The New Sudoku Players' Forum

[tarek]

I'm hoping that this would be the last of the terminology sessions.

I came to the conclusion that the term Empty rectangle must only be used to describe a Single grouped strong link in a box where the inference of the strong link is derived from a mini-column and mini-row within that box.

We shouldn't therefore use "Empty rectangle" to describe a pattern of 2 strong links (one in a line and the other a grouped strong link in box). The term should be used to simplify the description of that Grouped strong link when used within a pattern (e.g. W-wing using an empty rectangle) (e.g. 2 strong links pattern using an empty rectangle)

the following is an attempt to categorize these Grouped strong links in location with a view to simplify description and reduce current confusion about terminology:

Code: Select all

Empty mini-Area (EmA):
======================

1. Empty mini-Rectangle (EmR):
------------------------------

+---------+
| .  X (X)|
| X  /  / |
|(X) /  / |
+---------+
Commonly referred to as Empty Rectangle(ER)


2. Empty mini-Line (EmL):
-------------------------

These have 4 varieties

a. in a Line (rows)
+-------+------+-------+
|X(X) . |X . . | / / / |
|. .  . |. . . | . . . |
|. .  . |. . . | . . . |
+-------+------+-------+

b. in a Line (columns)
+-------+
| X . . |
|(X). . |
| . . . |
+-------+
| X . . |
| . . . |
| . . . |
+-------+
| / . . |
| / . . |
| / . . |
+-------+

c. in a box (mini-rows)
+--------+
| X(X)(X)|
| X(X) . |
| / /  / |
+--------+

d. in a box (mini-columns)
+-------+
| X  X /|
|(X)(X)/|
|(X) . /|
+-------+

The exemplars above are what defines each category when all parenthesized candidates are present (regardless on how the dotted cells are filled). Any reduction in the number of candidates within parenthesis with how the dotted cells are filled can lead to equivalence between some of these categories and may lead to a simple strong link in location (conjugate pair) when reduced to 2 candidate exemplar.

[Edit: corrected an error in exemplar]
[Edit2: Adjusted the wording of last paragraph]
[Edit3: Adjusted EmL 3 4 exemplar due to equivalence in some cases]

[tarek]

SpAce,
I haven't gone as far as looking to the weak links yet

StrmCkr,
Thanks … yes I agree but he decided to show all available Empty rectangles at once in his solver.

rjamil,
Thanks for the clarification. I'm also aware of that stupid typo I still make with the "/" on this keyboard I'm using

[StrmCkr]

http://forum.enjoysudoku.com/strong-links-weaklinks-t34655.html
here you go, all the "empty" mini line formations

[tarek]

http://forum.enjoysudoku.com/strong-links-weaklinks-t34655.html
here you go, all the "empty" mini line formations

Thanks,
Have you described or came across what I described above as EmL types c or d where the inference of a strong link is derived from 2 parallel mini lines in a box?

Code: Select all

+----------------------+----------------------+----------------------+
| 5689   59     569    | 1      2      3      |*589    7      4      |
| 1789   4      12379  | 89     5      789    |*12389  6     *389    |
| 15789  123579 1359   | 46     789    46     |*13589  12    *3589   |
+----------------------+----------------------+----------------------+
| 2      159    1589   | 356    389    1568-9 | 4      389    7      |
| 3      6      17     |^89     4      17     |^89     5      2      |
| 4      579    5789   | 2      3789   578-9  | 6      389    1      |
+----------------------+----------------------+----------------------+
| 15679  123579 135679 | 345    389    4589   | 17     12     3569   |
| 17     8      127    | 35     6     %59     | 127    4     %359    |
| 569    359    4      | 7      1      2      | 3589   89     35689  |
+----------------------+----------------------+----------------------+
3-Turbot Crane (using 1 grouped strong link)
9:* ^ % r46c6<>9
b3 has an EmL type c/d
b1r58\c79b5 fin r8c6 r46c6<>9

+-------------------+-------------------+-------------------+
| 268   7     249   | 1248  28    5     | 369   36    139   |
| 3     5     29    | 127   79    26    | 4     68    189   |
| 689   469   1     | 489   3     46    | 2     7     5     |
+-------------------+-------------------+-------------------+
| 7     1     359   | 23458 28   %234   |*39   *2348  6     |
| 269   269-3 8     | 234   1     7     | 5    *234  *239   |
| 4     23    235   | 2358  6     9     | 7     1     28    |
+-------------------+-------------------+-------------------+
| 259   8     7     | 239   4     1     | 36    2356  23    |
| 259  ^239   6     | 237   79    8     | 1     235   4     |
| 1    ^234  ^234   | 6     5    %23    | 8     9     7     |
+-------------------+-------------------+-------------------+
3-Turbot Crane (using 2 grouped strong links)
3:* ^ % r5c2<>3
b5 has an EmL type c/d
c6b67\r49b4 fins r5c89, r8c2

There are often Grouped Strong links in a line (Type a/b) that complement them unless the value is uncovered and placed in the complimentary line.

tarek

[tarek]

one reason why you may use these EmL c/d when there is actually a complementary EmL a/b is to avoid base sector intersection (i.e. creating an endofin). Despite the logic still holding, it may further complicate what should be an easier to spot technique. I have decided in the Sukaku explainer to prevent base sector overlap and this will deliver more EmL type c/d or miss some pattern eliminations. These would hopefully get picked up with the generalised technique solver or a complex fish catcher.

Tarek

[StrmCkr]

Yes i have actually alot since i program using mini sectors for rows, cols and again for row/col defined by box.
Which is 4x3x27 mini sectors
comes up with equivalent moves for m, s, l, w, h, wings when i implmented the box version.
a few confirmed versions are found in the m wing thread

[tarek]

Yes i have actually alot since i program using mini sectors for rows, cols and again for row/col defined by box.
Which is 4x3x27 mini sectors

Thanks

[tarek]

In Sukaku explainer the finalized L1 pattern names will be (X is the number of strong links):
X Skyscrapers: Parallel strong links in lines
X-String Kite: Mixed Line type Strong links (No boxes)
X Turbot Blocks: Only boxes strong links (No lines). "Block" is the word used by SE to describe "Box"
X-Turbot Crane: Box and Line mixture
Added in parenthesis would be the number of Grouped strong links if used

I hope that this is fair and would put an end to some the confusion about technique names. In the technique explanation I do mention that it is part of x-chains which is then part of AIC and mentioned that the popular name of "empty rectangle" is used to describe a type of grouped strong link in a box (EmR)

I did mention that I'll avoid (at this time) Strong link intersections in Sukaku Explainer to avoid the "endofin" just because to my eyes it complicates an otherwise a "simpler to spot technique"

[StrmCkr]

Based on empirical tests, Types D1 and D2 below are equivalent:

Code: Select all

 
-b  .  a |  .  .  . |  .  .  .       -b  .  . |  .  .  . |  .  .  .
-b ab  a |  .  .  . |  .  .  .       -b ab  . |  .  .  . |  .  .  .
-b  .  a |  .  .  . |  .  .  .       -b  .  . |  .  .  . |  .  .  .
---------+----------+----------      ---------+----------+----------
 . -b  a |  .  .  . |  .  .  .        . -b  . |  .  .  . |  .  .  .
ab -b  a |  .  .  . |  .  .  .       ab -b  . |  .  .  . |  .  .  .
 . -b  a |  .  .  . |  .  .  .        . -b  . |  .  .  . |  .  .  .
---------+----------+----------      ---------+----------+----------
 .  .  / |  .  .  . |  .  .  .        a  a  / |  .  .  . |  .  .  .
 .  .  / |  .  .  . |  .  .  .        a  a  / |  .  .  . |  .  .  .
 .  .  / |  .  .  . |  .  .  .        a  a  / |  .  .  . |  .  .  .
 Type D1:                             Type D2:

Found the thread with a clearer example. {w-wings}

Here is a technique set ive never seen used as its an inverted als works off the empty line intersections
http://sudopedia.enjoysudoku.com/Almost_Locked_Candidates.html

in simplicity terms it is a hidden als

[SpAce]

Based on empirical tests, Types D1 and D2 below are equivalent:

They're Grouped W-Wings:

(b=a)r2c2 - r123c3 = r456c3 - (a=b)r5c1 => -b r123c1,r456c2

(b=a)r2c2 - r789c2 = r789c1 - (a=b)r5c1 => -b r123c1,r456c2

Found the thread with a clearer example.

...of a completely different pattern! A much more interesting one, though, so thanks for that.

Here is a technique set ive never seen used as its an inverted als works off the empty line intersections
http://sudopedia.enjoysudoku.com/Almost_Locked_Candidates.html

The first example is a Grouped M2-Ring, just reusing some cells:

(x=y)r2c1 - r1c123 = (y-x)r1c4 = (x)r1c123 - loop => -xy b1p56789, -(~(xy)) r1c4

The same eliminations are available through a Sue de Coq / Doubly-Linked ALS-XZ. The above loop seems kind of like its hidden counterpart. I'm actually betting that a similar pattern always exists when a Sue de Coq is around. (Or rather, I'm sure of it.)

I don't know what to call the second example (a complex M2-Ring?), but it's a similar loop anyway:

(x=yz)r2c12 - (y|z)r1c123 = (yz-x)r1c45 = (x)r1c123 - loop => -xyz b1p6789, -(~(xyz)) r1c45

Again, a Sue de Coq with the same eliminations is available.

In both cases the cells r1c4 or r1c45 are not restricted to XY or XYZ values, unlike what the description seems to imply, but any other digits are eliminated from them afterwards. It's the same misconception as with the original M-Wing (until it was generalized). Only one bivalue/ALS node is needed for the pattern to work, as the other two strong links use location.

[StrmCkr]

The above loop seems kind of like its hidden counterpart

exactly what they are. the often forgotten and unused hidden als

unlike what the description seems to imply, but any other digits are eliminated from them afterwards. It's the same misconception as with the original M-Wing (until it was generalized).

good catch, also noted here

....its something that should have been developed further to find .... edit removed...

Code: Select all

    -bce abce  a |  .  .  . |  .  .  .       -bce abce  . |  .  .  . |  .  .  .
    -bce abce  a |  .  .  . |  .  .  .       -bce abce  . |  .  .  . |  .  .  .
    -bce abce  a |  .  .  . |  .  .  .       -bce abce  . |  .  .  . |  .  .  .
    ---------+----------+----------      ---------+----------+----------
    abce -bce  a |  .  .  . |  .  .  .       abce -bce  . |  .  .  . |  .  .  .
    abce -bce  a |  .  .  . |  .  .  .       abce -bce  . |  .  .  . |  .  .  .
    abce -bce  a |  .  .  . |  .  .  .       abce -bce  . |  .  .  . |  .  .  .
    ---------+----------+----------      ---------+----------+----------
     .  .  / |  .  .  . |  .  .  .        a  a  / |  .  .  . |  .  .  .
     .  .  / |  .  .  . |  .  .  .        a  a  / |  .  .  . |  .  .  .
     .  .  / |  .  .  . |  .  .  .        a  a  / |  .  .  . |  .  .  .
     Type D1:                             Type D2:

now these are interesting. als a linked to als b using a single candidate which is the restricted common.
this is also something not done anywhere.

Code: Select all

+----------------+------------------------+---------+
| .  (1234)  .   | .       .       .      | .  .  . |
| .  (1234)  (1) | .       .       .      | .  .  . |
| .  (1234)  .   | .       .       .      | .  .  . |
+----------------+------------------------+---------+
| .  .       .   | .       .       .      | .  .  . |
| .  -234    (1) | (1234)  (1234)  (1234) | .  .  . |
| .  .       .   | .       .       .      | .  .  . |
+----------------+------------------------+---------+
| .  .       .   | .       .       .      | .  .  . |
| .  .       .   | .       .       .      | .  .  . |
| .  .       .   | .       .       .      | .  .  . |
+----------------+------------------------+---------+

[SpAce]

exactly what they are. the often forgotten and unused hidden als
...
good catch, also noted here

Ok, thanks for the confirmation! So nothing new under the sun, as I expected.

still its something that should have been developed further to find stuff like these...

I don't see any relation to the previous hidden pattern, because the link types don't match and there's no looping or reuse of cells. As before, these are just complex W-Wings using the VLV link-pattern where the V is an ALS (instead of a bivalue cell) and L is a grouped strong link (instead of a simple bilocation link). Much simpler than the previous pattern, I think. I might call them Grouped ALS-W-Wings:

(bce=a)r456c1 - r456c3 = r123c3 - (a=bce)r123c2 => -bce r123c1,r456c2

(bce=a)r456c1 - r789c1 = r789c2 - (a=bce)r123c2 => -bce r123c1,r456c2

now these are interesting. als a linked to als b using a single candidate which is the restricted common.
this is also something not done anywhere.

Oh, I'm sure it's done. It's just another example of an ALS-W-Wing, only simpler than the previous ones because the bilocation strong link is not grouped:

(234=1)r123c2 - r2c3 = r5c3 - (1=234)r5c456 => -234 r5c2

Anyone who understands chains and ALSs is certainly capable of spotting and using any of these. Such multi-elimination end points are just rare catches, so they're not often seen. Still I'm quite sure I've used something like this several times.

[StrmCkr]

Anyone who understands chains and ALSs is certainly capable of spotting and using any of these. Such multi-elimination end points are just rare catches, so they're not often seen. Still I'm quite sure I've used something like this several times.

fair enough : seen in manual solving, lacking in coded solvers

[SpAce]

fair enough : seen in manual solving, lacking in coded solvers

That might be true. However, have you checked this out? I haven't (and won't if it's Windows-only), but it mentions having an "AlsWWing" technique. I wonder if it could mean something like this.

[StrmCkr]

im not sure as i cant get it to open in win10

but i did manage to find a real world example for the idea

Code: Select all

+--------------------+------------------+---------------------+
| 1       23   236   | 4      3567  367 | 5678   568(3)  9    |
| (3467)  5    (346) | (367)  8     9   | (167)  2       1(3) |
| 367     9    8     | 1      3567  2   | 567    56(3)   4    |
+--------------------+------------------+---------------------+
| 2346    234  1     | 367    367   5   | 468    9       38   |
| 5       8    346   | 9      2     36  | 46-1   (136)   7    |
| 36      7    9     | 8      4     1   | 2      (36)    5    |
+--------------------+------------------+---------------------+
| 39      6    7     | 5      1     8   | 39     4       2    |
| 8       1    35    | 2      9     4   | 35     7       6    |
| 249     24   245   | 367    367   367 | 1589   158     18   |
+--------------------+------------------+---------------------+

for giggles ALS - W - RING

Code: Select all

+-------------------+----------------------+-------------------+
| 1     (478)  26-8 | (278)   9     (2468) | 27   5     3      |
| 9     (78)   5    | (278)   1     3      | 4    6     27     |
| 2346  34(7)  236  | 5-2(7)  (26)  45-26  | 9    1     8      |
+-------------------+----------------------+-------------------+
| 7     1      2389 | 6       238   289    | 358  4     59     |
| 23    39-8   4    | 12389   5     1289   | 6    3789  79     |
| 5     6      389  | 389     4     7      | 38   2     1      |
+-------------------+----------------------+-------------------+
| 8     349    1    | 2359    236   2569   | 27   379   245679 |
| 36    5      7    | 4       2368  2689   | 1    389   269    |
| 346   2      369  | 13589   7     15689  | 358  389   4569   |
+-------------------+----------------------+-------------------+