The New Sudoku Players' Forum

[denis_berthier]

Code: Select all

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

Code: Select all

     +-------+-------+-------+
     ! . . . ! . 9 . ! 2 . . !
     ! . 1 2 ! . . 7 ! . . . !
     ! . . . ! 8 . . ! 7 6 1 !
     +-------+-------+-------+
     ! . . . ! 4 . . ! . . . !
     ! . . 3 ! . . 5 ! 9 8 . !
     ! . . 6 ! 1 8 . ! . . 7 !
     +-------+-------+-------+
     ! 9 . . ! 3 . . ! . . 6 !
     ! 2 . . ! 9 . . ! 4 3 . !
     ! . 6 5 ! . . . ! . . . !
     +-------+-------+-------+
....9.2...12..7......8..761...4.......3..598...618...79..3....62..9..43..65...... #   620 FNBTXY C27.m
SER = 7.2, 27 givens

[pjb]

Code: Select all

 678     3478    478    | 56     9      1      | 2      45     3458   
 68      1       2      | 56     34     7      | 358    459    34589 
 45      3459   g49     | 8      234    234    | 7      6      1     
------------------------+----------------------+---------------------
f78      25789  f789    | 4     e237    239    | 6      1      235   
 1       247     3      |d27     6      5      | 9      8      24     
 45      2459    6      | 1      8      239    | 35     245    7     
------------------------+----------------------+---------------------
 9       478     1478   | 3      1257  b28     | 158    27     6     
 2       78      178    | 9      157    6      | 4      3      58     
 3       6       5      |c27     14    a48     | 18     279    29     


(4=8)r9c6 - (8=2)r7c6 - (2=7)r9c4 - (7)r5c4 = (7)r4c5 - (7=9)r4c13 - (9=4)r3c3 => -4 r3c6; stte

Phil

[AnotherLife]

Code: Select all

.------------------.----------------.-----------------.
| 678  3478   478  | 56  9     1    | 2    45   3458  |
| 68   1      2    | 56  a34   7    | 358  459  34589 |
| 45   3459   c49  | 8   a234  23-4 | 7    6    1     |
:------------------+----------------+-----------------:
| b78  25789  b789 | 4   a237  239  | 6    1    235   |
| 1    247    3    | 27  6     5    | 9    8    24    |
| 45   2459   6    | 1   8     239  | 35   245  7     |
:------------------+----------------+-----------------:
| 9    478    1478 | 3   1257  28   | 158  27   6     |
| 2    78     178  | 9   157   6    | 4    3    58    |
| 3    6      5    | 27  14    48   | 18   279  29    |
'------------------'----------------'-----------------'

(4)r3c6 - (4=7)r234c5 - (7=9)r4c13 - (9=4)r3c3 =>-4 r3c6; sste

[Hajime]

(4)r3c6 - (4=7)r234c5 - (7=9)r4c13 - (9=4)r3c3 =>-4 r3c6; sste

Whoaah, how did you find this?

[AnotherLife]

Whoaah, how did you find this?

Hello, Hajime,
Actually, this is an ALS XY-Wing, and I have used computer assistance as almost everybody on this forum.

[denis_berthier]

Resolution state after Singles and whips[1]:

Code: Select all

   +-------------------+-------------------+-------------------+
   ! 4678  3478  478   ! 56    9     1     ! 2     45    3458  !
   ! 468   1     2     ! 56    346   7     ! 358   459   34589 !
   ! 45    3459  49    ! 8     234   234   ! 7     6     1     !
   +-------------------+-------------------+-------------------+
   ! 578   25789 789   ! 4     237   239   ! 6     1     235   !
   ! 1     247   3     ! 267   267   5     ! 9     8     24    !
   ! 45    2459  6     ! 1     8     239   ! 35    245   7     !
   +-------------------+-------------------+-------------------+
   ! 9     478   1478  ! 3     1257  28    ! 158   257   6     !
   ! 2     78    178   ! 9     157   6     ! 4     3     58    !
   ! 3     6     5     ! 27    1247  248   ! 18    279   289   !
   +-------------------+-------------------+-------------------+
149 candidates.

1) Simplest-first solution:
naked-pairs-in-a-column: c1{r3 r6}{n4 n5} ==> r4c1 ≠ 5, r2c1 ≠ 4, r1c1 ≠ 4
naked-pairs-in-a-column: c4{r1 r2}{n5 n6} ==> r5c4 ≠ 6
hidden-single-in-a-block ==> r5c5 = 6
naked-triplets-in-a-block: b9{r7c7 r8c9 r9c7}{n1 n5 n8} ==> r9c9 ≠ 8, r7c8 ≠ 5
naked-triplets-in-a-row: r9{c4 c8 c9}{n2 n7 n9} ==> r9c6 ≠ 2, r9c5 ≠ 7, r9c5 ≠ 2
finned-swordfish-in-rows: n4{r7 r5 r1}{c3 c2 c9} ==> r2c9 ≠ 4
biv-chain[3]: r8c2{n7 n8} - r8c9{n8 n5} - r4n5{c9 c2} ==> r4c2 ≠ 7
biv-chain[4]: r7c6{n8 n2} - c4n2{r9 r5} - r5n7{c4 c2} - r8c2{n7 n8} ==> r7c2 ≠ 8, r7c3 ≠ 8
whip[1]: b7n8{r8c3 .} ==> r8c9 ≠ 8
singles ==> r8c9 = 5, r4c2 = 5, r6c1 = 4, r3c1 = 5, r5c9 = 4, r7c5 = 5
whip[1]: b9n8{r9c7 .} ==> r2c7 ≠ 8
finned-x-wing-in-columns: n2{c9 c4}{r9 r4} ==> r4c6 ≠ 2, r4c5 ≠ 2
stte

2) 1-step solutions:
There are 11 W1-anti-backdoors: n1r9c7 n8r9c6 n4r9c5 n7r9c4 n7r7c8 n2r7c6 n2r5c4 n4r3c6 n5r2c4 n6r2c1 n6r1c4
6 of them give rise to a single step solution with whips, but most of them require long whips (of length ≥9). The simplest is with a whip[8]:
whip[8]: r3n2{c6 c5} - r3n3{c5 c2} - b2n3{r3c6 r2c5} - r4c5{n3 n7} - r5n7{c5 c2} - r8c2{n7 n8} - r7c2{n8 n4} - r1c2{n4 .} ==> r3c6 ≠ 4
stte

Notice that this is a really 1-step solution, with no "basic" steps before it. Whence the longer length of the chain necessary for the elimination.

[AnotherLife]

whip[8]: r3n2{c6 c5} - r3n3{c5 c2} - b2n3{r3c6 r2c5} - r4c5{n3 n7} - r5n7{c5 c2} - r8c2{n7 n8} - r7c2{n8 n4} - r1c2{n4 .} ==> r3c6 ≠ 4
stte

Notice that this is a really 1-step solution, with no "basic" steps before it. Whence the longer length of the chain necessary for the elimination.

Actually, this is a basic-step finish (two whips[1] and a locked pair still needed).

The same elimination can be reached via this AIC with ALS's: (4)r3c6 - (4=3)r3c123 - (3=2)r1578c2 - r5c4 = r9c4 - (2=4)r79c6 =>-4 r3c6; bste

Code: Select all

.-------------------.-----------------.-----------------.
| 4678  b3478  478  | 56   9     1    | 2    45   3458  |
| 468   1      2    | 56   346   7    | 358  459  34589 |
| a45   a3459  a49  | 8    234   23-4 | 7    6    1     |
:-------------------+-----------------+-----------------:
| 578   25789  789  | 4    237   239  | 6    1    235   |
| 1     b247   3    | c267  267   5   | 9    8    24    |
| 45    2459   6    | 1    8     239  | 35   245  7     |
:-------------------+-----------------+-----------------:
| 9     b478   1478 | 3    1257  e28  | 158  257  6     |
| 2     b78    178  | 9    157   6    | 4    3    58    |
| 3     6      5    | d27  1247  e248 | 18   279  289   |
'-------------------'-----------------'-----------------'

[denis_berthier]

whip[8]: r3n2{c6 c5} - r3n3{c5 c2} - b2n3{r3c6 r2c5} - r4c5{n3 n7} - r5n7{c5 c2} - r8c2{n7 n8} - r7c2{n8 n4} - r1c2{n4 .} ==> r3c6 ≠ 4
stte
Notice that this is a really 1-step solution, with no "basic" steps before it. Whence the longer length of the chain necessary for the elimination.

Actually, this is a basic-step finish (two whips[1] and a locked pair still needed).

No. Not if you start from the PM after Singles and whips[1], as I wrote. Only Singles and whips[1] are needed after this elimination. Which is not surprising as n4r3c6 is a W1-anti-backdoor.

The same elimination can be reached via this AIC with ALS's: (4)r3c6 - (4=3)r3c123 - (3=2)r1578c2 - r5c4 = r9c4 - (2=4)r79c6 =>-4 r3c6; bste

This chain is longer than mine (inner Subsets of size k have to be counted as adding length k).

[yzfwsf]

r3n2{c6 c5} - r3c3{n4 n9} - r3c1(n4 n5) - b2n3{r3c6 r2c5} - r4c5{n3 n7} - r5c3{n7 n8} - r1c2{n8 .} ==> r3c6 ≠ 4
Is this one whip(7)?

[denis_berthier]

r3n2{c6 c5} - r3c3{n4 n9} - r3c1(n4 n5) - b2n3{r3c6 r2c5} - r4c5{n3 n7} - r5c3{n7 n8} - r1c2{n8 .} ==> r3c6 ≠ 4
Is this one whip(7)?

In which resolution state?
In the RS I used, i.e.:

Code: Select all

   +-------------------+-------------------+-------------------+
   ! 4678  3478  478   ! 56    9     1     ! 2     45    3458  !
   ! 468   1     2     ! 56    346   7     ! 358   459   34589 !
   ! 45    3459  49    ! 8     234   234   ! 7     6     1     !
   +-------------------+-------------------+-------------------+
   ! 578   25789 789   ! 4     237   239   ! 6     1     235   !
   ! 1     247   3     ! 267   267   5     ! 9     8     24    !
   ! 45    2459  6     ! 1     8     239   ! 35    245   7     !
   +-------------------+-------------------+-------------------+
   ! 9     478   1478  ! 3     1257  28    ! 158   257   6     !
   ! 2     78    178   ! 9     157   6     ! 4     3     58    !
   ! 3     6     5     ! 27    1247  248   ! 18    279   289   !
   +-------------------+-------------------+-------------------+

cell r5c3 is decided; it can't be part of a whip.

[yzfwsf]

r3n2{c6 c5} - r3c3{n4 n9} - r3c1(n4 n5) - b2n3{r3c6 r2c5} - r4c5{n3 n7} - r5c3{n7 n8} - r1c2{n8 .} ==> r3c6 ≠ 4
Is this one whip(7)?

In which resolution state?
In the RS I used, i.e.:

Code: Select all

   +-------------------+-------------------+-------------------+
   ! 4678  3478  478   ! 56    9     1     ! 2     45    3458  !
   ! 468   1     2     ! 56    346   7     ! 358   459   34589 !
   ! 45    3459  49    ! 8     234   234   ! 7     6     1     !
   +-------------------+-------------------+-------------------+
   ! 578   25789 789   ! 4     237   239   ! 6     1     235   !
   ! 1     247   3     ! 267   267   5     ! 9     8     24    !
   ! 45    2459  6     ! 1     8     239   ! 35    245   7     !
   +-------------------+-------------------+-------------------+
   ! 9     478   1478  ! 3     1257  28    ! 158   257   6     !
   ! 2     78    178   ! 9     157   6     ! 4     3     58    !
   ! 3     6     5     ! 27    1247  248   ! 18    279   289   !
   +-------------------+-------------------+-------------------+

cell r5c3 is decided; it can't be part of a whip.

Yes,use your resolution state.
I found that the 7 truths pattern can indeed delete r3c6 effectively. If it were to be written in whip form, what should it look like?

Xsudo's analysis of these 7 truths is as follows
7 Truths = {2R3 3N13 4N135 3B2}
8 Links = {4r3 7r4 5c1 9c3 23c5 3n6 8b4}
1 Elimination --> r3c6<>4

[denis_berthier]

Yes,use your resolution state.
I found that the 7 truths pattern can indeed delete r3c6 effectively. If it were to be written in whip form, what should it look like?

Xsudo's analysis of these 7 truths is as follows
7 Truths = {2R3 3N13 4N135 3B2}
8 Links = {4r3 7r4 5c1 9c3 23c5 3n6 8b4}
1 Elimination --> r3c6<>4

There's no whip[7] based on n4r3c6.
Given a whip, there's not necessarily an Xsudo set cover pattern to account for it. Conversely, given an Xsudo set cover pattern, there's not necessarily a whip to account for it.

I can't answer in detail about this case, as notations such as 3N13 (or 3N1 3N3) make no sense to me. What are the digits after the N supposed to refer to: rows, columns...?

[yzfwsf]

xNy is equivalent to rxcy; for example, 3N1=r3c1

[denis_berthier]

xNy is equivalent to rxcy; for example, 3N1=r3c1

Even now, I can't guess what the other symbols mean: 2R3, 3B2, 5c1... There's a total lack of consistency in this notation.

[yzfwsf]

xNy is equivalent to rxcy; for example, 3N1=r3c1

Even now, I can't guess what the other symbols mean: 2R3, 3B2, 5c1... There's a total lack of consistency in this notation.

2R3=r3n2(L R)
3B2=b2n3(L R)
5C1=c1n5(L R)