The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |3..|.1.|..5|
 |...|...|6..|
 |.65|7..|21.|
 |---+---+---|
 |...|16.|.5.|
 |.18|.3.|49.|
 |.5.|.87|...|
 |---+---+---|
 |.27|..8|54.|
 |..6|...|...|
 |4..|.2.|..7|
 *-----------*


Play/Print this puzzle online

[Leren]

Code: Select all

*----------------------------------*
| 3  4-9 d249   |a29 1 6  | 8  7 5 |
| 29 7    1     | 8  5 29 | 6  3 4 |
| 8  6    5     | 7  4 3  | 2  1 9 |
|---------------+---------+--------|
| 29 349  234-9 | 1  6 49 | 7  5 8 |
| 7  1    8     | 25 3 25 | 4  9 6 |
| 6  5   c49    |b49 8 7  | 3  2 1 |
|---------------+---------+--------|
| 1  2    7     | 6  9 8  | 5  4 3 |
| 5  39   6     | 34 7 14 | 19 8 2 |
| 4  8    3-9   | 35 2 15 | 19 6 7 |
*----------------------------------*

I think this is called an H4 Wing : (9=2) r1c4 = 9 r6c4 - (9=4) r6c3 - (24=9) r1c3 => - 9 r1c2, r49c3; stte

Leren

[Cenoman]

Code: Select all

 +---------------------+-----------------+-----------------+
 |  3    49    z24+9   |  29   1    6    |  8    7    5    |
 | c29   7      1      |  8    5   d29   |  6    3    4    |
 |  8    6      5      |  7    4    3    |  2    1    9    |
 +---------------------+-----------------+-----------------+
 | b29  a34+9 zA23+49  |  1    6   e49   |  7    5    8    |
 |  7    1      8      |  25   3    25   |  4    9    6    |
 |  6    5    Bg49     | f49   8    7    |  3    2    1    |
 +---------------------+-----------------+-----------------+
 |  1    2      7      |  6    9    8    |  5    4    3    |
 |  5    39     6      |  34   7    14   |  19   8    2    |
 |  4    8      3-9    |  35   2    15   |  19   6    7    |
 +---------------------+-----------------+-----------------+

BUG+4
(9)r4c2 - r4c1 = r2c1 - r2c6 = r4c6 - r6c4 = (9)r6c3
(4)r4c3 - (4=9)r6c3
(9)r14c3
=> -9 r9c3; ste

[Ngisa]

Code: Select all

+----------------------+-------------------+----------------+
| 3      49      a249  |b29      1     6   | 8      7     5 |
| 29     7        1    | 8       5     29  | 6      3     4 |
| 8      6        5    | 7       4     3   | 2      1     9 |
+----------------------+-------------------+----------------+
| 29    f349     g349-2| 1       6     249 | 7      5     8 |
| 7      1        8    |c25      3     25  | 4      9     6 |
| 6      5        49   | 49      8     7   | 3      2     1 |
+----------------------+-------------------+----------------+
| 1      2        7    | 6       9     8   | 5      4     3 |
| 5     e39       6    | 34      7     14  | 19     8     2 |
| 4      8       d39   |c35      2     15  | 19     6     7 |
+----------------------+-------------------+----------------+


(2)r1c3 = r1c4 - (2=53)r59c4 - (3)r9c3 = r8c2 - r4c2 = (3)r4c3 => - 2r4c3; stte

Clement

[SteveG48]

Code: Select all

 *-----------------------------------------------------------*
 | 3     49   c249   | 9-2   1     6     | 8     7     5     |
 | 9-2   7     1     | 8     5    a29    | 6     3     4     |
 | 8     6     5     | 7     4     3     | 2     1     9     |
 *-------------------+-------------------+-------------------|
 | 29    349   2349  | 1     6    a49    | 7     5     8     |
 | 7     1     8     | 25    3     25    | 4     9     6     |
 | 6     5    c49    | 49    8     7     | 3     2     1     |
 *-------------------+-------------------+-------------------|
 | 1     2     7     | 6     9     8     | 5     4     3     |
 | 5     39    6     | 34    7    a14    | 19    8     2     |
 | 4     8    b39    |b35    2    a15    | 19    6     7     |
 *-----------------------------------------------------------*


(2=1459)r2489c6 - (5=39)r9c34 - (9=24)r16c3 => -2 r1c4,r2c1 ; stte

[SpAce]

Code: Select all

.-------------------.------------.----------.
| 3   49   a(2)-49  | b29  1  6  | 8   7  5 |
| 29  7      1      |  8   5  29 | 6   3  4 |
| 8   6      5      |  7   4  3  | 2   1  9 |
:-------------------+------------+----------:
| 29  349    2349   |  1   6  49 | 7   5  8 |
| 7   1      8      | b25  3  25 | 4   9  6 |
| 6   5    c(4)9    |  49  8  7  | 3   2  1 |
:-------------------+------------+----------:
| 1   2      7      |  6   9  8  | 5   4  3 |
| 5   39     6      |  34  7  14 | 19  8  2 |
| 4   8     c3(9)   | b35  2  15 | 19  6  7 |
'-------------------'------------'----------'

(2)r1c3 = (253)r159c4 - (3=94)r96c3 => -49 r1c3; stte

...or:

Code: Select all

.-----------------------.-----------------.-------------.
| 3      49     2"-49   | 9"-2'  1  6     | 8      7  5 |
| 9"-2'  7      1       | 8      5  2"-9' | 6      3  4 |
| 8      6      5       | 7      4  3     | 2      1  9 |
:-----------------------+-----------------+-------------:
| 2"-9'  3"-49  4-2'3'9 | 1      6  9"-4' | 7      5  8 |
| 7      1      8       | 2"-5'  3  5"-2' | 4      9  6 |
| 6      5      9"-4'   | 4"-9'  8  7     | 3      2  1 |
:-----------------------+-----------------+-------------:
| 1      2      7       | 6      9  8     | 5      4  3 |
| 5      9"-3'  6       | 3"-4'  7  4"-1' | 1"-9'  8  2 |
| 4      8      3"-9'   | 5"-3'  2  1"-5' | 9"-1'  6  7 |
'-----------------------'-----------------'-------------'

3D Medusa (24 eliminations):

Trap eliminations: -49 r1c3,r4c2, -9 r4c3 (all see both parities): 5 elims
Wrap eliminations: all '-candidates (contradiction in r4c3: two '-candidates in one cell): 19 elims

[SpAce]

I think this is called an H4 Wing : (9=2) r1c4 = 9 r6c4 - (9=4) r6c3 - (24=9) r1c3 => - 9 r1c2, r49c3; stte

I see two H4-Wings in those cells, but I don't see how your chain depicts them or supports all of those eliminations. It also has a few syntax problems (two adjacent strong links, missing '|' and no link for 2 in the last node). If I understand your meaning correctly, it only supports the first elimination but in a complicated way:

(9)r1c4 = (2)r1c4&(9,4)r6c43 - (2|4=9)r1c3 => -9 r1c2

As an H4-Wing I'd write it like this (compressed):

(9)r1c4 = (9,4)r6c43 - (4=29)r1c34 => -9 r1c2

It doesn't solve the puzzle, but the other H4-Wing does:

(9)r6c3 = (92)r61c4 - (2=49)r16c3 => -9 r49c3; stte

I don't see how you could easily (*) combine them into one chain, nor is it necessary because the second one is enough. Perhaps I misunderstood something?

(*) Not so easily it's possible:

(9)r1c4&r6c3 = r6c4 - (9=24)r1c4,r6c3 - (2|4=9)r1c3 => -9 r1c2, r49c3; stte

[Leren]

My move was based on a fun pattern I learnt about years ago. It's difficult to explain by eureka notation, so I'll illustrate it by the following exemplar diagram.

Code: Select all

-c  -c *abc  |*ac  -c  -c  | -c  -c  -c
 .   .   -c  |  /   .   .  |  .   .   .
 .   .   -c  |  /   .   .  |  .   .   .
-------------+-------------+-----------
 .   .   -c  |  /   .   .  |  .   .   .
 .   .   -c  |  /   .   .  |  .   .   .
 \   \  *bc  | *c   \   \  |  \   \   \
-------------+-------------+-----------
 .   .   -c  |  /   .   .  |  .   .   .
 .   .   -c  |  /   .   .  |  .   .   .
 .   .   -c  |  /   .   .  |  .   .   .

There is always 4 cells on 3 digits in a rectangle, in a pattern similar to the one shown. I've called the elimination digit c and the support digits a & b.

If there is a Strong link on c in Column 3 (shown by the /s) then one of r1c34 is c and you can eliminate c from all cells that can see them.

If there is a Strong link on c in Row 6 (shown by the \s) then one of r16c3 is c and you can eliminate c from all cells that can see them.

For this puzzle both cases applied. Leren

[SpAce]

My move was based on a fun pattern I learnt about years ago.
...

Yes, it's an interesting pattern. Good of you to spot it here! Perhaps it should be called a Siamese/Dual H4-Wing?

[Leren]

StrmCkr described various Hybrid Wings here and I think one of them might have matched my pattern but I can't be sure.

In any case, in my solver I gave it the working title of an N Wing, that just being the most reasonable next available letter in the alphabet. If none of StrmCkr's Hybrid wings matches the pattern how about we make N wing the official title !

Leren

[SpAce]

StrmCkr described various Hybrid Wings here and I think one of them might have matched my pattern but I can't be sure.

I can't find such an exemplar, but I think it should be there -- as a special case of H4-Wing.

In any case, in my solver I gave it the working title of an N Wing, that just being the most reasonable next available letter in the alphabet. If none of StrmCkr's Hybrid wings matches the pattern how about we make N wing the official title !

If someone asks me, the answer is no, sorry I think there are enough letters and more than enough types already. In fact, I don't even like the H4-Wing being its own type (I think it's a subtype of H3), and I don't see the point in H1 (which is really L3-Wing) or H5 and H6 at all. That leaves just H2 and H3 as distinct H-Wing types for me, but I don't think even they belong together under the same letter. Personally I'd prefer a simple and consistent wing classification, where a "wing" means three (uncompressed) strong links, and the types of the strong links would determine the main wing-class (letter). It mostly works that way already, but not quite. That would give us six distinct wings:

1. V-V-V : XY-Wing
2. V-V-L : H3-Wing
3. V-L-V : W-Wing
4. V-L-L : M-Wing / H2-Wing
5. L-V-L : S-Wing
6. L-L-L : L-Wing; Types (1),2,3 (depending on the number of different digits)

V = (bi)value strong link (can be ALS)
L = (bi)local strong link (can be grouped or AHS)

If I could, I'd make the H3-Wing just H-Wing (it being the only V-V-L type), and remove the H2-Wing by making it a subtype of M-Wing (because both are V-L-L). That'd be a prettier and more easily memorized classification. Any special cases with grouped or ALS/AHS nodes can be easily handled without more types just by adding ALS/AHS and/or Grouped prefix in the name.

[Leren]

I think the term "Wing" just means pattern - some identifiable pattern that you "see" and can make eliminations without having to justify the underlying theorem each time you see it.

I think the first named "Wing" was the humble X Wing, which in your structure classification would be L-L. Also I think that combining H and M Wings would cut across arguably the most instructive post ever made, which you can see here, which gave a classification of every possible M Wing and also included M Rings for good measure. An amusing piece of history about that post was that it was deleted from this forum due to "lack of interest" and sometime later, following howls of protest, including from me, it was reinstated.

Regarding H Wings, I think the H1 Wing was just named for classification completeness, and was never meant to be used. I asked the question why H2 and H3 Wings have the numbers 2 and 3 and was told there was no real answer, they just picked the 2 and 3 arbitrarily.

Thus endeth the history lesson, Leren

[SpAce]

I think the term "Wing" just means pattern - some identifiable pattern that you "see" and can make eliminations without having to justify the underlying theorem each time you see it.

That's one way to look at it, but it's way too wide and ambiguous a definition for me. We already have a term for it too: "pattern". Why should "wing" be a one-to-one synonym for it? Would you call Skyscraper a wing? What about UR Type 1? Both are among the easiest patterns to see but I'd never call them wings. What about a JExocet? Or an SK-Loop? They're also clearly identifiable patterns that can be "seen" and have well-defined elimination rules, but I doubt anyone would call them wings. If someone did, the term would lose all meaning.

Personally I only accept as "wings" two kinds of patterns plus one exception. One group is the chains/loops of three strong links (i.e. the one-letter wings/rings), most clearly described here. The other group is the (UVW)XYZ-Wings which are specific types of ALS-XZ, and they're pretty clearly defined as well. XY-Wing is the only one that belongs to both groups. X-Wing belongs to neither group, and it's the only exception I accept. More on that below.

I think the first named "Wing" was the humble X Wing, which in your structure classification would be L-L.

Correct, which means that it doesn't fit into either of my accepted wing-groups. Then again, X-Wing is such a cool name that I'd never change that, especially since it came first and is so ubiquitous. Still, based on the more recent naming conventions, it's clearly a misnomer. If anything, it should be called X-Ring because it's a loop, but even that's a misfit because it only has two strong links. Another misnomer is XY-Ring which has four strong links (uncompressed), but that too I accept for historical reasons.

Also I think that combining H and M Wings would cut across arguably the most instructive post ever made, which you can see here, which gave a classification of every possible M Wing and also included M Rings for good measure.

While a good post, I can't see how it could be even close to "the most instructive post ever made". M-Wings and M-Rings (which are logically also S-Rings, btw) are just specific patterns of generic chaining/looping concepts which are much more important to understand. There's really no need to memorize all those pattern variants (or any patterns at all) if you know your chaining fundamentals. That's why I consider all pattern catalogs as "nice to know" kind of stuff, but not necessary at all.

If solving sudoku was about memorizing patterns I would have quit a long time ago, but fortunately it isn't. I was able to find and use M-Wings/Rings and other patterns as generic chains/loops much before I learned they had established names. I've only recently even learned their names -- not because it makes any difference for solving but because it's helpful for communication. Also, I bothered to learn those names only after I figured out the logic behind the naming; otherwise I still wouldn't care because I simply refuse to memorize arbitrary and useless things.

[rjamil]

Hi Leren,

I think this is called an H4 Wing : (9=2) r1c4 = 9 r6c4 - (9=4) r6c3 - (24=9) r1c3 => - 9 r1c2, r49c3; stte

I strongly think that it's Dual H6-Wing (just like Dual Empty Rectangle).

R. Jamil

[SpAce]

I think this is called an H4 Wing : (9=2) r1c4 = 9 r6c4 - (9=4) r6c3 - (24=9) r1c3 => - 9 r1c2, r49c3; stte

I strongly think that it's Dual H6-Wing (just like Dual Empty Rectangle).

I agree with "Dual" (like I said before) but it should be Dual H4-Wing. I don't see any reason for the existence of the H5 and H6 types as they're just generalized H4s, and some of the diagrams don't make sense anyway (seem to be over-specified with unnecessary strong links). Too many types just complicate a simple concept.