The New Sudoku Players' Forum

[tarek]

Code: Select all

+-------+-------+-------+
| . 7 . | . 3 1 | 4 . . |
| 1 . . | 5 . . | . 6 2 |
| . . 6 | . 8 2 | . 7 . |
+-------+-------+-------+
| . 2 . | . . . | . . . |
| 8 . 9 | . . 4 | 5 . . |
| 3 . 4 | . 5 8 | . . . |
+-------+-------+-------+
| 2 . . | . 7 . | . . . |
| . 9 5 | . . . | . . 1 |
| . 8 . | . . . | . 5 . |
+-------+-------+-------+
.7..314..1..5...62..6.82.7..2.......8.9..45..3.4.58...2...7.....95.....1.8.....5.


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[Leren]

Code: Select all

*---------------------------------------------*
| 9   7  2  | 6     3    1   | 4    8     5   |
| 1   3  8  | 5     4    7   | 9    6     2   |
| 4   5  6  | 9     8    2   | 1    7     3   |
|-----------+----------------+----------------|
| 5   2  7  |b13    169  369 | 368  134   468 |
| 8  a16 9  |b1237 a126  4   | 5    123 ca67  |
| 3   16 4  |b127   5    8   | 26-7 129  c679 |
|-----------+----------------+----------------|
| 2   4  13 |b138   7    5   | 368  39   c689 |
| 67  9  5  | 2348  26   36  | 2378 234   1   |
| 67  8  13 | 1234  1269 369 | 237  5     4-7 |
*---------------------------------------------*

(7=2) r5c259 - (2=8) r4567c4 - (8=7) r567c9 => - 7 r6c7; r9c9; stte

Leren

[SpAce]

Code: Select all

.------------.-------------------.-------------------.
| 9   7   2  |  6      3     1   |  4     8      5   |
| 1   3   8  |  5      4     7   |  9     6      2   |
| 4   5   6  |  9      8     2   |  1     7      3   |
:------------+-------------------+-------------------:
| 5   2   7  |  13     169   369 | f368   134   g468 |
| 8   16  9  | b1237  c126   4   |  5    c123   a67  |
| 3   16  4  | d127    5     8   |  267   129    679 |
:------------+-------------------+-------------------:
| 2   4   13 |  138    7     5   |  368   39     689 |
| 67  9   5  | e2348   26    36  | e2378  234    1   |
| 67  8   13 | b1234   1269  369 |  237   5    ag4-7 |
'------------'-------------------'-------------------'

(7)r5c9|(4)r9c9 = (74-3|2)r59c4 = [(+32)r5c85 - r6c4 = (2,8)r8c47 - r4c7 = (84)r49c9] => -7 r9c9; stte

as a Kraken Column 2C4: Show

Code: Select all

(2-7)r5c4 = (7)r5c9
||
(2)r6c4 - r5c45 = (2-3)r5c8 = (3-7)r5c4 = (7)r5c9
||
(2-8)r8c4 = r8c7 - r4c7 = (8-4)r4c9 = (4)r9c9
||
(2-4)r9c4 = (4)r9c9

=> -7 r9c9; stte

8x8 PM: Show

Code: Select all

 4r9c9 4r4c9
       8r4c9 8r4c7
             8r8c7 8r8c4
 4r9c9 ................. 4r9c4
 7r5c9 ....................... 7r5c4
                   2r8c4 2r9c4 2r5c4 2r6c4
                                     2r5c45 2r5c8
                               3r5c4 ...... 3r5c8
=================================================
-7r9c9

Btw, appearances can deceive. While this is obviously way uglier and more complicated as an AIC than Leren's neat and elegant ALS-XY-Wing, which one is really more complicated? It's hard to say, because it depends on several factors, and I make no claims either way. (I think I'm leaning on Leren's, though. Edit: I actually meant I was leaning on Leren's being simpler, all things considered.) What is certain, however, is that as a matrix the ALS-XY-Wing doesn't look so simple any more:

9x9 BTM (Leren): Show

Code: Select all

 7r5c9 6r5c9
       6r5c2 1r5c2
       6r5c5 1r5c5 2r5c5
                   2r6c4 1r6c4 7r6c4
                   2r5c4 1r5c4 7r5c4 3r5c4
                         1r4c4 ..... 3r4c4
                         1r7c4 ..... 3r7c4 8r7c4
       6r7c9                               8r7c9 9r7c9
 7r6c9 6r6c9 ................................... 9r6c9
======================================================
-7r9c9

[Cenoman]

Code: Select all

 +-----------------+----------------------+---------------------+
 |  9    7    2    |  6      3      1     |  4      8     5     |
 |  1    3    8    |  5      4      7     |  9      6     2     |
 |  4    5    6    |  9      8      2     |  1      7     3     |
 +-----------------+----------------------+---------------------+
 |  5    2    7    |  13     169    369   | a36-8*  134  b468*  |
 |  8   d16   9    |  1237  d126    4     |  5      123  c67    |
 |  3    16   4    |  127    5      8     |  267    129   679   |
 +-----------------+----------------------+---------------------+
 |  2    4    13   |  138    7      5     |  368*   39    689*  |
 |  67   9    5    | f2348  e26     36    |ga2378   234   1     |
 |  67   8    13   | f1234  e1269   369   |  237    5    c47    |
 +-----------------+----------------------+---------------------+

UR(68)r47c79 using mixed internals-external
(3)r4c7|(8)r8c7 == (4)r4c9 - (4=76)r59c9 - (6=12)r5c25 - r89c5 = (24-8)r89c4 = (8)r8c7 => -8 r4c7; ste

[SteveG48]

Code: Select all

 *------------------------------------------------------------*
 | 9     7     2     |  6     3     1     | 4     8     5     |
 | 1     3     8     |  5     4     7     | 9     6     2     |
 | 4     5     6     |  9     8     2     | 1     7     3     |
 *-------------------+--------------------+-------------------|
 | 5     2     7     | c13    169   369   | 368   134   468   |
 | 8    a16    9     |bc1237 a126   4     | 5    a123   7-6   |
 | 3     16    4     |bc127   5     8     | 267   129   679   |
 *-------------------+--------------------+-------------------|
 | 2     4     13    | c138   7     5     | 368 bc39   d689   |
 | 67    9     5     |  2348  26    36    | 2378  234   1     |
 | 67    8     13    |  1234  1269  369   | 237   5     47    |
 *------------------------------------------------------------*


(6=123)r5c258 - 2r56c4|3r7c8 = (13789)r4567c4,r7c8 - (8|9=6)r7c9 => -6 r5c9 ; stte

Yarg. Practically the same as Leren's but not nearly as nice.

[SpAce]

Hi Steve,

(6=123)r5c258 - 2r56c4|3r7c8 = (13789)r4567c4,r7c8 - (8|9=6)r7c9 => -6 r5c9 ; stte

Yarg. Practically the same as Leren's but not nearly as nice.

I think it's different enough, and niceness is somewhat subjective. Personally I hate ALS terms without the passenger digits (hard to read against the grid, looks simpler than it really is), so everything is nicer than that Disregarding that easily fixed style issue we can of course agree that Leren's AIC is the cleanest. However, the (unfolded) matrix of yours is actually a bit nicer because it can be written as a TM:

9x9 TM: Show

Code: Select all

 6r5c2 1r5c2
 6r5c5 1r5c5 2r5c5
       1r5c8 2r5c8 3r5c8
       1r5c4 2r5c4 3r5c4 7r5c4
             2r6c4 ..... 7r6c4 1r6c4
                               1r4c4 3r4c4
                               1r7c4 3r7c4 8r7c4
                   3r7c8 ....................... 9r7c8
 6r7c9 ................................... 8r7c9 9r7c9
======================================================
-6r5c9

That's slightly different from your AIC, corresponding with:

(6=123)r5c258 - (2|3)r56c4,r7c8 ...

As for the following term, I might consider using an optional comma to (subjectively) improve readability:

(7138,9)r6547c4,r7c8

or perhaps:

(713,89)r654c4,r7c48 - (8|9=6)r7c9

The latter form makes the following weak link easier to read, but it kind of blurs the reason for 8r7c4, so neither is perfect. This might be stretching a bit too much, though it would give a pretty short AIC:

(6=123)r5c258 - (2|3)r56c4,r7c8 = (713,896)r654c4,r7c489 => -6 r5c9 ; stte

(This is pure speculation of possibilities. Nothing wrong with your original!)

From a resource management perspective, yours and Leren's are similar. Both use 9 cells, 7 digits, and 25 candidates. Mine uses 11 cells, 5 digits, and 17 candidates. That's what I meant earlier about the difficulty of judging complexity. For that I mostly look at the unfolded matrix form, though it doesn't necessarily tell the whole story either.