The New Sudoku Players' Forum

[P.O.]

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

7.4...5.....5..84..9..47.....9...623.5.3.......1..4....12..3.8....7.1....6......9


[marek stefanik]

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.------------------.------------------.----------------.
| 7     a238   4   | 1268  1238  268  | 5    9    126  |
| 1236  a23   a36  | 5     1239  269  | 8    4    7    |
| 12568  9     568 | 1268  4     7    | 123  136  126  |
:------------------+------------------+----------------:
|c48     47–8  9   | 18    1578  58   | 6    2    3    |
| 268    5    b68  | 3     2789  2689 | 14   17   148  |
| 2368   237–8 1   | 268   278   4    | 9    57   58   |
:------------------+------------------+----------------:
|d45     1     2   | 9     56    3    | 7    8    456  |
| 9     e34–8  358 | 7     2568  1    | 234  356  2456 |
| 358    6     7   | 4     258   258  | 123  135  9    |
'------------------'------------------'----------------'

(8=236)b1p256 – (6=8*)r5c3 – (8=4)r4c1 – 4r7c1 = 4r8c2 => –8r8c2, –8r46c2*, stte

Marek

[denis_berthier]

.
SER = 8.3

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Resolution state after Singles and whips[1]:
   +-------------------+-------------------+-------------------+
   ! 7     238   4     ! 1268  1238  268   ! 5     9     126   !
   ! 1236  23    36    ! 5     1239  269   ! 8     4     7     !
   ! 12568 9     568   ! 1268  4     7     ! 123   136   126   !
   +-------------------+-------------------+-------------------+
   ! 48    478   9     ! 18    1578  58    ! 6     2     3     !
   ! 268   5     68    ! 3     2789  2689  ! 14    17    148   !
   ! 2368  2378  1     ! 268   278   4     ! 9     57    58    !
   +-------------------+-------------------+-------------------+
   ! 45    1     2     ! 9     56    3     ! 7     8     456   !
   ! 9     348   358   ! 7     2568  1     ! 234   356   2456  !
   ! 358   6     7     ! 4     258   258   ! 123   135   9     !
   +-------------------+-------------------+-------------------+
146 candidates.

Here are 3 solutions from SudoRules, illustrating the trade-off between number of steps and length of the longest chain.

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***********************************************************************************************
***  SudoRules 20.1.s based on CSP-Rules 2.1.s, config = W+O+SFin
***  Using CLIPS 6.32-r813
***  Copyright Denis Berthier
***  Download from: https://github.com/denis-berthier/CSP-Rules-V2.1
***********************************************************************************************

1) Simplest-first solution in Z4 (using only short elementary reversible chains):

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biv-chain[3]: r6n6{c4 c1} - r5c3{n6 n8} - b6n8{r5c9 r6c9} ==> r6c4≠8
z-chain[3]: c6n9{r2 r5} - b5n6{r5c6 r6c4} - c4n2{r6 .} ==> r2c6≠2
     with z-candidates = n2r3c4 n2r1c4
z-chain[3]: r2n2{c2 c5} - c4n2{r1 r6} - c2n2{r6 .} ==> r3c1≠2
     with z-candidates = n2r2c1 n2r3c4 n2r2c2 n2r1c2
biv-chain[4]: r5c3{n6 n8} - r4c1{n8 n4} - r7c1{n4 n5} - b1n5{r3c1 r3c3} ==> r3c3≠6
z-chain[4]: c1n1{r3 r2} - b1n6{r2c1 r2c3} - c3n3{r2 r8} - c3n5{r8 .} ==> r3c1≠5
     with z-candidates = n6r3c1 n5r3c3
hidden-single-in-a-block ==> r3c3=5
biv-chain[3]: c3n8{r8 r5} - r4c1{n8 n4} - b7n4{r7c1 r8c2} ==> r8c2≠8
biv-chain[3]: r8n8{c5 c3} - c3n3{r8 r2} - b2n3{r2c5 r1c5} ==> r1c5≠8
biv-chain[3]: c3n3{r2 r8} - b7n8{r8c3 r9c1} - b1n8{r3c1 r1c2} ==> r1c2≠3
hidden-single-in-a-row ==> r1c5=3
biv-chain[3]: c5n9{r5 r2} - c5n1{r2 r4} - r4c4{n1 n8} ==> r5c5≠8
z-chain[3]: b3n2{r3c9 r1c9} - r1c2{n2 n8} - r3n8{c1 .} ==> r3c4≠2
     with z-candidates = n2r3c7 n8r3c4
whip[1]: r3n2{c9 .} ==> r1c9≠2
biv-chain[4]: r5c3{n8 n6} - b5n6{r5c6 r6c4} - c4n2{r6 r1} - r1c2{n2 n8} ==> r4c2≠8, r6c2≠8
stte

(I haven't tried to reduce the number of steps in Z4, but it could probably be.)

[Edit:] Indeed, here is a 3-step solution in Z4:

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z-chain[4]: r2c2{n2 n3} - r6n3{c2 c1} - r6n6{c1 c4} - c4n2{r6 .} ==> r2c5≠2, r2c6≠2
     with z-candidates = n2r3c4 n2r1c4
whip[1]: r2n2{c2 .} ==> r1c2≠2, r3c1≠2

biv-chain[3]: r1c2{n8 n3} - r2c3{n3 n6} - r5c3{n6 n8} ==> r6c2≠8, r3c3≠8, r4c2≠8

biv-chain[3]: r4c1{n8 n4} - b7n4{r7c1 r8c2} - c2n8{r8 r1} ==> r3c1≠8
stte

2) 2-step solution in W5:

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whip[5]: r2c2{n2 n3} - r6n3{c2 c1} - r6n6{c1 c4} - c4n2{r6 r3} - b3n2{r3c7 .} ==> r1c2≠2
whip[5]: r2c3{n3 n6} - r5c3{n6 n8} - c2n8{r6 r8} - c2n4{r8 r4} - r4c1{n4 .} ==> r1c2≠3
stte

3) 3-step solution in Z5:

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z-chain[4]: r2c2{n2 n3} - r6n3{c2 c1} - r6n6{c1 c4} - c4n2{r6 .} ==> r2c5≠2, r2c6≠2
     with z-candidates = n2r3c4 n2r1c4
whip[1]: r2n2{c2 .} ==> r1c2≠2, r3c1≠2

z-chain[5]: c3n3{r8 r2} - r1c2{n3 n8} - b7n8{r8c2 r9c1} - r4c1{n8 n4} - r7c1{n4 .} ==> r8c3≠5
     with z-candidates = n8r8c3 n5r7c1
hidden-single-in-a-column ==> r3c3=5

z-chain[5]: r4c1{n8 n4} - r7c1{n4 n5} - r9c1{n5 n3} - r6n3{c1 c2} - r1c2{n3 .} ==> r3c1≠8
     with z-candidates = n8r9c1 n8r1c2
stte

[eleven]

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 *---------------------------------------------------------------------*
 |  7       8-23   4     |  1268   1238   268    |  5     9     126    |
 |  1236  ca23    c36    |  5      1239   269    |  8     4     7      |
 |  12568   9      568   |  1268   4      7      |  123   136   126    |
 |-----------------------+-----------------------+---------------------|
 |  48      478    9     |  18     1578   58     |  6     2     3      |
 | b268     5     c68    |  3      2789   2689   |  14    17    148    |
 | b2368   a23+78  1     |  268    278    4      |  9     57    58     |
 |-----------------------+-----------------------+---------------------|
 |  45      1      2     |  9      56     3      |  7     8     456    |
 |  9       348    358   |  7      2568   1      |  234   356   2456   |
 |  358     6      7     |  4      258    258    |  123   135   9      |
 *---------------------------------------------------------------------*

23r26c2 = (23-6)r45c1 = r5c3 - (6=32)r2c23 => -23r1c2, stte

[AnotherLife]

.
SER = 8.3

Hi Denis,
In the latest release of Sukaku Explainer this puzzle is rated SER 6.4, which is more appropriate to the fact that it is solvable by a standard pattern and a basic AIC. It is good that some changes have already been made to the current rating system.

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.--------------------.------------------.----------------.
| 7      a238   4    | 1268  1238  268  | 5    9    126  |
| 1236   a23    a36  | 5     1239  269  | 8    4    7    |
| 12568  9      56-8 | 1268  4     7    | 123  136  126  |
:--------------------+------------------+----------------:
| 48     47-8   9    | 18    1578  58   | 6    2    3    |
| 268    5      b68  | 3     2789  2689 | 14   17   148  |
| 2368   237-8  1    | 268   278   4    | 9    57   58   |
:--------------------+------------------+----------------:
| 45     1      2    | 9     56    3    | 7    8    456  |
| 9      348    358  | 7     2568  1    | 234  356  2456 |
| 358    6      7    | 4     258   258  | 123  135  9    |
'--------------------'------------------'----------------'

1. WXYZ-Wing
(8=236)b1p256 - (6=8)r5c3 => -8 r3c3, r4c2, r6c2

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.-------------------.------------------.----------------.
| 7       a238  4   | 1268  1238  268  | 5    9    126  |
| 1236    23    36  | 5     1239  269  | 8    4    7    |
| 1256-8  9     56  | 1268  4     7    | 123  136  126  |
:-------------------+------------------+----------------:
| d48     c47   9   | 18    1578  58   | 6    2    3    |
| 268     5     68  | 3     2789  2689 | 14   17   148  |
| 2368    237   1   | 268   278   4    | 9    57   58   |
:-------------------+------------------+----------------:
| 45      1     2   | 9     56    3    | 7    8    456  |
| 9       b348  358 | 7     2568  1    | 234  356  2456 |
| 358     6     7   | 4     258   258  | 123  135  9    |
'-------------------'------------------'----------------'

2. Basic AIC
(8)r1c2 = (8-4)r8c2 = r4c2 - (4=8)r4c1 => -8 r3c1, ste

[denis_berthier]

Almost none of the rules used by SE is standard by any means.
The only interest of Sudoku Explainer is, it was a common reference for everybody. The idea of making local changes to it is the most stupid one I ever heard.

[AnotherLife]

Difficulty rating

EDIT
I cannot attach the image to the post because the board attachment quota has been reached. I don't understand what's wrong with yandex.ru server for some participants of the forum.

[P.O.]

same as what i found: n8r1c2 is a backdoor, the solutions exploit this fact by making it a naked-single or a hidden-single;

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after singles and intersections:

 7       a(23)±8   4      1268   1238   268    5      9      126             
 1236    a(23)    b-3+6   5      1239   269    8      4      7               
 1256×8   9        56×8   1268   4      7      123    136    126             
c(48)     47×8     9      18     1578   58     6      2      3               
 268      5       c6+8    3      2789   2689   14     17     148             
 2368     237×8    1      268    278    4      9      57     58             
c(45)     1        2      9      56     3      7      8      456             
 9        348     b+358   7      2568   1      234    356    2456           
c3(58)    6        7      4      258    258    123    135    9               
       
                    / r2c3{n3 n6} - r5c3{n6 n8} => r3c3 r4c2 r6c2 <> 8
c2{r1n8 r1r2n2n3} -
                    \ c3n3{r2 r8} - c1{r4r7r9}{n4n5n8} => r3c1 <> 8
ste.


[eleven]

Almost none of the rules used by SE is standard by any means.
The only interest of Sudoku Explainer is, it was a common reference for everybody. The idea of making local changes to it is the most stupid one I ever heard.

I can't see anything stupid, when commonly used solving techniques are added, which had not been known at that time.
So for manual solvers the Sukaku rating is more convenient.

[denis_berthier]

Almost none of the rules used by SE is standard by any means.
The only interest of Sudoku Explainer is, it was a common reference for everybody. The idea of making local changes to it is the most stupid one I ever heard.

I can't see anything stupid, when commonly used solving techniques are added, which had not been known at that time.
So for manual solvers the Sukaku rating is more convenient.

Manual solvers don't care for a rating. 99.9% of manual solvers use only Singles and T&E.

[yzfwsf]

Manual solvers don't care for a rating. 99.9% of manual solvers use only Singles and T&E.

Manual players are divided into two categories: Speed contest players and technique players. I think you only mean speed contest players here.

[denis_berthier]

Manual solvers don't care for a rating. 99.9% of manual solvers use only Singles and T&E.

Manual players are divided into two categories: Speed contest players and technique players. I think you only mean speed contest players here.

No, I mean the standard player you meet in the bus.

[eleven]

You are probably right.
But i think, these 0.1% are still more than those, who are interested in a specific academic rating.

[denis_berthier]

That sounds like a tautology,, doesn't it?