The New Sudoku Players' Forum

[SpAce]

No, i read that thread now, but i can't see a common point.

I think the common point is that both methods recognize that there must be at least one 3 in the pattern (which is one way to see the 3-eliminations). However, yours goes further by proving also the 4-eliminations, and I don't see how subset counting would do that directly. Nice logic!

[StrmCkr]

thanks even, missed another typo..

Code: Select all

+-----------------+---------+--------------+
| .     .      .  | .  .  . | .     .   .  |
| .     (123)  .  | .  .  . | (14)  -2  -2 |
| (34)  -2     -2 | .  .  . | (24)  .   .  |
+-----------------+---------+--------------+
| .     .      .  | .  .  . | .     .   .  |
| .     .      .  | .  .  . | .     .   .  |
| .     .      .  | .  .  . | .     .   .  |
+-----------------+---------+--------------+
| .     .      .  | .  .  . | .     .   .  |
| .     .      .  | .  .  . | .     .   .  |
| .     .      .  | .  .  . | .     .   .  |
+-----------------+---------+--------------+

rambling on a possible method to detect these:

the idea here is that 3 als can be linked by a Common restricted Digit, when that occurs a 4th als that contains a digit common to two end points and these digits are restricted to set D&C and D&A then the sets are set to be a locked set respective to the RC digits. }

Set A) [24] @ R3C7
Set B) [14] @ R2C7
Set C) [34] @R3C1
Set D) [123] @ R2C2

RC: AB(4),AC(4) DB(1), DC(3)
any Common digits in A & D are restricted to A or D
Since the placement of two different digits in D's turns B or C into locked sets both restricting A to a locked set by the same digit.
thus any non restricted common digit to D & A cannot exist out side of A&D

[tarek]

Any excuse really to let me throw in this link again!!! I still can't get my head round how I did it

I also had a go to show a double linked ALS-XY rule diagram too
http://forum.enjoysudoku.com/almost-locked-sets-als-for-beginners-t3403-15.html#p22822

[StrmCkr]

Tarek, als xy can go all the way up to. Triple linked lol

[SpAce]

tarek, StrmCkr, could you produce real examples (or even imagined ones) of those doubly and triply linked ALS-XY-Wings? I remember having a discussion about them with StrmCkr a while back, but I don't think I fully understood the logic. If I remember correctly, those examples back then could be seen as something simpler.

[tarek]

No real world examples with me at the moment

[rjamil]

Code: Select all

Almost Locked Set XY-Wing: A=r3c27 {234}, B=r23c2 {124}, C=r2c7 {13}, X,Y=1,3, Z=2,4 => r3c13<>2, r3c13<>4
+------------------+---------+----------------+
| .     .      .   | .  .  . | .     .      . |
| .     (124)  .   | .  .  . | (13)  .      . |
| (24)  -24    -24 | .  .  . | .     (234)  . |
+------------------+---------+----------------+
| .     .      .   | .  .  . | .     .      . |
| .     .      .   | .  .  . | .     .      . |
| .     .      .   | .  .  . | .     .      . |
+------------------+---------+----------------+
| .     .      .   | .  .  . | .     .      . |
| .     .      .   | .  .  . | .     .      . |
| .     .      .   | .  .  . | .     .      . |
+------------------+---------+----------------+

Code: Select all

 might actually break the mold.
+-----------------+---------+--------------+
| .     .      .  | .  .  . | .     .   .  |
| .     (123)  .  | .  .  . | (14)  -2  -2 |
| (34)  -2     -2 | .  .  . | (24)  .   .  |
+-----------------+---------+--------------+
| .     .      .  | .  .  . | .     .   .  |
| .     .      .  | .  .  . | .     .   .  |
| .     .      .  | .  .  . | .     .   .  |
+-----------------+---------+--------------+
| .     .      .  | .  .  . | .     .   .  |
| .     .      .  | .  .  . | .     .   .  |
| .     .      .  | .  .  . | .     .   .  |
+-----------------+---------+--------------+

Let me convert the clue digits in to variables as follows:

Code: Select all

  ---------------+---------------+---------------  ---------------+---------------+---------------
01) .   xyz   .  |  .    .    .  | -XZ  xz   -XZ 02) .   xyz   .  |  .    .    .  |  .   wy    .
    .    .    .  |  .    .    .  |  .    .    .      .    .    .  |  .    .    .  |  .    .    .
    .    .   wy  |  .    .    .  | wxz   .    .     -XZ  -XZ  xz  |  .    .    .  | wxz   .    .
  ---------------+---------------+---------------  ---------------+---------------+---------------

  ---------------+---------------+---------------
03) .   xyz   .  |  .    .    .  | -Z   wx   -Z
    .    .    .  |  .    .    .  |  .    .    .
   -Z   -Z   wy  |  .    .    .  | wz    .    .
  ---------------+---------------+---------------

  ---------------+---------------+---------------  ---------------+---------------+---------------
04) .   xyz   .  |  .    .    .  | -Z   wxz  -Z  05) .   xyz   .  |  .    .    .  |  .   wx    .
    .    .    .  |  .    .    .  |  .    .    .      .    .    .  |  .    .    .  |  .    .    .
    .    .   wy  |  .    .    .  | wz    .    .     -Z   -Z   wyz |  .    .    .  | wz    .    .
  ---------------+---------------+---------------  ---------------+---------------+---------------

I think, there are no more variations/forms/configurations of the above mentioned WXYZ-Wing patterns.

Removed unnecessary material.

Added: pattern 2.
Added as on 20200201: patterns 4 & 5.

R. Jamil

[StrmCkr]

I posted the only hand built copies of the double and triple link that I had, of course they should all hold smaller logic as you could consider any 2 of the three als as a double linked als xz...

I built them in my solver just to test the logic.
and the smaller logic usually removes them from the later step, (but if I skip the lesser logic the xy finds them with extra eliminations that happen after the als xz is performed)

Real word application is potential step compression.

http://forum.enjoysudoku.com/post269956.html#p269956 link for the post/article with the double and triple linked als-xy examples.

[StrmCkr]

Code: Select all

    +-----------------+---------+--------------+
    | .     .      .  | .  .  . | .     .   .  |
    | .     (123)  .  | .  .  . | (14)  -2  -2 |
    | (34)  -2     -2 | .  .  . | (24)  .   .  |
    +-----------------+---------+--------------+
    | .     .      .  | .  .  . | .     .   .  |
    | .     .      .  | .  .  . | .     .   .  |
    | .     .      .  | .  .  . | .     .   .  |
    +-----------------+---------+--------------+
    | .     .      .  | .  .  . | .     .   .  |
    | .     .      .  | .  .  . | .     .   .  |
    | .     .      .  | .  .  . | .     .   .  |
    +-----------------+---------+--------------+

AaLS - 2RC rule did produce the eliminations for this with out needing to go more complicated like my last post suggested.

Set a) [123] @ R2C2
Set b) [234] @ R3C17
Set C) [124] @ R23C7
X:3,Y:1
Z:2 => R2C89, R3C23 <> 2

to read
A & C is restricted by digit 1
A & B is restricted by digit 3
the non restricted common digit of sets abc {2} can be excluded from all cells that see those cells

2 ALS 2 restricted common rule
------------------------------
If A have degrees of freedom of 2
and B and C are ALS
with
x restricted common to A and B
y restricted common to A and C
and z common to A B C
then you cant have z in a cell that can see all the z candidates in A B C

Code: Select all

triple link example
+--------------------+------------------+-----------------+
| 9     27-4   8     | 1     57  4567   | 456  245   3    |
| (45)  1      (35)  | 3456  2   34567  | 9    8     67   |
| 6     (247)  (235) | 3459  8   3459-7 | 1    45-2  (27) |
+--------------------+------------------+-----------------+
| 3     24     25    | 58    9   1      | 7    6     48   |
| 7     6      9     | 358   4   358    | 2    15    18   |
| 45    8      1     | 7     6   2      | 345  345   9    |
+--------------------+------------------+-----------------+
| 8     39     7     | 246   1   46     | 346  2349  5    |
| 1     5      4     | 2689  3   689    | 68   7     26   |
| 2     39     6     | 458   57  4578   | 348  1349  14   |
+--------------------+------------------+-----------------+


Set A) [45] @ R2C1
set B) [247] @ R3C29
Set C) [235] @ R23C3
X:4, Y:5 Z:2,4,7
=>> R1C2 <> 4, R3C6 <> 6 , R4C8 <> 2

{A & B restricted by 4
A & C restricted by 5
B & C restricted by 2}

you might recognize the above more appropriately as a sue de coq

[SpAce]

AaLS - 2RC rule did produce the eliminations for this with out needing to go more complicated like my last post suggested.

Set a) [123] @ R2C2
Set b) [234] @ R3C17
Set C) [124] @ R23C7
X:3,Y:1
Z:2 => R2C89, R3C23 <> 2

So I actually got it right, here?

Code: Select all

AALS A: (123)r2c2
 ALS B: (124)r23c7
 ALS C: (234)r3c17

X=1, Y=3, Z=2

[StrmCkr]

So I actually got it right, here?

yup

[SpAce]

So I actually got it right, here?

yup

Lucky guesswork, then!

[eleven]

You're in love with sets and links, are you?
5 cells, 5 digits, each restricted to a unit. So each must be there.

[StrmCkr]

Simply put eleven N cells. With N digits. Subset counting works nicely.

[SpAce]

You're in love with sets and links, are you?

Which one of us? (I guess we both are to a degree.)

5 cells, 5 digits, each restricted to a unit. So each must be there.

You're talking about StrmCkr's "triple-linked" example? Yes, clear Rank 0 logic, of course. Also easy to express as a loop (direct translation):

(4=5)r2c1 - (5=3'2)r23c3 - (2=7'4)r3c92 - loop

...but also as:

(2=7)r3c9 - (7=345'2)b1p8469 - loop; (aka DL-ALS-XZ, Sue de Coq)

So, the ability to see it as a triply-linked ALS-XY-Wing seems more or less academic if it can be reduced to a doubly-linked ALS-XZ. In this case it's because both sets A and C are fully contained in box 1, so we can just as well see them as a single set. How about an example with three truly separated sets?

Here's a mock one:

Code: Select all

.---------------------------------.---------------------------------.---------------------------------.
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
| 123456789  123        123456789 | 123456789  123456789  123456789 | 123456789  16         123456789 |
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
:---------------------------------+---------------------------------+---------------------------------:
| 123456789  23         123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
:---------------------------------+---------------------------------+---------------------------------:
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  56         123456789 |
| 123456789  234        123456789 | 123456789  123456789  123456789 | 45         123456789  123456789 |
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
'---------------------------------'---------------------------------'---------------------------------'


Triply-Linked ALS-XY-Wing {A:(1234)r248c2, B:(456)b9p24, C:(16)r2c8; X:4, Y:6, Z:1}

(1=23'4)r248c2 -[4r8]- (4=5'6)b9p42 -[6c8]- (6=1)r2c8 -[1r2]- loop => -1 r2, -23 c2, -4 r8, -5 b9, -6c8

aka:

Alien 6-Fish (Rank 0): {248N2 27N8 8N7} \ {1r2 23c2 4r8 5b9 6c8}

Any real-world examples of such a beast?

Btw, a more logical (and considerably more wieldy) name for a triply-linked ALS-XY-Wing would of course be: ALS-XY-Ring -- since all other looping wings are called rings (except X-Wing).