The New Sudoku Players' Forum

[tarek]

I couldn't crack this nut

Code: Select all

+-------+-------+-------+
| . . 1 | . 7 . | . 8 . |
| . . 4 | . . 9 | . 5 2 |
| 5 9 . | . 6 . | 7 . . |
+-------+-------+-------+
| . . . | . . . | 3 . 5 |
| 9 . 2 | . . 1 | . . . |
| . 5 . | . 9 . | . . . |
+-------+-------+-------+
| . . 6 | 2 . . | . . . |
| 8 7 . | . . . | . . 1 |
| . 1 . | 9 . . | . 4 . |
+-------+-------+-------+
..1.7..8...4..9.5259..6.7........3.59.2..1....5..9......62.....87......1.1.9...4.


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[pjb]

Two steps using almost xy-wings

Code: Select all

 36      2       1      | 345    7      345    | 469    8      3469   
 7      a368*    4      | 138   b38     9      |e16*    5      2     
 5       9       8-3    | 1348   6      2      | 7     f13*    34     
------------------------+----------------------+---------------------
 1       468     78     | 4678   2      468    | 3      9      5     
 9       348     2      | 34578  45     1      | 48     6      478   
 346     5       378    | 34678  9      3468   | 12     12     478   
------------------------+----------------------+---------------------
 34      34      6      | 2      1      58     | 589    7      89     
 8       7       9      | 3456   45     3456   | 25     23     1     
 2       1       5      | 9     c38     7      |d68     4      368   


Almost xy-wing at r3c8, r2c7 and r2c2, with (8)r2c2 - (8=3)r2c5 - (3=8)r9c5 - (8=6)r9c7 - (6=1)r2c7 - (1=3)r3c8, => -3 r3c3
3s at r3c8 and r3c9 only ones in row/column.

Code: Select all

 36      2       1      | 45     7      345    | 469    8      469   
 7       36      4      | 18     38     9      | 16     5      2     
 5       9       8      |b14     6      2      | 7      13    c34     
------------------------+----------------------+---------------------
 1       468     7      |a468*   2      468    | 3      9      5     
 9       48      2      | 3      5      1      | 48     6      7     
 46      5       3      | 7      9      46-8   | 12     12    d48     
------------------------+----------------------+---------------------
 34      34      6      | 2      1      58*    | 589    7      89     
 8       7       9      | 56*    4      356    | 25     23     1     
 2       1       5      | 9      38     7      | 68     4      368   


Almost xy-wing at r7c6, r8c4 and r4c4, with (4)r4c4 - r3c4 = r3c9 - (4=8)r6c9, => -8 r6c6; stte

Phil

[Mauriès Robert]

Hi Phil,

Almost xy-wing at r3c8, r2c7 and r2c2, with (8)r2c2 - (8=3)r2c5 - (3=8)r9c5 - (8=6)r9c7 - (6=1)r2c7 - (1=3)r3c8, => -3 r3c3

I don't see how Almost xy-wing to r3c8, r2c7 and r2c2 serves you to build the AIC (8)r2c2 - (8=3)r2c5 - (3=8)r9c5 - (8=6)r9c7 - (6=1)r2c7 - (1=3)r3c8?
One can build this AIC without worrying about the wing Almost xy because the 8s form a pair in b1.
Ditto for the other Almost xy-wing.
Sincerely
Robert

[Cenoman]

A one-stepper, presented as a net:

Code: Select all

 +--------------------+----------------------+--------------------+
 |  36    2     1     |  345     7    345    |  469   8    3469   |
 |  7     368   4     |  138     38   9      |  16    5    2      |
 |  5     9     38    |  348-1   6    2      |  7     13   34     |
 +--------------------+----------------------+--------------------+
 |  1     468   78    |  4678    2    468    |  3     9    5      |
 |  9     348   2     |  34578   45   1      |  48    6    478    |
 |  346   5     378   |  34678   9    3468   |  12    12   478    |
 +--------------------+----------------------+--------------------+
 |  34    34    6     |  2       1    58     |  589   7    89     |
 |  8     7     9     |  3456    45   3456   |  25    23   1      |
 |  2     1     5     |  9       38   7      |  68    4    368    |
 +--------------------+----------------------+--------------------+

(8)r4c2-(8=374)b4p359-r5c79=r6c9-r3c9=(4)r3c4 *
 ||
(8)r4c3-r3c3=(8)r3c4 *
 ||
(8)r4c4-r46c6=8r7c6-(8=2593)b9p1345-(3=1)r3c8 *
 ||
(8)r4c6 - r7c6 = r9c5 - (8=6)r9c7 - r9c9 = r1c9 - r1c1 = r6c1 - (6)r6c6
        \                                                        ||
          - - - - - - - - - - - - - - - - - - - - - - - - - - - (6)r4c6
                                                                 ||
                                                                (6)r8c6 - (3)r8c6
                                                                           ||
                                                                          (3)r6c6-r6c3=(38)r3c34 *
                                                                           ||
                                                                          (3)r6c6-(3=81)r2c45 *
--------------
=> -1r3c4; ste

[pjb]

Hi Robert

Don't see the problem.
If the 8 at r2c2 is false, then an XY-wing exists which eliminates 3 from r3c3.
If the 8 at r2c2 is true, then the 3 at r3c8 is true following simple xy chain.
Either way, the 3 at r3c3 is false.

Phil

[Ajò Dimonios]

Hi Robert, Hi Phil

This can be seen, if we start and close the chain in r2c2 starting with 8 true in r2c2, as a discontinuous nice loop that eliminates 8 in r2c2.

Paolo

[pjb]

Hi Ajo

Good observation. The following chain eliminates 8 from r2c2:
(8=3)r3c3 - (3=1)r3c8 - (1=6)r2c7 - (6=8)r9c7 - (8=3)r9c5 - (3=8)r2c5 => -8 r2c2, yielding same position.
Simpler than invoking the xy-wing

Phil

[Mauriès Robert]

Hi Phil and Paolo,

Don't see the problem.
If the 8 at r2c2 is false, then an XY-wing exists which eliminates 3 from r3c3.
If the 8 at r2c2 is true, then the 3 at r3c8 is true following simple xy chain.
Either way, the 3 at r3c3 is false.

Thank you, Phil, that makes more sense.

The following chain eliminates 8 from r2c2:
(8=3)r3c3 - (3=1)r3c8 - (1=6)r2c7 - (6=8)r9c7 - (8=3)r9c5 - (3=8)r2c5 => -8 r2c2, yielding same position.
Simpler than invoking the xy-wing

This is in a way what I wanted to point out, we don't need the XY-wing to conclude, either by this chain starting on the strong link 8=3, or by noticing that the chain (8)r2c2 - (8=3)r2c5 - (3=8)r9c5 - (8=6)r9c7 - (6=1)r2c7 - (1=3)r3c8 allows us to conclude -8r2c2 since it corresponds to a contradiction in the r3c3 cell empty.
Robert

[Cenoman]

Hi Phil, Robert, Paolo

I am confused with the discussion about this puzzle solution.

Phil's first almost XY-wing is questioned, whereas to me this is no problem. Written as a kraken, Phil's chain reads:
(3)r2c2
(6)r2c2 - (6=1)r2c7 - (1=3)r3c8
(8)r2c2 - r2c5 = r9c5 - (8=6)r9c7 - (6=1)r2c7 - (1=3)r3c8
=> -3 r3c3;

So what ?
Of course, Paolo's suggested AIC is more aesthetic. Note one more simplification in r2c5, r9c5:
(8=3)r3c3 - (3=1)r3c8 - (1=6)r2c7 - (6=8)r9c7 - r9c5 = (8)r2c5 => -8 r2c2

Phil's second almost XY-wing is not questioned, whereas it should be !
Again, written as a kraken:
(4)r4c4 - r3c4 = r3c9 - (4=8)r6c9
(6)r4c4 - (6=5)r8c4 - (5=8)r7c6
(8)r4c4
=> -8r6c6; stte

No problem with the logic. The pattern is valid, so is the elimination. Note that an AIC does the same job
(8=4)r6c9 - r3c9 = r3c4 - (4=356)r1c146 - r6c1 = (6)r6c6 => -8 r6c6

My concern is the "stte" conclusion. I can't get a better result than five placements with 8r6c6 elimination (up to 52 solved cells) either with singles or with basics. Have I missed something ?
I guess that you need a third step to have the puzzle solved.

[eleven]

I just liked the xy-wing way, because it's a way to spot it. Ok, you can turn them into AIC's, but why should you ?
(and yes, its not stte)

[Mauriès Robert]

Hi Cenoman and Eleven,
My initial intervention with Phil was only to say that it is not useful to use the AIC to eliminate 3r3c3, the Almost XY wing is enough since if 8r2c2 is true, 3r3c3 is also eliminated. So I did not study Phil's resolution any further.
Robert