The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |8.3|.7.|.1.|
 |2..|4.9|8.6|
 |...|1..|...|
 |---+---+---|
 |...|...|..7|
 |1.7|8.5|6.4|
 |4..|...|...|
 |---+---+---|
 |...|..8|...|
 |5.9|7.4|..8|
 |.1.|.9.|4.2|
 *-----------*


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[SpAce]

Code: Select all

.-----------------.--------------------.---------------------.
| 8    4      3   | a(5)6   7      a26 | 29-5   1       9-5  |
| 2    57     1   |   4     35      9  | 8      357     6    |
| 679  5679   56  |   1     8      a23 | 2357   4      b3(5) |
:-----------------+--------------------+---------------------:
| 369  35689  256 |   2369  4       1  | 359    23589   7    |
| 1    39     7   |   8     23      5  | 6      239     4    |
| 4    35689  256 |   2369  236     7  | 1359   23589   1359 |
:-----------------+--------------------+---------------------:
| 367  2367   4   |   2356  12356   8  | 13579  35679   1359 |
| 5    236    9   |   7     1236    4  | 13     36      8    |
| 367  1      8   |   356   9       36 | 4      3567    2    |
'-----------------'--------------------'---------------------'

WXYZ-Wing:

(5=623)b2p139 - (3=5)r3c9 => -5 r1c79; stte

[Cenoman]

Code: Select all

 +----------------------+----------------------+-------------------------+
 |  8     4       3     |  56     7       26   |  259     1       59     |
 |  2     57      1     |  4      35      9    |  8      b357     6      |
 |  679   5679    56    |  1      8      c2-3  | b2357    4      a35     |
 +----------------------+----------------------+-------------------------+
 |  369   35689   256   |  2369   4       1    |  359     23589   7      |
 |  1     39      7     |  8      23      5    |  6       239     4      |
 |  4     35689   256   |  2369   236     7    |  1359    23589   1359   |
 +----------------------+----------------------+-------------------------+
 |  367   2367    4     |  2356   12356   8    |  13579   35679   1359   |
 |  5     236     9     |  7      1236    4    |  13      36      8      |
 |  367   1       8     |  356    9       36   |  4       3567    2      |
 +----------------------+----------------------+-------------------------+

(3)r3c9 = (37-2)b3p57 = (2)r3c6 => -3 r3c6; ste

[Ngisa]

Code: Select all

+---------------------+------------------+------------------------+
| 8      4        3   | 56      7     26 | 259      1        59   |
| 2     b57       1   | 4     fa3-5    9 | 8        357      6    |
|c679   c5679     56  | 1       8     e23|d2357     4        35   |
+---------------------+------------------+------------------------+
| 369    35689    256 | 2369    4      1 | 359      23589    7    |
| 1      39       7   | 8       23     5 | 6        239      4    |
| 4      35689    256 | 2369    236    7 | 1359     23589    1359 |
+---------------------+------------------+------------------------+
| 367    2367     4   | 2356    12356 8  | 13579    35679    1359 |
| 5      236      9   | 7       1236  4  | 13       36       8    |
| 367    1        8   | 356     9     36 | 4        3567     2    |
+---------------------+------------------+------------------------+


(5)r2c5 -(5=7)r2c2 - r3c12 = (7-2)r3c7 = (2-3)r3c6 = (3)r2c5 => - 5r2c5; stte

Clement

[Sudtyro2]

Code: Select all

+-------------------+-----------------+----------------------+
|  8     4      3   | 56   7     26   |  259     1      59   |
|  2    f57*    1   | 4   g35    9    |  8       357*   6    |
|  679  e5679#  56  | 1    8   ga23   | b2357*   4      35   |
+-------------------+-----------------+----------------------+
|  369   35689  256 | 2369 4     1    |  359     23589  7    |
|  1     39     7   | 8    23    5    |  6       239    4    |
|  4     35689  256 | 2369 236   7    |  1359    23589  1359 |
+-------------------+-----------------+----------------------+
| d367#  2367*  4   | 2356 12356 8    | c13579* d35679# 1359 |
|  5     236    9   | 7    1236  4    |  13      36     8    |
|  367   1      8   | 356  9     36   |  4       3567   2    |
+-------------------+-----------------+----------------------+

In 7s, a 5-link oddagon(*) with three guardians(#) used to form a discontinuous loop.
2r3c6 = (2-7)r3c7 = r7c7 - [r7c18 == r3c2] - (7=5)r2c2 - (5=32)b2p59 => +2r3c6; stte

SteveC

[SteveG48]

Code: Select all

 *--------------------------------------------------------------------*
 | 8      4      3      | 56     7      6-2    |b259    1     b59     |
 | 2      57     1      | 4      35     9      | 8      357    6      |
 | 679    5679   56     | 1      8     a23     | 357-2  4     a35     |
 *----------------------+----------------------+----------------------|
 | 369    35689  256    | 2369   4      1      | 359    23589  7      |
 | 1      39     7      | 8      23     5      | 6      239    4      |
 | 4      35689  256    | 2369   236    7      | 1359   23589  1359   |
 *----------------------+----------------------+----------------------|
 | 367    2367   4      | 2356   12356  8      | 13579  35679  1359   |
 | 5      236    9      | 7      1236   4      | 13     36     8      |
 | 367    1      8      | 356    9      36     | 4      3567   2      |
 *--------------------------------------------------------------------*


(2=35)r3c69 - (5=29)r1c79 => -2 r1c6,r3c7 ; stte

[SpAce]

In 7s, a 5-link oddagon(*) with three guardians(#)

Very nice!

used to form a discontinuous loop.

Why bother with closing the loop, though? It just adds length and complexity for no reason:

2r3c6 = (2-7)r3c7 = r7c7 - [r7c18 == r3c2] - (7=5)r2c2 - (5=32)b2p59 => +2r3c6; stte

Could be simply:

2r3c6 = (2-7)r3c7 = r7c7 - [r7c18 == r3c2] - (7=53)r2c25 => -3 r3c6; stte

Or even shorter with my favorite shortcuts:

(7)r[3=7]c7 - r7c18 == (7,5)r32c2 - (5=32)b2p59 => -2 r3c7; stte

[Sudtyro2]

Why bother with closing the loop, though? It just adds length and complexity for no reason:

2r3c6 = (2-7)r3c7 = r7c7 - [r7c18 == r3c2] - (7=5)r2c2 - (5=32)b2p59 => +2r3c6; stte

Main reason in this case is that the one (longer) chain provides a single placement having three simultaneous stte eliminations.

SteveC

[SpAce]

Why bother with closing the loop, though? It just adds length and complexity for no reason:

2r3c6 = (2-7)r3c7 = r7c7 - [r7c18 == r3c2] - (7=5)r2c2 - (5=32)b2p59 => +2r3c6; stte

Main reason in this case is that the one (longer) chain provides a single placement having three simultaneous stte eliminations.

And that's significant how, exactly? The end result is the same if you eliminate any one of those three (isn't that why they're called stte eliminations?), because the placement follows them all. Adding that extra term is just stating the obvious. Thus all I see is a longer chain without any obvious benefits. Otherwise I'd do the same with my chain:

(5=623)b2p139 - (3=5)r3c9 => -5 r1c79; stte

-->

(5=623)b2p139 - (3=5)r3c9 - r1c79 = (5)r1c4 => +5 r1c4; stte ==> -6 r1c4; -5 r2c5, r1c79, r79c4

That's four simultaneous stte eliminations (and a total of six direct eliminations)! Yet I think it's way less efficient and elegant than the original. Don't you?

There are some situations where a placing DNL is actually more elegant than the corresponding eliminating AIC, but in my experience they mostly occur in split-node or other net situations when one of the ends would otherwise remain split. Then it's neater to add an extra pair of links to collect all loose ends into a single cable box, but I don't see such a reason here. (Then again, you're quite free to do it for any or no reason if you prefer it -- it's fully correct, of course, and it's all that matters. I just don't understand your stated reasoning.)