The New Sudoku Players' Forum

[AnotherLife]

This is another puzzle rated Extreme 8.3 but solvable manually in a few moves without Cell/Region Forcing Chains. Who wants to try?

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|..4|...|5..|
|.8.|7.4|.2.|
|7..|.6.|..4|
|---+---+---|
|.4.|6.9|.3.|
|..6|.4.|9..|
|.7.|5.3|.4.|
|---+---+---|
|3..|.5.|..6|
|.6.|9.2|.5.|
|..8|...|2..|

..4...5...8.7.4.2.7...6...4.4.6.9.3...6.4.9...7.5.3.4.3...5...6.6.9.2.5...8...2..


[Cenoman]

Four steps:

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 +----------------------+-----------------------+------------------------+
 |  129    129   4      |  1238   12389   18    |  5       6      7      |
 |  6      8     5      |  7      19      4     |  13      2      139    |
 |  7      129   3      |  12     6       5     |  18      189    4      |
 +----------------------+-----------------------+------------------------+
 |  1258   4     12     |  6      128-7   9     |  178*    3      1258   |
 |  1258   3     6      |  128    4       178   |  9       178*   1258   |
 |  1289   7     129    |  5      128     3     |  6       4      128    |
 +----------------------+-----------------------+------------------------+
 |  3      129   1279   |  148    5       178   |  1478    1789   6      |
 |  14     6     17     |  9      1378    2     |  13478   5      138    |
 |  149    5     8      |  134    137*    6     |  2       179*   139    |
 +----------------------+-----------------------+------------------------+

1. X-chain: (7)r9c5 = r9c8 - r5c8 = r4c7 => -7 r4c5; 2 placements & ls

Code: Select all

 +---------------------+----------------------+----------------------+
 |  29     129   4     |  1238   12389  E18   |  5      6     7      |
 |  6      8     5     |  7    Dc19      4    |  13     2   Cd139    |
 |  7      129   3     |  12     6       5    |  18    e189   4      |
 +---------------------+----------------------+----------------------+
 |  1258   4     12    |  6     b128     9    |  7      3     1258   |
 |  1258   3     6     | a128    4       7    |  9     f8-1   1258   |
 |  1289   7     129   |  5     b128     3    |  6      4     128    |
 +---------------------+----------------------+----------------------+
 |  3      29    279   |  148    5      F18   |  48-1  A79    6      |
 |  14     6     17    |  9      1378    2    |  1348   5     138    |
 |  149    5     8     |  134    137     6    |  2     A179  B139    |
 +---------------------+----------------------+----------------------+

2. (1)r5c4 = r46c5 - (1=9)r2c5 - r2c9 = (9-8)r3c8 = (8)r5c8 => -1 r5c8
3. (1=79)r79c8 - r9c9 = r2c9 - (9=1)r2c5 - r1c6 = (1)r7c6 => -1 r7c7; 10 placements & ls

Code: Select all

 +---------------------+------------------+-------------------+
 |  29     129   4     |  3    129   8    |  5    6     7     |
 |  6      8     5     |  7   a19    4    |  3-1  2    b39    |
 |  7      129   3     |  12   6     5    |  8    19    4     |
 +---------------------+------------------+-------------------+
 |  1258   4     12    |  6    128   9    |  7    3     125   |
 |  125    3     6     |  12   4     7    |  9    8     125   |
 |  1289   7     129   |  5    128   3    |  6    4     12    |
 +---------------------+------------------+-------------------+
 |  3      29    279   |  8    5     1    |  4    79    6     |
 |  4      6    e17    |  9    37    2    | f13   5     8     |
 | d19     5     8     |  4    37    6    |  2    179  c39    |
 +---------------------+------------------+-------------------+

4. (1=9)r2c5 - r2c9 = r9c9 - (9=1)r9c1 - r8c3 = (1)r8c7 => -1 r2c7; ste

[AnotherLife]

Thank you, Cenoman. Let me slightly change your solution so as to show that we need only standard patterns and an AIC with a group to solve this puzzle.

Code: Select all

.-----------------.------------------.--------------------.
| 129   129  4    | 1238  12389  18  | 5       6     7    |
| 6     8    5    | 7     19     4   | 13      2     139  |
| 7     129  3    | 12    6      5   | 18      189   4    |
:-----------------+------------------+--------------------:
| 1258  4    12   | 6     1278*  9   | 178*    3     1258 |
| 1258  3    6    | 128   4      178 | 9       18-7  1258 |
| 1289  7    129  | 5     128    3   | 6       4     128  |
:-----------------+------------------+--------------------:
| 3     129  1279 | 148   5      178 | 148-7   1789  6    |
| 14    6    17   | 9     1378   2   | 1348-7  5     138  |
| 149   5    8    | 134   137*   6   | 2       179*  139  |
'-----------------'------------------'--------------------'


1.Skyscraper (7): (7)r4c7 = r4c5 - r9c5 = r9c8 => -7 r5c8, r78c7; 2 singles and lcls steps

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+---------------------+-----------------------+----------------------+
 |  29     129   4     |  1238   12389   18   |  5      6     7      |
 |  6      8     5     |  7      c19     4    |  13     2     d139   |
 |  7      129   3     |  12     6       5    |  18     e189  4      |
 +---------------------+----------------------+----------------------+
 |  1258   4     12    |  6      b128    9    |  7      3     1258   |
 |  1258   3     6     |  a128   4       7    |  9      f8-1  1258   |
 |  1289   7     129   |  5      b128    3    |  6      4     128    |
 +---------------------+----------------------+----------------------+
 |  3      29    279   |  148    5       18   |  148    79    6      |
 |  14     6     17    |  9      1378    2    |  1348   5     138    |
 |  149    5     8     |  134    137     6    |  2      179   139    |
 +---------------------+----------------------+----------------------+


2.AIC with a group: (1)r5c4 = r46c5 - (1=9)r2c5 - r2c9 = (9-8)r3c8 = (8)r5c8 => -1 r5c8; 3 singles and lcls steps

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.----------------.---------------.---------------.
| 29    129  4   | 38  1239  8-1 | 5    6    7   |
| 6     8    5   | 7   19*   4   | 13*   2   39  |
| 7     129  3   | 12  6     5   | 8    19   4   |
:----------------+---------------+---------------:
| 1258  4    12  | 6   128   9   | 7    3    125 |
| 125   3    6   | 12  4     7   | 9    8    125 |
| 1289  7    129 | 5   128   3   | 6    4    12  |
:----------------+---------------+---------------:
| 3     29   279 | 48  5     18* | 14*  79   6   |
| 14    6    17  | 9   37-1  2   | 134  5    8   |
| 149   5    8   | 34  37-1  6   | 2    179  9   |
'----------------'---------------'---------------'


3.Skyscraper (1): (1)r2c5 = r2c7 - r7c7 = r7c6 => -1 r1c6, r89c5; 7 singles

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.----------------.------------.--------------.
| 29    129  4   | 3   129  8 | 5   6    7   |
| 6     8    5   | 7   19   4 | 13  2    39* |
| 7     129  3   | 12  6    5 | 8   19*  4   |
:----------------+------------+--------------:
| 1258  4    12  | 6   128  9 | 7   3    125 |
| 125   3    6   | 12  4    7 | 9   8    125 |
| 1289  7    129 | 5   128  3 | 6   4    12  |
:----------------+------------+--------------:
| 3     29   279 | 8   5    1 | 4   79   6   |
| 4     6    17  | 9   37   2 | 13  5    8   |
| 19*   5    8   | 4   37   6 | 2   79-1 39* |
'----------------'------------'--------------'


4.W-wing: (1=9)r3c8 - r2c9 = r9c9 - (9=1)r9c1 => -1 r9c8; ste

The current rating system is based on outdated methods, and it does not take account of alternate inference chains with groups and almost locked sets. This technique is easier to apply than forcing chains (krakens), so many sudokus get inflated ratings, take on a frightening look, and deter people from solving them.

[denis_berthier]

.

Code: Select all

Resolution state after Singles and whips[1]:
   +-------------------+-------------------+-------------------+
   ! 129   129   4     ! 1238  12389 18    ! 5     6     7     !
   ! 6     8     5     ! 7     19    4     ! 13    2     139   !
   ! 7     129   3     ! 12    6     5     ! 18    189   4     !
   +-------------------+-------------------+-------------------+
   ! 1258  4     12    ! 6     1278  9     ! 178   3     1258  !
   ! 1258  3     6     ! 128   4     178   ! 9     178   1258  !
   ! 1289  7     129   ! 5     128   3     ! 6     4     128   !
   +-------------------+-------------------+-------------------+
   ! 3     129   1279  ! 148   5     178   ! 1478  1789  6     !
   ! 14    6     17    ! 9     1378  2     ! 13478 5     138   !
   ! 149   5     8     ! 134   137   6     ! 2     179   139   !
   +-------------------+-------------------+-------------------+
133 candidates.

As the point turns out to be about rating, and more particularly about the SER, the number of steps is irrelevant. Here is my simplest-first solution, using only reversible chains:

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finned-x-wing-in-rows: n7{r9 r5}{c8 c5} ==> r4c5≠7
singles ==> r5c6=7, r4c7=7
finned-x-wing-in-columns: n1{c6 c2}{r7 r1} ==> r1c1≠1
whip[1]: b1n1{r3c2 .} ==> r7c2≠1
naked-triplets-in-a-row: r7{c4 c6 c7}{n4 n8 n1} ==> r7c8≠8, r7c8≠1, r7c3≠1
z-chain[3]: r7n1{c6 c7} - c7n4{r7 r8} - r8c1{n4 .} ==> r8c5≠1
z-chain[3]: b3n9{r2c9 r3c8} - c8n8{r3 r5} - b6n1{r5c8 .} ==> r2c9≠1
finned-x-wing-in-rows: n1{r2 r7}{c7 c5} ==> r9c5≠1
biv-chain[2]: r2n1{c7 c5} - c6n1{r1 r7} ==> r7c7≠1
whip[1]: r7n1{c6 .} ==> r9c4≠1
biv-chain[4]: r1c6{n8 n1} - b8n1{r7c6 r7c4} - b8n4{r7c4 r9c4} - c4n3{r9 r1} ==> r1c4≠8
z-chain[4]: c5n9{r1 r2} - b3n9{r2c9 r3c8} - c8n8{r3 r5} - b5n8{r5c4 .} ==> r1c5≠8
hidden-single-in-a-block ==> r1c6=8
naked-single ==> r7c6=1
z-chain[4]: r3n8{c7 c8} - r5c8{n8 n1} - c4n1{r5 r1} - c2n1{r1 .} ==> r3c7≠1
stte

It corresponds to a relatively easy puzzle, in Z4.

Everybody here knows the SER methods are outdated and forcing-anything rules are rarely useful if the "anything" rule is already present.
The SER is the only de facto standard. It has a good statistical correlation with other pure logic ratings (W, gW, B, gB, S+any of the previous...).
Expecting it to be a good predictor for any puzzle is over-stretching its meaning.

As for the use of g-candidates in chains, I agree they may be nice in some cases, but they very rarely change the above-mentioned pure logic ratings.
For this puzzle, they don't change anything.

[AnotherLife]

Hello, Denis,
In my opinion, your ratings do not reflect the actual complexity of sudokus for manual solving. In the above example your z-chains are equivalent to some AICs with groups, so they can be easily found by a human. You also rated one of my previous puzzles as Z4,

Code: Select all

   +----------------+----------------+----------------+
   ! 15   8    7    ! 3    6    15   ! 9    2    4    !
   ! 245  3    9    ! 8    47   257  ! 1    6    57   !
   ! 6    14   1245 ! 9    147  1257 ! 8    357  357  !
   +----------------+----------------+----------------+
   ! 1237 17   123  ! 5    9    6    ! 237  4    8    !
   ! 3457 6    345  ! 2    137  8    ! 357  9    1357 !
   ! 8    9    235  ! 17   137  4    ! 2357 1357 6    !
   +----------------+----------------+----------------+
   ! 147  147  8    ! 6    2    3    ! 457  157  9    !
   ! 1347 2    6    ! 147  5    9    ! 347  8    137  !
   ! 9    5    134  ! 147  8    17   ! 6    137  2    !
   +----------------+----------------+----------------+


but the corresponding z-chain[4]: b7n3{r8c1 r9c3} - r9n4{c3 c4} - b8n1{r9c4 r9c6} - r1n1{c6 .} ==> r8c1≠1 is equivalent to a forcing chain (kraken), and the puzzle is unsolvable via AICs with groups and almost locked sets. HoDoKu and Andrew Stuart's Solver give it an 'Extreme' grade.

[denis_berthier]

Hello, Denis,
In my opinion, your ratings do not reflect the actual complexity of sudokus for manual solving. In the above example your z-chains are equivalent to some AICs with groups, so they can be easily found by a human. You also rated one of my previous puzzles as Z4,
...
but the corresponding z-chain[4]: b7n3{r8c1 r9c3} - r9n4{c3 c4} - b8n1{r9c4 r9c6} - r1n1{c6 .} ==> r8c1≠1 is equivalent to a forcing chain (kraken), and the puzzle is unsolvable via AICs with groups and almost locked sets. HoDoKu and Andrew Stuart's Solver give it an 'Extreme' grade.

Hi AnotherLife,
My point is, there's nothing as the "actual complexity of sudokus for manual solving". Two different players will use different sets of rules, in different orders, and have different ideas of the complexity of a puzzle.

Statistically, a rating gives an approximative idea of the impression of difficulty of a puzzle for someone. But the way the rating approximates the difficulty for someone will depend on the rules that are most familiar to him.

Moreover, for any given rating system and even for any fixed rating within it, there's some variability between the puzzles when you compare them according to other criteria. This is unavoidable.

I often write that my pure logic ratings (Z, W, gW, ...) are universal. But I'm clear about what it means: they are meaningful for any finite Constraint Satisfaction Problem (and I've indeed applied them to many different kinds of puzzles). It doesn't mean that they can capture all there can be in anyone's particular sense of difficulty.

I think you're expecting too much of a rating system.

[AnotherLife]

I often write that my pure logic ratings (Z, W, gW, ...) are universal. But I'm clear about what it means: they are meaningful for any finite Constraint Satisfaction Problem (and I've indeed applied them to many different kinds of puzzles).

Your software has been designed for a broad range of problems, so it cannot catch the peculiarities of the specific task, that is, the sudoku case. I think that in general your z-chains are not equivalent even to krakens, and the human solver will have to apply dynamic forcing chains (forcing nets) instead of them. As I don't use your programs and cannot do it myself, you can ask your students to find such examples. So my point is that a rating system oriented to manual solving cannot be based on z-chains. The same is true of whips.

I think you're expecting too much of a rating system.

As I am not a programmer and I cannot devise my own software, I believe it is possible to update this list so that it should include at least AICs with groups and ALS's, and the ratings become more or less relevant.

[denis_berthier]

I often write that my pure logic ratings (Z, W, gW, ...) are universal. But I'm clear about what it means: they are meaningful for any finite Constraint Satisfaction Problem (and I've indeed applied them to many different kinds of puzzles).

Your software has been designed for a broad range of problems, so it cannot catch the peculiarities of the specific task, that is, the sudoku case.

It's not about my software (which is only an implementation), it's about my resolution theories.
What a strange way of reasoning: because something is general, it cannot catch the specificities of a problem. That goes against the whole evolution of science.

I think that in general your z-chains are not equivalent even to krakens,

That's totally obvious.

my point is that a rating system oriented to manual solving cannot be based on z-chains. The same is true of whips.

As long as you don't have anything concrete to propose...

[AnotherLife]

What a strange way of reasoning: because something is general, it cannot catch the specificities of a problem.

I think that locked sets and almost locked sets are specific for the sudoku case. Is this the reason why you have not implemented the ALS-based methods in your software? Its power would have greatly increased.

[denis_berthier]

What a strange way of reasoning: because something is general, it cannot catch the specificities of a problem. That goes against the whole evolution of science.

I think that locked sets and almost locked sets are specific for the sudoku case. Is this the reason why you have not implemented the ALS-based methods in your software?

Did it ever occur to you that what you think, based on your prejudices, may be false? Subsets and Subset chains are considered in my books in the fully general context of finite CSPs, where I've proven that they are reversible (which is absolutely not obvious). They have nothing specific to Sudoku.

The purpose of CSP-Rules has never been to be the nth hotpot of solving techniques. It is based on a consistent vision of pattern-based solving and it includes only a coherent selection of rules that I have evaluated for their interest. Statistical analyses based on extremely large collections of puzzles prove that whips make a central backbone for any rating system.

ALS-chains are not worth much as long as there are not also AAAALS, AHS, AAAAHHHHS... chains. This was largely talked about some 15 years ago.
I didn't include them in CSP-Rules because they rarely allow to solve a puzzle not solvable by whips or g-whips.
Now, CSP-Rules is public and anyone can add them if they like. (I'm not gonna do it.)

...your software. ]Its power would have greatly increased.

and this is based on what data?

[AnotherLife]

Thanks for the information, Denis. I got your point of view.