The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |..1|..6|..3|
 |.4.|..1|8.6|
 |..2|4..|5..|
 |---+---+---|
 |7.5|3..|...|
 |4..|...|..1|
 |...|..2|3.5|
 |---+---+---|
 |..9|..4|6..|
 |2.6|8..|.9.|
 |5..|2..|1..|
 *-----------*


Play/Print this puzzle online

[SCLT]

Code: Select all

+---------------------+---------------------+-------------------+
|  8      5       1   |  79     2      6    |  479   47    3    |
|  39     4       7   |  59     359    1    |  8     2     6    |
| a369*  a369*    2   |  4      8     b37   |  5     1     79   |
+---------------------+---------------------+-------------------+
|  7      1269    5   |  3     C149    8    |  249   46    49   |
|  4      269     3   |  5679   579    57   |  279   8     1    |
| A169*  A169*    8   | B1679  B1479   2    |  3     467   5    |
+---------------------+---------------------+-------------------+
|  13     8       9   |  17     137    4    |  6     5     2    |
|  2     E1-3     6   |  8     D135   c35   |  47    9     47   |
|  5      7       4   |  2      6      9    |  1     3     8    |
+---------------------+---------------------+-------------------+


UR (*) on 6/9 r36c12, using internals:

3r3c12 - r3c6 = r8c6 (abc)
1r6c12 - r6c45 = r4c5 - r8c5 = r8c2 (ABCDE)

=> -3 r8c2 ; stte

[Ngisa]

Code: Select all

+--------------------+-----------------------+--------------------+
| 8       5        1 | 9-7       2        6  | 479     47      3  |
|c39      4        7 | 59       d359      1  | 8       2       6  |
| 369     369      2 | 4         8       e37 | 5       1       79 |
+--------------------+-----------------------+--------------------+
| 7       1269     5 | 3         149      8  | 249     46      49 |
| 4       269      3 | 5679      579      57 | 279     8       1  |
| 169     169      8 | 1679      1479     2  | 3       467     5  |
+--------------------+-----------------------+--------------------+
|b13      8        9 |a17        137      4  | 6       5       2  |
| 2       13       6 | 8         135      35 | 47      9       47 |
| 5       7        4 | 2         6        9  | 1       3       8  |
+--------------------+-----------------------+--------------------+


(7=1)r7c4 - (1=3)r7c1 - r2c1 = r2c5 - (3=7)r3c6 => - 7r1c4; stte


Clement

[Sudtyro2]

Code: Select all

+---------------+-------------------+------------+
| 8     5    1  | c79     2      6  | 479 47  3  |
| 39    4    7  |  59     359    1  | 8   2   6  |
| 369   369  2  |  4      8     d37 | 5   1   79 |
+---------------+-------------------+------------+
| 7    B1269 5  |  3     C149#   8  | 249 46  49 |
| 4     269  3  |  5679   579    57 | 279 8   1  |
| 169* A169# 8  | a1679#  1479*  2  | 3   467 5  |
+---------------+-------------------+------------+
| 13*   8    9  | b17     137#   4  | 6   5   2  |
| 2     13*  6  |  8     e35-1* d35 | 47  9   47 |
| 5     7    4  |  2      6      9  | 1   3   8  |
+---------------+-------------------+------------+

In 1s, a 5-link oddagon(*) having four guardians(#) => - 1r8c5; stte

Code: Select all

1r6c4 - (1=7)r7c4 - r1c4 = (73-5)r38c6 = 5r8c5 - 1r8c5; abcde
1r6c2 - r4c2 = 1r4c5                           - 1r8c5; ABC
1r47c5                                         - 1r8c5;

Or, more simply, the Kraken (1)c4 => - 1r8c5; stte

SteveC

[Cenoman]

Code: Select all

 +--------------------+---------------------+-------------------+
 |  8     5      1    | b79     2      6    |  479   47    3    |
 |  9-3   4      7    | b59    b359    1    |  8     2     6    |
 |  369   369    2    |  4      8      37   |  5     1     79   |
 +--------------------+---------------------+-------------------+
 |  7     1269   5    |  3      149    8    |  249   46    49   |
 |  4     269    3    |  5679   579    57   |  279   8     1    |
 |  169   169    8    |  1679   1479   2    |  3     467   5    |
 +--------------------+---------------------+-------------------+
 | a13    8      9    | a17     17-3   4    |  6     5     2    |
 |  2     13     6    |  8      135    35   |  47    9     47   |
 |  5     7      4    |  2      6      9    |  1     3     8    |
 +--------------------+---------------------+-------------------+

(13=7)r7c14 - (7=593)b2p145 => -3 r2c1,r7c5; ste

[SpAce]

Or, more simply, the Kraken (1)c4 => - 1r8c5; stte

Or even more simply as an AIC: (1)r7c4 =...= (5)r8c5. While perfectly correct, I'd say two-way Krakens are similarly questionable as two-way Death Blossoms. Then again, it doesn't hurt to present different POVs of the same chain, especially since basic AICs are pretty boring Thus, let me turn that into a (sort of) Kraken not usually seen:

Kraken Candidate (7)r1c4:

(7)r1c4(true) - (7=1)r7c4
+
(7)r1c4(false) = (73-5)r38c6 = (5)r8c5

=> -1 r8c5

PS. This particular "Kraken" is obviously the most useless type, as it can only be two-way and thus always presentable as a simple AIC. SudokuWiki calls these "Digit Forcing Chains" and oddly enough uses them quite often. I have no clue why, because it could just as easily use AICs (or rather Discontinuous Nice Loops as its only real AICs are XY Chains). It seems like a totally unnecessary and confusing complication in that solver. Does anyone have a theory why it does that?

[pjb]

Code: Select all

 8       5       1      |a79     2      6      | 479    47     3     
d39      4       7      | 5-9    35-9   1      | 8      2      6     
 369     369     2      | 4      8      37     | 5      1      79     
------------------------+----------------------+---------------------
 7       1269    5      | 3      149    8      | 249    46     49     
 4       269     3      | 5679   579    57     | 279    8      1     
 169     169     8      | 1679   1479   2      | 3      467    5     
------------------------+----------------------+---------------------
c13      8       9      |b17     137    4      | 6      5      2     
 2       13      6      | 8      135    35     | 47     9      47     
 5       7       4      | 2      6      9      | 1      3      8     


(9=7)r1c4 - (7=1)r7c4 - (1=3)r7c1 - (3=9)r2c1 => -9 r2c45; stte

Phil

[SCLT]

Does anyone have a theory why it does that?

I think that Andrew Stuart has once said that he has set a limit on the length of chain that his solver will find, in order to reduce computation time.

This means that techniques like "Digit Forcing Chain", which stitch together two chains, can in effect find chains that are twice as long, so might stumble upon some that earlier single-chain techniques miss.

[SpAce]

I think that Andrew Stuart has once said that he has set a limit on the length of chain that his solver will find, in order to reduce computation time. This means that techniques like "Digit Forcing Chain", which stitch together two chains, can in effect find chains that are twice as long, so might stumble upon some that earlier single-chain techniques miss.

I get that there might be implementation issues involved, but that doesn't explain why the end result is not presented as a single AIC. It makes zero sense, since the two chains form an AIC without any modification (just add them up), so there would be no price to pay at all. Andrew's description of the Digit Forcing Chain does not make the obvious connection to AIC either, but instead implies that it's somehow a more advanced technique. It's quite confusing for a newcomer who's just started learning about chains (was for me anyway, though I pretty quickly discovered the truth).

That being said, I'm glad that he does present the technique as an additional (if not very useful) POV of chaining logic missing from most other sources. The simple fact that a candidate has an internal strong link between its two states is quite fundamental to understanding AICs (which have -- implicitly -- the same switching logic at both ends). For example, Phil's AIC above could be presented as an explicit Kraken Candidate / Digit Forcing Chain like this:

(9)r1c4(true)
+
(9)r1c4(false) = (7)r1c4 - (7=1)r7c4 - (1=3)r7c1 - (3=9)r2c1



=> -9 r2c45

The same could be done with any candidate in the chain; the (true) and (false) branches just traverse the chain in opposite directions. For instance:

(7)r7c4 (true) - (7=9)r1c4
+
(7)r7c4 (false) = (1)r7c4 - (1=3)r7c1 - (3=9)r2c1

(Similary any bivalue strong link could be presented as a Kraken Cell, and any bilocation strong link as a Kraken Unit.)