The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |.6.|..5|...|
 |35.|...|...|
 |..7|.82|...|
 |---+---+---|
 |...|9..|1.2|
 |..5|...|3..|
 |8.6|..1|...|
 |---+---+---|
 |...|47.|8..|
 |...|...|.94|
 |...|6..|.2.|
 *-----------*


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[Cenoman]

Code: Select all

 +---------------------+------------------+---------------------+
 |  124    6     8     |  137   9    5    |  24     34    17    |
 |  3      5     29    |  17    6    4    |  29     17    8     |
 | d149    14    7     |  13    8    2    | a456-9  345   56    |
 +---------------------+------------------+---------------------+
 |  47     347   34    |  9     5    6    |  1      8     2     |
 |  12     12    5     |  8     4    7    |  3      6     9     |
 |  8      9     6     |  2     3    1    |  45     457   57    |
 +---------------------+------------------+---------------------+
 |  56     23    239   |  4     7    39   |  8      15    156   |
 |  67     38    1     |  5     2    38   | b67     9     4     |
 | c4579   478   49    |  6     1    89   | b57     2     3     |
 +---------------------+------------------+---------------------+

(6)r3c7 = (67-5)r89c7 = (5-9)r9c1 = (9)r3c1 => -9 r3c7; ste

[SteveG48]

Code: Select all

 *-----------------------------------------------------------*
 |b124   6     8     | 137   9     5     | 2-4  a34    17    |
 | 3     5     29    | 17    6     4     | 29    17    8     |
 |b149   14    7     | 13    8     2     |a4569 a345  a56    |
 *-------------------+-------------------+-------------------|
 |b47    347   34    | 9     5     6     | 1     8     2     |
 |b12    12    5     | 8     4     7     | 3     6     9     |
 | 8     9     6     | 2     3     1     |c45    457   57    |
 *-------------------+-------------------+-------------------|
 | 56    23    239   | 4     7     39    | 8     15    156   |
 |b67    38    1     | 5     2     38    |c67    9     4     |
 | 4579  478   49    | 6     1     89    |c57    2     3     |
 *-----------------------------------------------------------*


(4=3569)b3p2789 - (9=12467)r13458c1 - (6=457)r689c7 => -4 r1c7 ; stte

[Ngisa]

Code: Select all

+----------------------+------------------+----------------------+
| 124      6       8   | 137     9     5  | 24       34      17  |
| 3        5       2-9 | 17     6     4   |f29       17      8   |
|a149      14      7   | 13      8     2  |e4569     345     56  |
+----------------------+------------------+----------------------+
| 47       347     34  | 9       5     6  | 1        8       2   |
| 12       12      5   | 8       4     7  | 3        6       9   |
| 8        9       6   | 2       3     1  | 457      457     57  |
+----------------------+------------------+----------------------+
| 56       23      239 | 4       7     39 | 8        15      156 |
| 67       38      1   | 5       2     38 |d67       9       4   |
|b4579     478     49  | 6       1     89 |c57       2       3   |
+----------------------+------------------+----------------------+


(9)r3c1 = (9-5)r9c1 = (5-7)r9c7 = (7-6)r8c7 = (6-9)r3c7 = r2c7 => - 9r2c3; stte.

Clement

[SpAce]

Code: Select all

.------------------.------------.-------------------.
|aBo124   6    8   | 137  9  5  |B24    34  b17     |
|   3     5    29  | 17   6  4  | 29    17   8      |
|  p149   14   7   | 13   8  2  |q4569  345 r5(6)   |
:------------------+------------+-------------------:
|   47    347  34  | 9    5  6  | 1     8    2      |
|  p12    12   5   | 8    4  7  | 3     6    9      |
|   8     9    6   | 2    3  1  |B45    457  57     |
:------------------+------------+-------------------:
|   56    23   239 | 4    7  39 | 8     15  c(1)5-6 |
|   67    38   1   | 5    2  38 |B(6)7  9    4      |
|   4579  478  49  | 6    1  89 |B57    2    3      |
'------------------'------------'-------------------'

Kraken Cell (124)r1c1

(1)r1c1 - r1c9 = (1)r7c9
||
(2)r1c1 - (2=4576)r1698c7
||
(4-1|2)r1c1 = (21-9)r53c1 = (9-6)r3c7 = (6)r3c9

=> -6 r7c9; stte

[Cenoman]

Couldn't refrain myself from adding this one:

Code: Select all

 +---------------------+------------------+---------------------+
 |  124    6     8     | a137*  9    5    | b24    b34    17*   |
 |  3      5     29    |  17*   6    4    | b29     17*   8     |
 | D149    14    7     |  13    8    2    | z456-9  345  y56    |
 +---------------------+------------------+---------------------+
 |  47     347   34    |  9     5    6    |  1      8     2     |
 |  12     12    5     |  8     4    7    |  3      6     9     |
 |  8      9     6     |  2     3    1    | A45     457*  57*   |
 +---------------------+------------------+---------------------+
 |  56     23    239   |  4     7    39   |  8      15*  x156*  |
 |  67     38    1     |  5     2    38   |  67     9     4     |
 | C4579   478   49    |  6     1    89   | B57     2     3     |
 +---------------------+------------------+---------------------+

DP(17)r12c4,b3p35,(57)r6c89,(15)r7c89 (*), using mixed internals-externals:
(3)r1c4 - (342=9)b3p124
(5)r6c7 - r9c7 = (5-9)r9c1 = (9)r3c1
(6) r7c9 - r3c9 = (6)r3c7
=> -9 r3c7; ste

[SpAce]

Couldn't refrain myself from adding this one:
...
DP(17)r12c4,b3p35,(57)r6c89,(15)r7c89 (*), using mixed internals-externals:
(3)r1c4 - (342=9)b3p124
(5)r6c7 - r9c7 = (5-9)r9c1 = (9)r3c1
(6) r7c9 - r3c9 = (6)r3c7
=> -9 r3c7; ste

Well, I'm glad you couldn't refrain yourself, Cenoman! I was hoping someone would produce a solution with that DP. It was the first thing that caught my eye in this puzzle, but while testing the internals I found that Kraken Cell instead and took the easy way out.

[pjb]

Code: Select all

 124     6       8      | 137    9      5      | 24     34     17     
 3       5       29     | 17     6      4      | 29     17     8     
a149     14      7      | 13     8      2      |b4569   345    56     
------------------------+----------------------+---------------------
 47      347     34     | 9      5      6      | 1      8      2     
 12      12      5      | 8      4      7      | 3      6      9     
 8       9       6      | 2      3      1      | 45     457    57     
------------------------+----------------------+---------------------
 56      23      239    | 4      7      39     | 8      15     156   
 67      38      1      | 5      2      38     |c67     9      4     
e457-9   478     49     | 6      1      89     |d57     2      3     


(9)r3c1 = (9-6)r3c7 = (6-7)r8c7 = (7-5)r9c7 = r9c1 => -9 r9c1; stte

Phil

PS Oops, same as Cenoman, something different
Almost xy-wing of 129 at r2c3, r35c1:
(4-9)r3c1 = (9-5)r9c1 = r9c7 - (5=4)r6c7 - (4=2)r1c7 => -2 r1c1; stte

Phil

[SpAce]

Almost xy-wing of 129 at r2c3, r35c1:
(4-9)r3c1 = (9-5)r9c1 = r9c7 - (5=4)r6c7 - (4=2)r1c7 => -2 r1c1; stte

Hi Phil. Perhaps I'm blind, but I don't understand how your chain works. I'm guessing you meant something like this but left out some parts:

(4)r1c1

||
(4-9)r3c1 = (9-5)r9c1 = r9c7 - (5=4)r6c7 - (4=2)r1c7
||
(4)r3c2 - r3c1 = XY-Wing[(2=9)r2c3 - (9=1)r3c1 - (1=2)r5c1]



=> -2 r1c1; stte

Am I close to correct? I would like that approach! Of course this would be simpler but more boring:

(2=9)r2c3 - r3c1 = (9-5)r9c1 = r9c7 - (5=4)r6c7 - (4=2)r1c7 => -2 r1c1; stte

[pjb]

SpAce: If the 4 at r3c1 is false, there exists an XY wing that eliminates 2 from r1c1. If the 4 is true, the 9 at r3c1 is false, and the chain indicated shows the 2 at r1c7 is true. Thus either way the 2 at r1c1 can be eliminated. Your chain amounts to the same thing, but is simpler.
Thanks, Phil

[SpAce]

SpAce: If the 4 at r3c1 is false, there exists an XY wing that eliminates 2 from r1c1. If the 4 is true, the 9 at r3c1 is false, and the chain indicated shows the 2 at r1c7 is true. Thus either way the 2 at r1c1 can be eliminated.

Thanks, Phil! I should have seen that there was no need to involve the (4)r1c1 but for some reason I didn't. Of course your chain works as an AIC and doesn't need the kraken hub -- thanks for making me see that! However, I still think it should have the XY-Wing as a node and start (and end) with a strong link to make it clearer as well as a fully self-contained AIC:

XY-Wing[(2=9)r2c3 - (9=1)r3c1 - (1=2)r5c1]

 = (4-9)r3c1 = (9-5)r9c1 = r9c7 - (5=4)r6c7 - (4=2)r1c7 => -2 r1c1; stte

or perhaps easier to read if we turn it around:

(2=4)r1c7 - (4=5)r6c7 - r9c7 = (5-9)r9c1 = (9-4)r3c1 = XY-Wing[(2=9)r2c3 - (9=1)r3c1 - (1=2)r5c1]

 => -2 r1c1; stte

(Or however you want to mark that XY-Wing -- I just happen to like explicit nested chains, but it could be simpler.)

Very nice anyway! I like it when non-trivial almost-patterns are used as nodes. I don't often spot those opportunities myself. (Even though XY-Wing is more or less a trivial pattern by itself, I don't think it's trivial when used as a node in a larger chain. Same goes for things like almost-Skyscrapers etc.)