The New Sudoku Players' Forum

[yzfwsf]

My solver has implemented a new technique called XYZ-Ring on Chinese forums.
I wonder if there have been similar discussions on our forum? The overall structure
of this technique is an XYZ-Wing with an additional Z strong chain, which causes Z
to appear at most once within XYZ-Wing, resulting in a Rank=0 structure.
If the Z in the overall structure can be completely covered by two houses, it is called
Complete XYZ-Ring. Otherwise, it is called Half XYZ-Ring. It is obvious that Complete XYZ-Ring
can also be replaced by ALS Continuous Loop

Code: Select all

,----------------,---------------------,---------------,
| 136  2      46 | 139    5     369    | 7    1349  8  |
| 5    #34    7  | 1239   239   8      | 134  6     49 |
| 136  8      9  | 4      367   367    | 5    13    2  |
:----------------+---------------------+---------------:
| 4    9      3  | 8      1     5      | 2    7     6  |
| 2    6      5  | 39     3479  3479   | 8    349   1  |
| 8    7      1  | 6      2349  2349   | 34   5     49 |
:----------------+---------------------+---------------:
| 7    1-45   8  | 259    2469  2469   | 146  124   3  |
| 9    1*3-4  46 | 7      8     2*346  | 146  124   5  |
| 36   #345   2  | #35    -346   1     | 9    8     7  |
'----------------'---------------------'---------------'

Complete XYZ-Ring: 345 in r9c2,r9c4,r2c2+3r8 => r78c2<>4, r9c5<>3

Code: Select all

,---------------,-------------------,-----------------,
| 136  2    *46 | 139   5     369   | 7     13*49  8  |
| 5    34   7   | 1239  239   8     | #14   6      49 |
| 136  8    9   | 4     367   367   | 5     13     2  |
:---------------+-------------------+-----------------:
| 4    9    3   | 8     1     5     | 2     7      6  |
| 2    6    5   | 39    3479  3479  | 8     49     1  |
| 8    7    1   | 6     249   249   | 3     5      49 |
:---------------+-------------------+-----------------:
| 7    15   8   | 259   2469  2469  | -146  124    3  |
| 9    13   #46 | 7     8     234-6 | #146  124    5  |
| 36   345  2   | 35    46    1     | 9     8      7  |
'---------------'-------------------'-----------------'

Half XYZ-Ring: 146 in r8c7,r8c3,r2c7+4r1 => r8c6<>6, r7c7<>1

Code: Select all

,--------------------,------------------,---------------,
| 9      2      4578 | 6     1457  147  | 158  3 18     |
| 56*78  1      5678 | 35    2     #37  | 568  4 9      |
| 3      456    456  | 8     145   9    | 7    2 16     |
:--------------------+------------------+---------------:
| 4      68     168  | 23    9     5    | 16   7 23     |
| 256*7  3      1567 | 124   467   467  | 9    8 1246   |
| 2-6*7  #67    9    | 1234  8     #367 | 14-6 5 1234-6 |
:--------------------+------------------+---------------:
| 1      478    478  | 9     3     48   | 2    6 5      |
| 568    9      3    | 45    456   2    | 48   1 7      |
| 568    4568   2    | 7     1456  1468 | 3    9 48     |
'--------------------'------------------'---------------'

Half XYZ-Ring: 367 in r6c6,r6c2,r2c6+7c1 => r6c179<>6

[eleven]

Nice pattern, AFAIK it has not been discussed in this form here.
However the strong link obviously forces the xyz cells to become a "remote triple", which was mentioned here for the first time (i believe, StrmCkr used the term for another pattern here).

[rjamil]

Hi yzfwsf,

If I am not wrong then your XYZ-Ring pattern seems to me as XYZ-Transport Ring patterns and discussed in detail in this thread.

However, your Half XYZ-Ring pattern may be similar to as XYZ-Transport patterns.

Need confirmation from StrmCkr for further/better understanding.

R. Jamil

[yzfwsf]

Hi: rjamil
I'm not sure if your discussion covers this pattern.
The following is the general form of Half XYZ-Ring:

Code: Select all

,----------------,---------------------,---------------,
| -x   xyz   -x  |  -x     -x     -x   |  -x  xz    -x |
|       -y       |                     |               |
|       -y       |                     |               |
:---------------- --------------------- ---------------:
|       -yz      |                     |               |
| z     z-y  z   |  \      \      \    |  \    z    \  |
|       yz       |                     |               |
:---------------- --------------------- ---------------:
|       -y       |                     |               |
|       -y       |                     |               |
|       -y       |                     |               |
'----------------'---------------------'---------------'

Well, I found that it is similar to the 61st type in the post you mentioned, but there seems to be an error in the elimination in that post.

Another form for Half Ring:

Code: Select all

,----------------,---------------------,---------------,
| -xyz xyz  -xyz | -x      -x     -x   | -x   xz    -x |
|  -y  -y    -yz |                     |               |
|  -y  -y     yz |                     |               |
:---------------- --------------------- ---------------:
|                |                     |               |
| \    \      z  |  \      \       \   | \    z    \   |
|                |                     |               |
:---------------- --------------------- ---------------:
|                |                     |               |
|                |                     |               |
|                |                     |               |
'----------------'---------------------'---------------'

[StrmCkr]

"Nice pattern, AFAIK it has not been discussed in this form here."

actually it has been discussed with very little attention, its under als-xz etc transport, and easily applies to any of the "b.a.r.n.s." XY,XYZ,WXYZ ETC Wings that are in the barns class.

the "complete rings" are part of the als - w wing/ring family where you can also account for the RCC to complete the Ring

i guess you missed that class type in your solver as I cross checked and yours doesn't pick it up.?

an als nodes for the linking digit could actually see the entirety of the strong link and still link to it.

Code: Select all

+-----------------+--------------------+---------------+
| 136  2       46 | 139   5     369    | 7    1349  8  |
| 5    (34)    7  | 1239  239   8      | 134  6     49 |
| 136  8       9  | 4     367   367    | 5    13    2  |
+-----------------+--------------------+---------------+
| 4    9       3  | 8     1     5      | 2    7     6  |
| 2    6       5  | 39    3479  3479   | 8    349   1  |
| 8    7       1  | 6     2349  2349   | 34   5     49 |
+-----------------+--------------------+---------------+
| 7    15-4    8  | 259   2469  2469   | 146  124   3  |
| 9    1-4(3)  46 | 7     8     246(3) | 146  124   5  |
| 36   (345)   2  | (35)  46-3  1      | 9    8     7  |
+-----------------+--------------------+---------------+

[yzfwsf]

Hi StrmCkr:
This pattern is different from ALS-W-Wing, especially for Half Ring, where Z-strong chains cannot affect XYZ cell.The code for ALS-W-Wing cannot find this structure.

[StrmCkr]

I have it in mine, and my als transport code also picks up the ring types,

Als+ DOF transport picks off the "half" xyz version

[yzfwsf]

Code: Select all

+-----------------+--------------------+---------------+
| 136  2       46 | 139   5     369    | 7    1349  8  |
| 5    (34)    7  | 1239  239   8      | 134  6     49 |
| 136  8       9  | 4     367   367    | 5    13    2  |
+-----------------+--------------------+---------------+
| 4    9       3  | 8     1     5      | 2    7     6  |
| 2    6       5  | 39    3479  3479   | 8    349   1  |
| 8    7       1  | 6     2349  2349   | 34   5     49 |
+-----------------+--------------------+---------------+
| 7    15-4    8  | 259   2469  2469   | 146  124   3  |
| 9    1-4(3)  46 | 7     8     246(3) | 146  124   5  |
| 36   (345)   2  | (35)  46-3  1      | 9    8     7  |
+-----------------+--------------------+---------------+

My code can find it:
Almost Locked Set W-Wing: A=r29c2-{345}, B=r9c4-{35}, connect by 3r8 ; 5 also in same House , so Rank0 logic => r7c2<>4 r8c2<>4 r9c5<>3
But this one is a complete XYZ-Wing, not a Half Ring.

[StrmCkr]

the Half Ring,

I've merely hinted at that als transport applies to further DOF & pretty much any thing that can be chained.
for that one

A) 367 AALS r6c6
b ) 67 r6c2
c) 37 r2c6
x: 3,6
BC connected to (7) R56c1 = r2c1
=> RCC are locked to sets.

i find this view point slightly easier to follow when trying to write out a chain as the "pivot" cell extra digit throws a wrench in chain writing as all the "7's" dont actually see the strong link only portions do.

I definitely did not post anything on als+Dof transport methods on here directly.

as the xyz etc transport pages pretty much had rja contributing and its very long winded and covered much, i'll have to comb over it again {added to the bottom}
see if i can hit a match on it, i am pretty sure not every variation is listed it should be complete but it is extensive and he soloed much of it.


as for discussions:
similar reasons as to why there is no real topics on ALS-Dof methods outside of death blossoms, sue de coqs: DDS or ADDS
complex and most wont do anything with them.

where is the ALS-DOF chains?
or like my last post on ALS rules for ALS-DOF linking the two header als DOF networks together to lock the sub networks for a unionized elim this ones pretty neat


I will say I am happy some one else is working with the obscure techniques advancement is always appreciated and the more you pack into yours the more ecstatic i become!

good job, to bad we do not have access to said site id love to look over it

edits: adding stuff.

Well, I found that it is similar to the 61st type in the post you mentioned, but there seems to be an error in the elimination in that post.

61 is a xy- ring transport, should look like this.

Code: Select all

+-----------------+------------+--------------+
| .    -2     .   | .   .   .  | .   -3    .  |
| -1   (12)   -1  | -1  -1  -1 | -1  (13)  -1 |
| .    -2     .   | .   .   .  | .   -3    .  |
+-----------------+------------+--------------+
| .    -2     .   | .   .   .  | .   -3    .  |
| .    -2     .   | .   .   .  | .   -3    .  |
| .    -2     .   | .   .   .  | .   -3    .  |
+-----------------+------------+--------------+
| (3)  -2(3)  (3) | .   .   .  | .   (3)   .  |
| -3   (23)   -3  | .   .   .  | .   -3    .  |
| -3   -23    -3  | .   .   .  | .   -3    .  |
+-----------------+------------+--------------+

the transport that closely matches is http://forum.enjoysudoku.com/post272251.html#p272251 type 54 under xyz - ring.

Code: Select all

+-----------------+-----------------+----------------+
| .    3-2    .   | .    .      .   | .    .     .   |
| -13  (123)  -13 | -13  -1(3)  -13 | -13  (13)  -13 |
| .    -2     .   | .    .      .   | .    .     .   |
+-----------------+-----------------+----------------+
| .    -2     .   | .    .      .   | .    .     .   |
| .    -2     .   | .    .      .   | .    .     .   |
| .    -2     .   | .    .      .   | .    .     .   |
+-----------------+-----------------+----------------+
| -3   (23)   -3  | -3   (3)    -3  | -3   -3    -3  |
| .    -2     .   | .    .      .   | .    .     .   |
| .    -2     .   | .    .      .   | .    .     .   |
+-----------------+-----------------+----------------+

the sub class that's omitted is swapping c8 into box 2, which extends the number of "3"s in the box
gives this:

Code: Select all

+---------------+------------------+------------+
| .   3-2    .  | .    (3)    .    | .   .   .  |
| -1  (123)  -1 | -13  -1(3)  (13) | -1  -1  -1 |
| .   -2     .  | .    (3)    .    | .   .   .  |
+---------------+------------------+------------+
| .   -2     .  | .    .      .    | .   .   .  |
| .   -2     .  | .    .      .    | .   .   .  |
| .   -2     .  | .    .      .    | .   .   .  |
+---------------+------------------+------------+
| .   (23)   .  | .    (3)    .    | .   .   .  |
| .   -2     .  | .    .      .    | .   .   .  |
| .   -2     .  | .    .      .    | .   .   .  |
+---------------+------------------+------------+

and there we go, the half ring.

"eleven, old days for sure... "remote triple" that discussion changed how Remote pairs worked and allowed the ERi constructions that under pinned to shine its worth."

[yzfwsf]

Hi StrmCkr:
xyz环 https://www.bilibili.com/read/cv14064799/

[StrmCkr]

Thanks, the als w wing dosent load on my version (I'm not running your last one as it's missing the language package and has some weird screen size changes that makes it harder for me to use so I rolled back to the previous build.

I'll have to check again maybe the copy past didn't work correctly.