The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |76.|4.8|...|
 |89.|.75|..3|
 |..3|...|...|
 |---+---+---|
 |.7.|...|...|
 |..5|362|1..|
 |...|...|.6.|
 |---+---+---|
 |...|...|4..|
 |1..|54.|.87|
 |...|2.7|.36|
 *-----------*


Play/Print this puzzle online

[Leren]

Code: Select all

*------------------------------------------------*
| 7   6    b12   | 4   3   8   | 259  1259  1259 |
| 8   9    b24   | 1   7   5   | 6    24    3    |
| 45  145   3    | 69  2   69  | 7    14    8    |
|----------------+-------------+-----------------|
|c236 7    b1469 |c89  589 14  |c38  c259  c2459 |
|a49  8     5    | 3   6   2   | 1    7     9-4  |
| 23  1234 b149  | 7   589 14  | 38   6     2459 |
|----------------+-------------+-----------------|
| 236 235   7    | 689 89  369 | 4    1259  1259 |
| 1   23    69   | 5   4   369 | 29   8     7    |
| 459 45    8    | 2   1   7   | 59   3     6    |
*------------------------------------------------*

ALS XY Wing: (4=9) r5c1 - (9=6) r1246c3 - (6=4) r4c145789 => - 4 r5c9; stte,

Leren

[SpAce]

Code: Select all

.--------------------------.----------------.-----------------.
|    7       6       12    | 4    3     8   | 259  1259  1259 |
|    8       9      b2#4   | 1    7     5   | 6    24    3    |
|    45+     45+1    3     | 69   2     69  | 7    14    8    |
:--------------------------+----------------+-----------------:
|    236     7      c1469  | 89   589   14  | 38   259   2459 |
| A(%4)-9    8       5     | 3    6     2   | 1    7     49   |
|    23     d1234  cd14(9) | 7    589  d14  | 38   6     2459 |
:--------------------------+----------------+-----------------:
|    236     235     7     | 689  89    369 | 4    1259  1259 |
|    1       23      69    | 5    4     369 | 29   8     7    |
|   a45(+9)  45+     8     | 2    1     7   | 59   3     6    |
'--------------------------'----------------'-----------------'

SIS 4b4 (Almost-ERI with obstacle %4r5c1) & UR[45]r39c12 using mixed +internals/#externals:

(%4)r5c1 = [(9)r9c1 == (4)r2c3 - r46c3 =%= (419)r6c263] => -9 r5c1; stte

Added. Slightly simplified:

(9)r9c1 == (4)r2c3 - r46c3 = (4)r5c1|(419)r6c263 => -9 r5c1; stte

[SpAce]

ALS XY Wing: (4=9) r5c1 - (9=6) r1246c3 - (6=4) r4c145789 => - 9 r5c9; stte,

or perhaps notated as : (4=9) r5c1 - (9=6) r1246c3 [ = (6-4) r4c3] = (4) r4c9 => - 9 r5c9; stte.

Or perhaps not. It's about as far from standard AIC notation as can be, and makes little sense anyway (there's no strong link 4r4c3=4r4c9 because of 4r4c6). If you want to avoid the huge third ALS, I think you need something like this:

(4=9)r5c1 - (9=214)r612c3 - (1|4)r4c3 = (14)r4c69 => -4 r4c3,r5c9

or:

(4=9)r5c1 - r46c3 = (96-1|4)r84c3 = (14)r4c69 => -4 r2c3,r5c9

Edit 1: Removed an unnecessary comma (usually it's the other way).
Edit 2: Added the second option.

[Cenoman]

Code: Select all

 +----------------------+--------------------+----------------------+
 |  7     6      12     |  4     3     8     |  259   1259   1259   |
 |  8     9      24     |  1     7     5     |  6     24     3      |
 |  45    145    3      |  69    2     69    |  7     14     8      |
 +----------------------+--------------------+----------------------+
 | a236   7      1469   |  89    589   14    |  38    259    2459   |
 |  49    8      5      |  3     6     2     |  1     7      49     |
 | a23   b1234  b149    |  7     589  b14    |  38    6      2459   |
 +----------------------+--------------------+----------------------+
 |  23-6  235    7      |  689   89    369   |  4     1259   1259   |
 |  1     23    c69     |  5     4     369   |  29    8      7      |
 |  459   45     8      |  2     1     7     |  59    3      6      |
 +----------------------+--------------------+----------------------+

(6=23)r46c1 - (2|3=149)r6c236 - (9=6)r8c3 => -6 r7c1; ste

(a, b: doubly linked ALS-AALS)

[Ngisa]

Code: Select all

+---------------------+-------------------+---------------------+
| 7      6       12   | 4      3      8   | 259    1259    1259 |
| 8      9       24   | 1      7      5   | 6      24      3    |
| 45     145     3    | 69     2      69  | 7      14      8    |
+---------------------+-------------------+---------------------+
|b236    7      c1469 | 89     589    14  | 38     259     2459 |
| 49     8       5    | 3      6      2   | 1      7       49   |
|a23    a1234   a149  | 7      589   a14  | 38     6       2459 |
+---------------------+-------------------+---------------------+
| 236    235     7    | 689    89     369 | 4      1259    1259 |
| 1      23     d6-9  | 5      4      369 | 29     8       7    |
| 459    45      8    | 2      1      7   | 59     3       6    |
+---------------------+-------------------+---------------------+


(9=1423)r6c1236 - (23=6)r4c1 - r4c3 = (6)r8c3 => - 9r8c3; stte

Clement

[Sudtyro2]

(9=1423)r6c1236 - (23=6)r4c1 - r4c3 = (6)r8c3 => - 9r8c3; stte

Hi Clement,
Good chain, but I think your second node should be written as (2|3=6)r4c1 to indicate that both 2 and 3 are false.
See Cenoman's second node as an example.

SteveC

[eleven]

Code: Select all

 *------------------------------------------------------------------*
 |  7     6       12    |  4     3     8     |  259   1259   1259   |
 |  8     9       24    |  1     7     5     |  6     24     3      |
 |  45    145     3     |  69    2     69    |  7     14     8      |
 |----------------------+--------------------+----------------------|
 |  236   7      c1469  |  89    589   14    |  38    259    2459   |
 | c49    8       5     |  3     6     2     |  1     7      49     |
 |  23    23-14 ca149   |  7     589  a14    |  38    6      2459   |
 |----------------------+--------------------+----------------------|
 |  236   235     7     |  689   89    369   |  4     1259   1259   |
 |  1     23     b69    |  5     4     369   |  29    8      7      |
 |  459   45      8     |  2     1     7     |  59    3      6      |
 *------------------------------------------------------------------*

(14=9)r6c36 - (9=6)r8c3 - (6=914)b6p349 => -14r6c2, stte

[SteveG48]

Code: Select all

 *-----------------------------------------------------------*
 | 7     6     12    | 4     3     8     | 259   1259  1259  |
 | 8     9     24    | 1     7     5     | 6     24    3     |
 | 45    145   3     | 69    2     69    | 7     14    8     |
 *-------------------+-------------------+-------------------|
 | 236   7     1469  | 89    589   14    | 38    259   2459  |
 | 4-9   8     5     | 3     6     2     | 1     7     49    |
 | 23   b1234 a149   | 7     589  a14    | 38    6     2459  |
 *-------------------+-------------------+-------------------|
 | 236  b235   7     | 689   89    369   | 4    c1259 c1259  |
 | 1    b23    6-9   | 5     4     369   | 29    8     7     |
 |e459  e45    8     | 2     1     7     |d59    3     6     |
 *-----------------------------------------------------------*


(9=14)r6c36 - (1|4=235)r678c2 - 5r7c89 = 5r9c7 - (5=49)r9c127 => -9 r5c1,r8c3 ; stte

[SpAce]

(9=1423)r6c1236 - (23=6)r4c1 - r4c3 = (6)r8c3 => - 9r8c3; stte

Good chain

Yes, it is.

but I think your second node should be written as (2|3=6)r4c1

Correct. But I think you, like everyone before, are going to be disappointed if you think mentioning it will change anything As far back as I remember, Clement has had his own style, and I think we ought to accept that. While the notation is sometimes slightly incorrect (by strict AIC standards) in these situations, it hardly ever causes actual interpretation problems.

to indicate that both 2 and 3 are false.

Being the damned nitpicker that I am, I must say that's not necessarily an intuitive explanation to why the '|' (OR) is need when you talk about both. Natural language would rather suggest using "AND" there (which is what Clement's original translates to). That's why I used to make the same mistake in my early days. To really grasp the reason why it's incorrect, I think one needs to be able to translate AICs into logic gates (ORs and NANDs) and know De Morgan's laws. That's why writing complex AICs correctly isn't always easy (but it can be quite satisfying).

One way to catch notation errors is to run the chain backwards and see if it still makes sense. It often reveals these (and other) kinds of problems and may suggest fixes as well. For example, here the reversed node (6=23)r4c1 would imply placing two digits (2 AND 3) into a single cell, which is clearly impossible. Thus, either we have a contradiction situation (we don't) or it must be (2 OR 3), i.e. (6=2|3).

See Cenoman's second node as an example.

Yeah, it's a beautiful chain too. SteveG48's chain has another example of the correct usage of '|'. Both of my earlier posts above have also a couple of examples, though a bit different situations.

Btw, here's proof that it hasn't always been easy for me either. Mostly thanks to eleven, I finally started to see the light.

[SpAce]

(14=9)r6c36 - (9=6)r8c3 - (6=914)b4p349 => -14r6c2, stte

Lovely symmetry!

Btw, I'm not suggesting this as a viable alternative (harder to understand, and a bit iffy with adjacent terms overlapping), but I think it's kind of pretty too:

(14)r6c36 = (96)r68c3 - (96=14)b4p349 => -14 r6c2; stte

(It's also somewhat related to the preceding notation discussion. Here the lack of the '|' (OR) is important, because it's all ANDs. That's why it's also important to use the '|' when needed, because otherwise the distinction is lost when its absence truly means AND.)

[Leren]

SpAce wrote : there's no strong link 4r4c3=4r4c9 because of 4r4c6

Thanks for spotting that and the elimination typo. I'll stick with the large ALS. Leren

[SpAce]

Thanks for spotting that and the elimination typo. I'll stick with the large ALS. Leren

Ok! It's kind of cool anyway, being so huge