17March25

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17March25

Postby Yogi » Sun Mar 16, 2025 7:33 pm

000051000040000030000000000070430600500000102000000000200800000000300070108000000
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Re: 17March25

Postby Cenoman » Sun Mar 16, 2025 10:25 pm

Code: Select all
 +-----------------------+----------------------+-----------------------+
 |  3      2689   269    |  2679   5      1     |  4789   269    4679   |
 |  679    4      2569   |  2679   6789   689   |  579    3      1      |
 |  6789   1      2569   |  2679   4      3     |  5789   2569   5679   |
 +-----------------------+----------------------+-----------------------+
 |  89     7      1      |  4      3      2     |  6      589    59     |
 |  5     e689    3      | f679   f6789  f689   |  1      4      2      |
 |  4689   2689   2469   |  1      8-69   5     |  37     89     37     |
 +-----------------------+----------------------+-----------------------+
 |  2     d369    7      |  8     a69     4     |  359    1      3569   |
 | c469    5     c469    |  3      1     b69    |  2      7      8      |
 |  1     d369    8      |  5      2      7     |  349    69     3469   |
 +-----------------------+----------------------+-----------------------+

Remote Pair (69)[r7c5 = r8c6 - r8c13 = r79c2 - r5c2 = r5c456] => -69 r6c5; ste
(Double Empty Rectangle b7 with group pairs (6,9) @ b8, r5)
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Re: 17March25

Postby P.O. » Mon Mar 17, 2025 5:56 pm

basics:
Hidden Text: Show
Code: Select all
( n1r6c4   n1r4c3   n2r4c6   n3r3c6   n4r3c5   n5r6c6   n5r9c4
  n7r7c3   n1r2c9   n1r3c2   n1r7c8   n1r8c5   n2r9c5   n2r8c7
  n7r9c6   n8r8c9 )

intersections:
((((8 0) (2 5 2) (6 7 8 9)) ((8 0) (2 6 2) (6 8 9)))
 (((7 0) (6 7 6) (3 4 7 8 9)) ((7 0) (6 9 6) (3 4 7 9)))
 (((5 0) (7 7 9) (3 4 5 9)) ((5 0) (7 9 9) (3 4 5 6 9)))
 (((5 0) (7 2 7) (3 6 9)) ((5 0) (8 2 7) (5 6 9)))
 (((4 0) (9 7 9) (3 4 9)) ((4 0) (9 8 9) (4 6 9)) ((4 0) (9 9 9) (3 4 6 9)))
 (((4 0) (8 1 7) (4 6 9)) ((4 0) (8 3 7) (4 6 9)))
 (((3 0) (7 2 7) (3 6 9)) ((3 0) (9 2 7) (3 6 9)))
 (((3 0) (6 7 6) (3 4 7 8 9)) ((3 0) (6 9 6) (3 4 7 9)))
 ( n5r8c2   n4r5c8   n4r7c6   n3r1c1   n3r5c3 ))

TRIPLET BOX: ((4 8 6) (5 8 9)) ((4 9 6) (5 9)) ((6 8 6) (8 9))
(((6 7 6) (3 7 8 9)) ((6 9 6) (3 7 9)))

intersection:
((((8 0) (1 7 3) (4 7 8 9)) ((8 0) (3 7 3) (5 7 8 9))))

Code: Select all
3     2689  269   2679  5     1     4789  269   4679           
679   4     2569  2679  6789  689   579   3     1             
6789  1     2569  2679  4     3     5789  2569  5679           
89    7     1     4     3     2     6     589   59             
5     689   3     679   6789  689   1     4     2             
4689  2689  2469  1     689   5     37    89    37             
2     369   7     8     69    4     359   1     3569           
469   5     469   3     1     69    2     7     8             
1     369   8     5     2     7     349   69    3469           

9r7c2579 => r5c2 <> 6,9
 r7c2=9  - r7c5{n9 n6} - b5n6{r56c5 r5c46} - r5c2{n69 n8}
 r7c5=9  - r8c6{n9 n6} - b7n6{r8c13 r79c2} - b4n6{r56c2 r6c13} - r6c5{n69 n8} - r5n8{c56 c2}
 r5c79=9 - r9n9{c789 c2} - r7c5{n9 n6} - b5n6{r56c5 r5c46} - r5c2{n69 n8}
ste.
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Re: 17March25

Postby rjamil » Wed Mar 19, 2025 1:56 am

Code: Select all
 +---------------------+-----------------+---------------------+
 | 36789  23689  2369  | 2679  5     1   | 4789   24689  4679  |
 | 6789   4      2569  | 2679  6789  689 | 5789   3      1     |
 | 6789   1      2569  | 2679  4     3   | 5789   25689  5679  |
 +---------------------+-----------------+---------------------+
 | 89     7      1     | 4     3     2   | 6      589    59    |
 | 5      3689   3469  | 679   6789  689 | 1      489    2     |
 | 34689  23689  23469 | 1     6789  5   | 34789  489    3479  |
 +---------------------+-----------------+---------------------+
 | 2      3569   7     | 8     69    469 | 3459   1      34569 |
 | 469    569    4569  | 3     1     469 | 2      7      8     |
 | 1      369    8     | 5     2     7   | 349    469    3469  |
 +---------------------+-----------------+---------------------+

Single-digit POM: 3 @ r1c123 r2c8 r3c6 r4c5 r5c23 r6c12379 r7c279 r8c4 r9c279
Digit 3 not in 4 Templates => -3 @ r1c2 r1c3 r5c2 r6c1 r6c2 r6c3
Digit 3 in all 4 Templates => 3 @ r1c1 r5c3

Single-digit POM: 4 @ r1c789 r2c2 r3c5 r4c4 r5c8 r6c13789 r7c679 r8c136 r9c789
Digit 4 not in 4 Templates => -4 @ r1c8 r6c7 r6c8 r6c9 r7c7 r7c9 r8c6 r9c8
Digit 4 in all 4 Templates => 4 @ r5c8 r7c6

Single-digit POM: 5 @ r1c5 r2c37 r3c3789 r4c89 r5c1 r6c6 r7c279 r8c23 r9c4
Digit 5 not in 4 Templates => -5 @ r7c2 r8c3
Digit 5 in all 4 Templates => 5 @ r8c2

Single-digit POM: 6 @ r1c23489 r2c13456 r3c13489 r4c7 r5c2456 r6c1235 r7c259 r8c136 r9c289
Digit 6 not in 58 Templates => -6 @ r5c2 r6c5

Single-digit POM: 7 @ r1c479 r2c1457 r3c1479 r4c2 r5c45 r6c579 r7c3 r8c8 r9c6
Digit 7 not in 9 Templates => -7 @ r6c5

Single-digit POM: 8 @ r1c278 r2c1567 r3c178 r4c18 r5c256 r6c12578 r7c4 r8c9 r9c3
Digit 8 not in 9 Templates => -8 @ r1c8 r2c1 r2c7

Single-digit POM: 9 @ r1c234789 r2c134567 r3c134789 r4c189 r5c2456 r6c1235789 r7c2579 r8c136 r9c2789
Digit 9 not in 225 Templates => -9 @ r5c2 r6c5

stte.

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Re: 17March25

Postby pjb » Thu Mar 20, 2025 8:19 am

My take on the pattern overlay method:
Code: Select all
 3       2689    269    | 2679   5      1      | 4789   269    4679   
 679     4       2569   | 2679   6789   689    | 579    3      1     
 6789    1       2569   | 2679   4      3      | 5789   2569   5679   
------------------------+----------------------+---------------------
 89      7       1      | 4      3      2      | 6      589    59     
 5       689     3      | 679    6789   689    | 1      4      2     
 4689    2689    2469   | 1      689    5      | 37     89     37     
------------------------+----------------------+---------------------
 2       369     7      | 8      69     4      | 359    1      3569   
 469     5       469    | 3      1      69     | 2      7      8     
 1       369     8      | 5      2      7      | 349    69     3469   

No pattern of 6 includes r5c2 or r6c5 so 6 can be deleted from r5c2 and r6c5 =>
Naked pairs of 89 at r6c58 => -8 r6c12, -9 r6c123
Then
All patterns of 9 include r4c1 so this can be made equal to 9; stte

Phil
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Re: 17March25

Postby rjamil » Thu Mar 20, 2025 7:11 pm

pjb wrote:My take on the pattern overlay method:
---
No pattern of 6 includes r5c2 or r6c5 so 6 can be deleted from r5c2 and r6c5 =>
Naked pairs of 89 at r6c58 => -8 r6c12, -9 r6c123
Then
All patterns of 9 include r4c1 so this can be made equal to 9; stte

Phil

Hi pjb,

Thanks for sharing your POM solution. At first glance, it's seems to me that it contain first occurrance of POM elimination/placement move at a time. However, My solution found digit 3 both, i.e., elimination and placement move first. Could you please explain how you get digit 6 elimination first?

R. Jamil

Ok. After checking in your online solver, got following steps:
Code: Select all
3s at r5c23 only ones in row/column => -3 r6c123.
4s at r9c79 only ones in row/column => -4 r7c79.
Naked triplets of 589 at r4c89, r6c8 => -8 r6c7, -9 r6c79

5s at r8c23 only ones in row/column => -5 r7c2.
Naked pairs of 37 at r6c79 => -7 r6c5

8s at r123c7 only ones in row/column => -8 r13c8.
8s at r2c56 only ones in box => -8 r2c17.
No pattern of 6 includes r5c2, r6c5 so 6 can be deleted from r5c2, r6c5
Naked pairs of 89 at r6c58 => -8 r6c12, -9 r6c123

All patterns of 9 include r4c1 so this can be made equal to 9

Hense, it is clear now.
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Re: 17March25

Postby denis_berthier » Fri Mar 21, 2025 4:04 am

.
If you want a solution by templates, here one in T1, with two non-whip[1] templates[1]:

Code: Select all
Resolution state after Singles and whips[1]:
   +-------------------+-------------------+-------------------+
   ! 3     2689  269   ! 2679  5     1     ! 4789  2689  4679  !
   ! 679   4     2569  ! 2679  6789  689   ! 579   3     1     !
   ! 6789  1     2569  ! 2679  4     3     ! 5789  25689 5679  !
   +-------------------+-------------------+-------------------+
   ! 89    7     1     ! 4     3     2     ! 6     589   59    !
   ! 5     689   3     ! 679   6789  689   ! 1     4     2     !
   ! 4689  2689  2469  ! 1     689   5     ! 3789  89    379   !
   +-------------------+-------------------+-------------------+
   ! 2     369   7     ! 8     69    4     ! 359   1     3569  !
   ! 469   5     469   ! 3     1     69    ! 2     7     8     !
   ! 1     369   8     ! 5     2     7     ! 349   69    3469  !
   +-------------------+-------------------+-------------------+
145 candidates.


candidate in no template[1] for digit 9 ==> r6c5≠9
whip[1]: b5n9{r5c6 .} ==> r5c2≠9
candidate in no template[1] for digit 6 ==> r6c5≠6
stte
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