because they're asymmetrical: VVL <-> LVV (H3-Wing) and VLL <-> LLV (M-Wing / H2-Wing). That also explains why we only have six and not eight (2^3) distinct configurations. All the others are symmetrical so their links look the same no matter how you write or read them.

Well, actually I have an impression about eureka notations is that it may only be used for advanced techniques.

Since I am in learning stage and focus on human style techniques therefore avoiding eureka notations is natural reaction.

R. Jamil

[SpAce]

Well, actually I have an impression about eureka notations is that it may only be used for advanced techniques.

Your impression is completely misguided.

Since I am in learning stage and focus on human style techniques therefore avoiding eureka notations is natural reaction.

I guess that makes me and a lot of other players non-human, then. As far as I know, you don't do any manual solving yourself, so what makes you think you have any idea what "human style techniques" actually are? Do you think WXYZ-Wing is a human style technique? M-Wing? H-Wings? S-Wing? L-Wings? Do you think most human players easily spot them with a naked eye or look for them specifically, just because they happen to be named patterns?

I can tell you right now that I've almost never spotted any of them directly (except in p&p solving where I have better visual cues) nor looked for them specifically. Yet I've found plenty of them and presented them as such (after learning their names), but I also find much longer unnamed chains with the same exact process. Most of the time those named patterns aren't any easier to find manually despite being simpler in principle. The process that reveals both kinds is exactly the same, at least for me, which makes pretty much all chains equally "human style techniques", regardless of their length and (to some degree) complexity. Chains of any length are actually very easy to find for a human player if you just have a proper technique (like coloring) for that. And when you do, then it makes no difference if the chain is a short wing or something way longer and more complicated. The logic is exactly the same, and both kinds are best expressed in Eureka.

Only a few small patterns are relatively easy to spot directly (such as Remote Pair, X-Wing and other Turbot Fishes, Y-Wing, XYZ-Wing, W-Wing, and especially various DPs), and I may look for those first before attempting more generic and effective methods. However, to look for something like an M-Wing specifically makes zero sense to me, because it doesn't really have easily spottable tell-tale signs with the mediocre filtering capability of Hodoku, for example (in p&p I'd be much more likely to spot one, however). It would be mostly a wasted effort. It's much more efficient to use a generic method that finds any chain, including those short wings if they happen to be available.

Of course I can only speak for myself, but somehow I bet the process is not all that different for most human players capable of solving non-basic puzzles. If I'm correct about that, it pretty much breaks your apparent idea of "human style techniques". As far as I'm concerned, the easiest and the most effective human style technique for puzzles in the semi-advanced SE 6.0-8.9 range is coloring, not pattern spotting, and its results are best expressed with Eureka. On the other hand, pattern spotting works well for easier puzzles, and harder puzzles pretty much require some form of it (with much harder patterns). Most of the named mid-range patterns you're concentrating on aren't any more or less human style techniques than longer chains, as far as I'm concerned.