The New Sudoku Players' Forum

[P.O.]

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2  9  .  1  .  .  .  6  .
.  1  .  .  .  2  .  .  .
8  .  3  .  6  .  .  .  2
.  4  .  7  .  .  .  9  3
.  .  7  .  1  .  .  4  .
.  .  .  .  4  3  5  .  .
.  .  .  .  .  4  .  .  1
5  .  .  .  2  1  .  3  .
.  2  1  6  .  .  8  5  .

29.1...6..1...2...8.3.6...2.4.7...93..7.1..4.....435.......4..15...21.3..216..85.

2      9      45     1      3578   578    347    6      4578           
467    1      456    34589  35789  2      3479   78     45789           
8      57     3      459    6      579    1479   17     2               
16     4      2568   7      58     568    126    9      3               
369    3568   7      2589   1      5689   26     4      68             
169    68     2689   289    4      3      5      1278   678             
3679   3678   689    3589   35789  4      2679   27     1               
5      678    4689   89     2      1      4679   3      4679           
3479   2      1      6      379    79     8      5      479       


[jco]

Code: Select all

.--------------------------------------------------------------------.
| 2      9      45     | 1      3578   578    | 347    6      4578   |
|b467    1      456    | 34589  35789  2      | 3479   78     45789  |
| 8     c57     3      | 459    6      579    | 1479   17     2      |
|----------------------+----------------------+----------------------|
| 16     4      2568   | 7      58     568    | 126    9      3      |
|e369   d3568   7      | 2589   1      5689   | 26     4      68     |
| 169    68     2689   | 289    4      3      | 5      1278   678    |
|----------------------+----------------------+----------------------|
| 3679   3678   689    | 3589   35789  4      | 2679   27     1      |
| 5      678    4689   | 89     2      1      | 4679   3      4679   |
|a479-3  2      1      | 6      379    79     | 8      5      479    |
'--------------------------------------------------------------------'

1. (4)r9c1 = (4-7)r2c1 = (7-5)r3c2 = (5-3)r5c2 = (3)r5c1 => -3 r9c1 [4 placements]
-----

Code: Select all

.--------------------------------------------------------------------.
| 2      9      45*    | 1      578    578    | 3      6      4578*  |
|f47-6*  1      45+6   | 3      5789   2      | 479    78     45789  |
| 8     e57     3      | 4      6      579    |c179   d17     2      |
|----------------------+----------------------+----------------------|
|a16     4      2568   | 7      58     568    |b126    9      3      |
| 369    3568   7      | 2589   1      5689   | 26     4      68     |
| 169    68     2689   | 289    4      3      | 5      1278   678    |
|----------------------+----------------------+----------------------|
| 3679   3678   689    | 589    5789   4      | 2679   27     1      |
| 5      678    4689   | 89     2      1      | 4679   3      4679   |
| 479*   2      1      | 6      3      79     | 8      5      79-4   |
'--------------------------------------------------------------------'

2. (6=1)r4c1 - (1)r4c7 = (1)r3c7 - (1=7)r3c8 - (7)r3c2 = (7)r2c1 => -6 r2c1 [+6 r2c3]
3. Kite (4): r9c1 = r2c1 - r1c3 = 4r1c9 => -4 r9c9; ste

[P.O.]

thank you for your answer, my solution:

Code: Select all

1r4c7 => r1c379 <> 4
 r4c7=1 - r4c1{n1 n6} - 58r4c56 - b4n5{r4c3 r5c2} - r3c2{n5 n7} - r2c1{n67 n4} - r9n4{c1 c9}
 r4c7=1 - r4c1{n1 n6} - 58r4c56 - b4n5{r4c3 r5c2} - c2n3{r5 r7} - c4n3{r7 r2} - r1n3{c5 c7}
 
=> r4c7 <> 1
ste.


[Hajime]

Code: Select all

+--------------+----------------+---------------+ 
|  2    9   45 |  1    3578  578| 347   6   4578| 
| 467   1   456|34589 35789   2 |3479  78  45789| 
|  8   57    3 | 459    6    579|1479  17    2  | 
+--------------+----------------+---------------+ 
| 1-6   4 a2568|  7    a58  a568| 126   9    3  | 
| 369 3568   7 | 2589   1   5689| 26    4    68 | 
| 169 a68  2689| 289    4     3 |  5  1278  678 | 
+--------------+----------------+---------------+ 
|3679 3678  689| 3589 35789   4 |2679  27    1  | 
|  5   678 4689|  89    2     1 |4679   3   4679| 
|3479   2    1 |  6    379   79 |  8    5   479 | 
+-----------------------------------------------+ 

WXYZ-Wing on a{2568} b4r4 => (-6)r4c1; stte
[not yet proper eureka notation]

[Hajime]

The plan was....
WXYZ-Wing on "a"-marked cells with candidates {2568}
Hinge cell is r4c3, wing at r4c56 and other wing at r6c2 .
Candidate 9 is the Z in WXYZ method . (-6)r4c1; stte

I see now that according to the definition of WXYZ wing there are two
"non-restricted common digit"s 6 and 8 in stead of 1

But r4c1 sees al the 4 cells that has 4 candidates. Was I lucky?

[jco]

Code: Select all

+---------------+----------------+---------------+
|  2    9    45 |  1    3578  578| 347   6   4578|
| 467   1    456|34589 35789   2 |3479  78  45789|
|  8   57     3 | 459    6    579|1479  17    2  |
+---------------+----------------+---------------+
| 1-6   4  a2568|  7    a58  a568| 126   9    3  |
| 369 3568    7 | 2589   1   5689| 26    4    68 |
| 169 a*2*6 2689| 289    4     3 |  5  1278  678 |
+---------------+----------------+---------------+
|3679 3678   689| 3589 35789   4 |2679  27    1  |
|  5   678  4689|  89    2     1 |4679   3   4679|
|3479   2     1 |  6    379   79 |  8    5   479 |
+------------------------------------------------+

I see it working if you had (26)r6c2 instead of (68)r6c2 (as depicted above).
The logic would be: either (6)r6c2 or (568) would be locked at r4c356,
so in any case (6)r4c1 is false.

[Hajime]

But there is already a 2 in column 2. So 26 can not be in r6c2.

[DonM]

It’s rare to see WXYZ-wing used. I’m always interested in learning something new about rare patterns. My understanding has been that there are 2 ways to test if a WXYZ pattern is valid depending on whether it is type 1 or 2. (I think there are some rare variants.)

Anyway, test 1 requires showing that if the various digits in the hinge cell were placed, the Z digit in the pattern would remove the Z digit in the target cell r4c1. In this case, in the hinge cell r4c3, the test works for three of the digits, but not the digit 2. If r4c3 was 2 then you would have a naked pair 16 in r4c1,r4c7. The 6 in r4c1 would not be eliminated.

The alternative test would be that no matter what the placement in r4c2, 6 would be eliminated in r4c1: the placement of one digit, 6, in r4c2 (26) would eliminate 6 in r4c1 and the placement of the other digit (2 here) would have to create a locked set in the other 3 cells in row 4 which would also eliminate 6 in r4c1 -which it doesn’t here.

I could be missing something and am always ready to learn.

[jco]

But there is already a 2 in column 2. So 26 can not be in r6c2.

I know. My point is that if in that cell your had (26) instead of (68) at r6c2
(forget for the moment that you have (2)r9c2), then that idea would work.
In the actual configuration that WXYZ idea does not seem to work because you
don't get a locked set if (6)r6c2 is false.
Alternatively, for the puzzle configuration if r4c1=6 no contradiction arises, while in a proper WXYZ that would
lead to some contradiction.

PS: in that hypothetical illustrative situation, one would get three cells in row 4 with only (58) in each, if r4c1=6.