The New Sudoku Players' Forum

[morl]

000 | 004 | 800
400 | 050 | 020
008 | 009 | 004
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200 | 030 | 100
050 | 100 | 009
007 | 000 | 040
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700 | 200 | 600
060 | 080 | 000
009 | 005 | 003

[SpAce]

I solved it, all right, but I don't think this really counts (Edit: I originally stopped solving when I accidentally found a backdoor, but now I've solved the rest of it.)

1. Kraken Cell (149)r7c5 (AHS): -8 r2c6 (*a)
2. Skyscraper (Grouped): (4)r5c3 = r5c5 - r7c5 = (4)r7c23 => -4 r8c3
3. AIC (ANS): (9)r8c4 = r7c5 - (9=6)r6c5 - r9c5 = r9c4 - (6=37)r13c4 => -37 r8c4
4. AIC (AHS): (9)r2c7 = r2c2 - r1c1 = HP:(91-3)r6c12 = (3)r6c7 => -3 r2c7
5. Kraken Cell (127)r3c2 (Net): +9r2c7 (*b)
6. AIN (ANS, AHS): -5 r8c7 (*c)
7. AIN-Loop: -16 r1c1, -9 r6c2 (*d)
(8. Found accidentally a backdoor (lol): -9 r1c1; stte)

(Added.) Forgetting previous step 8, these are the rest of my steps:

8. AIN (ANS): -5 r3c8 (*e)
9. AIC (ANS, Grouped): (6)r3c1 = r12c3 - (6=43)r45c3 - (3)r5c78 = (3-5)r6c7 = (5)r3c7 => -5 r3c1
10. AIC: (2)r6c9 = r8c9 - r8c2 = (2-5)r1c3 = (5-9)r1c1 = r1c2 - r4c2 = (9-5)r4c4 = (5)r6c4 => -5 r6c9
11. AIC (ANS): (4)r5c5 = (4-9)r4c4 = r4c2 - r1c2 = (9-5)r1c1 = (5-2)r1c3 = r8c3 - r8c9 = r6c9 - (2=37)r65c6 => -7 r5c5
12. AIC-Loop: (2)r9c7 = r9c2 - r8c3 = (2-5)r1c3 = (5-9)r1c1 = r1c2 - r4c2 = r4c4 - (9=4)r8c4 - r8c7 = (4)r9c7 - loop => -16 r1c3, -7 r9c7
13. AIC (AHS, Grouped): (4=6)r5c5 - r456 = (6-1)r2c6 = HP:(12-7)r13c5 = (7)r9c5 => -4 r9c5
14. AIC (AHS): (3=2)r6c7 - r6c9 = r8c9 - (2=4)r9c7 - r8c7 = (4-9)r8c4 = r7c5 - r6c5 = HP:(91)r6c12 => -3 r6c12
15. AIC-Hydra: (6=9)r6c5 - r7c5 = (9-4)r8c4 = r8c7 - (4=2)r9c7 - r8c9 = (#2)r6c9 - r6c6 = (#2)r5c6 => -6 r6c9, r5c6
16. AIC: (5)r8c1 = (5-9)r1c1 = r6c1 - r6c5 = r7c5 - r7c8 = (9)r8c8 => -5 r8c8
17. AIC (Grouped): (6)r3c1 = r2c3 - r2c6 = r46c6 - (6=9)r6c5 - r6c1 = (9-5)r1c1 = (5-3)r8c1 = (3)r5c1 => -6 r5c1
18. AIC (ANS, AHS, Split-Node): (1=358)r589c1 - (5|8)r8c9,r9c8 = HP:(58-9)r7c89 = r7c5 - r6c5 = (9)r6c1 => -1 r6c1
19. AIC (Grouped): (1=6)r2c3 - r3c1 = (6-9)r6c1 = (9-8)r4c2 = r79c2 - (8=1)r9c1 => -1 r3c1, r78c3; lclste

This is all raw data from my real-time solving notes. I haven't done any post-analysis or editing, so there are probably redundant, inefficient and too complicated steps around. But, it got solved anyhow. I guess I can now claim to have solved my first SE 9.0.

Step details (*a, *b, *c, *d, *e):

Hidden Text: Show

(*a) Step 1:

Code: Select all

(1)r7c5 - r13c5 =============== (1)r2c6
 ||
(4)r7c5 - r5c5 = HP:(45-8)r46 = (8)r2c4
 ||
(9)r7c5 - r6c5 = HP:(95-8)r46 = (8)r2c4

=> -8 r2c6

(*b) Step 5:

Code: Select all

(1)r3c2 - r6c2=(1-9)r6c1=r1c1-r1c8 ============================ (9)r2c7
 ||
(2)r3c2 - r9c2=(2-4)r9c7=(4-9)r8c7 ============================ (9)r2c7
 ||
(7)r3c2 - r3c4 =|= (3)r3c4-r1c4=(3-9)r1c8 ===================== (9)r2c7
                |
                |= (6)r3c4-r9c4=r9c5-(6=9)r6c5-r7c5=r7c8-r1c8 = (9)r2c7

=> +9r2c7

(*c) Step 6:

Code: Select all

(4)r8c7 =&= (4-2)r9c7 ==========================================|= HP:(27)r8c79
         &                                                      |
         &= (4-9)r8c4 =&= (9-7)r8c8 ============================|
                       &                                        |
                       &= r7c5-(9=6)r6c5-(6=287)r456c6-(7)r8c6 =|

=> -5 r8c7

(*d) Step 7:

Code: Select all

(9)r1c1=r1c2-r4c2=(9)r4c4 -|- (9=4)r8c4-r8c7=(4-2)r9c7=r9c2-r8c3=(2-5)r1c3 =|= (5)r1c1 - loop
                           |                                                |
                           |- (5)r4c4=r6c4-r6c7=r3c7-(5)r3c1 ===============|

=> -16 r1c1, -9 r6c2

(*e) Step 8:

Code: Select all

(5)r3c7=r6c7-r6c4=&=(5)r4c4-|-(9)r4c4=r4c2-r1c2=(9-5)r1c1=========================================|=(5)r3c1
                  &         |                                                                     |
                  &         |-(4)r4c4=r5c5-(4)r7c5==============|=(9)r7c5-(9=4)r8c4-r8c7          |
                  &                                             |  =(4-2)r9c7=r9c2-r8c3=(2-5)r1c3=|
                  &=(96)r6c45-(6)r456c6=(6-1)r2c6=r13c5-(1)r7c5=|

=> -5 r3c8

I was actually pretty pissed when I realized I'd found a backdoor because it killed my motivation to try to work out the rest normally. My only excuse is that I found the backdoor (and everything else) using just pencil and paper, as always. I'm actually pretty sure I would have got stuck at some point anyway, but now we'll never know Edit: I guess we now know, after all!

[Leren]

..2....1..51.234..63..1425......7..1.63.8174..1743.8.5.76.48...3.5.7...4...3.5.7.

Hodoku's solution used 27 non-basic moves, including no less than 10 forcing chains, for a score of 10,746.

My own solver used 20 moves, with 16 forcing chains, for a Hodoku based score of 9,358.

Leren

[Cenoman]

Ten steps, including two krakens, without net:
Edit (10 steps, 2 krakens instead of 9 steps, 3 krakens)

Code: Select all

 +--------------------------+--------------------------+--------------------------+
 |  13569   12379   12356   |  367      1267   4       |  8       135679   1567   |
 |  4       1379    136     |  3678     5      13678   |  379     2        167    |
 |  1356    1237    8       |  367      1267   9       |  357     13567    4      |
 +--------------------------+--------------------------+--------------------------+
 |  2       489     46      |  456789   3      678     |  1       5678     5678   |
 |  368     5       346     |  1        467    2678    |  237     3678     9      |
 |  13689   1389    7       |  5689     69     268     |  235     4        2568   |
 +--------------------------+--------------------------+--------------------------+
 |  7       1348    1345    |  2        149    13      |  6       1589     158    |
 |  135     6       12345   |  3479     8      137     |  24579   1579     1257   |
 |  18      1248    9       |  467      1467   5       |  247     178      3      |
 +--------------------------+--------------------------+--------------------------+

1. (1)r6c2 = r6c1 - (1=8)r9c1 - (846=3)b4p346 - r5c78 = (3)r6c7 => -3 r6c2
2. (9)r8c4 = r7c5 - (9=6)r6c5 - r9c5 = r9c4 - (6=37)r13c4 => -37 r8c4 (borrowed to SpAce)
3. (3678=4)r1239c4 - (4913=7)b8p2346 - (7=268)r456c6 => -68 r46c4; 1 placement (+8r2c4)
Edit: new step 3. (takes place of a kraken)

Code: Select all

 +--------------------------+-----------------------+--------------------------+
 |  13569   12379   12356   |  367    1267   4      |  8       135679   1567   |
 |  4       1379    136     |  8      5      167    |  379     2        167    |
 |  1356    1237    8       |  367    1267   9      |  357     13567    4      |
 +--------------------------+-----------------------+--------------------------+
 |  2       489     46      |  4579   3      678    |  1       5678     5678   |
 |  368     5       346     |  1      467    2678   |  237     3678     9      |
 |  13689   189     7       |  59     69     268    |  235     4        2568   |
 +--------------------------+-----------------------+--------------------------+
 |  7       1348    1345    |  2      149    13     |  6       1589     158    |
 |  135     6       12345   |  49     8      137    |  24579   1579     1257   |
 |  18      1248    9       |  467    1467   5      |  247     178      3      |
 +--------------------------+-----------------------+--------------------------+

4. Kraken cell (135)r8c1
||(1)r8c1 - (1=8)r9c1 - (846=3)b4p346 - r5c78 = (3)r6c7
||(3)r8c1 - r56c1 = r5c3 - r5c78 = (3)r6c7
||(5)r8c1 - r78c3 = (5-2)r1c3 = r8c3 - r9c2 = (2*-4)r9c7 = r8c7 - (4=9)r8c4 - (9=5)r6c4
=> -2 r6c7*, -5 r6c7; 1 placement (+3r6c7)
5. Kraken row (7)r8c6789
||(7)r8c6 - (728=6)r456c6 - (6=9)r6c5 - r7c5 = (9-4)r8c4 = (4)r8c7
||(7)r8c7
||(7-9)r8c8 = (49)r8c47
||(7-2)r8c9 = (249)r289c7
=> -5 r8c7; 1 placement (+5r3c7)

Code: Select all

 +------------------------+-----------------------+------------------------+
 |  1569   1279   1256    |  367    1267   4      |  8      13679   167    |
 |  4      1379   136     |  8      5      167    |  79     2       167    |
 |  16     127    8       |  367    1267   9      |  5      1367    4      |
 +------------------------+-----------------------+------------------------+
 |  2      489    46      |  4579   3      678    |  1      5678    5678   |
 |  368    5      346     |  1      467    2678   |  27     678     9      |
 |  1689   189    7       |  59     69     268    |  3      4       2568   |
 +------------------------+-----------------------+------------------------+
 |  7      1348   1345    |  2      149    13     |  6      1589    158    |
 |  135    6      12345   |  49     8      137    |  2479   1579    1257   |
 |  18     1248   9       |  467    1467   5      |  247    178     3      |
 +------------------------+-----------------------+------------------------+

6. (6)r2c6 = r456c6 - (6=9)r6c5 - (9=1683)r3569c1 - (3=46)r45c3 => -6 r2c3
7. (1=3)r2c3 - r2c2 = r7c2 - (3=1)r7c6 => -1 r2c6, -1 r7c3

Code: Select all

 +------------------------+---------------------+------------------------+
 |  1569   1279   1256    |  367   12    4      |  8      13679   167    |
 |  4      1379   13      |  8     5     67     |  79     2       167    |
 |  16     127    8       |  367   12    9      |  5      1367    4      |
 +------------------------+---------------------+------------------------+
 |  2      489    46      |  459   3     678    |  1      5678    5678   |
 |  368    5      346     |  1     467   2678   |  27     678     9      |
 |  1689   189    7       |  59    69    268    |  3      4       2568   |
 +------------------------+---------------------+------------------------+
 |  7      1348   1345    |  2     49    13     |  6      1589    158    |
 |  135    6      12345   |  49    8     13     |  2479   1579    1257   |
 |  18     24     9       |  67    67    5      |  24     18      3      |
 +------------------------+---------------------+------------------------+

8. (7=2)r5c7 - r9c7 = (2-4)r9c2 = r7c23 - r7c5 = (4)r5c5 => -7 r5c5; 3 placements
9. (6=9)r6c5 - r6c1 = (9-5)r1c1 = (5-2)r1c3 = r8c3 - r8c9 = (2)r6c9 => -6 r6c9
10. (4=6)r4c3 - r6c1 = r6c5 - (6=4)r5c5 => -4 r4c4,r5c3; stte
Edit: step 9 inserted (was missing, old step 9 now step 10)

[SpAce]

Nine steps, including three krakens, without net:

Wow! That sounds impressive with this puzzle. I haven't looked at your steps yet, nor the Hodoku or other solutions, because I might still try to work out at least a few moves on my own. My main grid is still at the state after my step 7, so I could continue from there if I find the motivation.

Finding the backdoor was a bit of a downer, but it's a risk when looking for krakens or net solutions and digging too deep. It has happened to me a couple of times, and then I've never bothered to continue to solve the puzzle normally. I'd like to try this time, as it's an interesting puzzle, but we'll see.

What kind of algorithm does your program use to find krakens? I'm wondering if there might be something manually applicable. I've only recently started finding those at all. It's always happened so that I've first discovered a contradiction and then reversed it. I can't really see how they could be found directly, or at least it would seem like a very arbitrary process.

[SpAce]

Hodoku's solution used 27 non-basic moves, including no less than 10 forcing chains, for a score of 10,746.

My own solver used 20 moves, with 16 forcing chains, for a Hodoku based score of 9,358.

And SudokuWiki apparently can't solve it at all using logical techniques. I haven't stepped through this with any solver (yet), because I might still want to see what I can find on my own, but I tried to grade it with SudokuWiki and it couldn't. That was quite discouraging, as it probably means that I wouldn't have had a chance to solve it without the "lucky" break.

[SpAce]

Well, looks like I got it done after all (new steps added to the original post). Not pretty but who's counting style points?

[totuan]

Hi spAce and All,
Nice puzzle and solution!
For your step 1, I suggest to present as AIC:

(8)r2c4=(58-49)r46c4=(49)r89c4-(49=1)r7c5-r78c6=r2c6 => r2c6<>8

To increace skill – at least I think that , you can reference solutions on AU site from July/2011 (tough page) that presented by kobold, Steve K… They use a lot of combinations of parterns like AALS, M-wing, Fish… that are quite interesting.


totuan

[SpAce]

Nice puzzle and solution!
For your step 1, I suggest to present as AIC:

(8)r2c4=(58-49)r46c4=(49)r89c4-(49=1)r7c5-r78c6=r2c6 => r2c6<>8

Thanks, totuan! That's definitely a cleaner way to do it! I leave my solution as is because that's how I saw it at the time, but I wish I'd seen it your way. I've also just recently started to find and use krakens so I might have been overeager to use one unnecessarily

To increace skill – at least I think that , you can reference solutions on AU site from July/2011 (tough page) that presented by kobold, Steve K… They use a lot of combinations of parterns like AALS, M-wing, Fish… that are quite interesting.

Thanks for that tip, too! I've looked at some things on that page, but not enough. There's a plethora of good information there! It's a bit harder to read those chains because of the different coordinate system, but I think I'll manage.

[Leren]

SpAce wrote : And SudokuWiki apparently can't solve it at all using logical techniques.

Andrew's solver has Kraken style forcing chain moves but not complex network varieties. Here are a few from the Hodoku solution.

Forcing Net Contradiction in c5 => r1c2<>9

r1c2=9 r1c5<>9 r1c2=9 r1c6<>9 r1c6=6 (r1c7<>6 r1c7=3 r4c7<>3) r6c6<>6 r6c8=6 r4c7<>6 r4c7=9 r4c5<>9r1c2=9 (r3c3<>9) r1c6<>9 r1c6=6 (r1c7<>6 r1c7=3 r4c7<>3) r6c6<>6 r6c8=6 r4c7<>6 r4c7=9 r4c3<>9 r9c3=9 r9c5<>9

Forcing Net Contradiction in c5 => r1c2<>9

r1c2=9 r1c5<>9 r1c2=9 r1c6<>9 r1c6=6 (r1c7<>6 r1c7=3 r4c7<>3) r6c6<>6 r6c8=6 r4c7<>6 r4c7=9 r4c5<>9 r1c2=9 (r3c3<>9) r1c6<>9 r1c6=6 (r1c7<>6 r1c7=3 r4c7<>3) r6c6<>6 r6c8=6 r4c7<>6 r4c7=9 r4c3<>9 r9c3=9 r9c5<>

Forcing Net Verity => r6c8=6

r2c8=6 (r2c8<>8 r8c8=8 r8c2<>8) (r1c9<>6) r2c9<>6 r9c9=6 (r8c7<>6) (r9c7<>6) r9c5<>6 r9c5=9 r9c7<>9 r9c7=1 r8c7<>1 r8c7=9 r8c2<>9 r8c2=2 r8c6<>2 r6c6=2 r6c6<>6 r6c8=6
r4c8=6 (r4c8<>3 r4c7=3 r1c7<>3 r1c9=3 r1c9<>6) (r4c8<>3 r4c7=3 r1c7<>3) r6c8<>6 r6c6=6 r1c6<>6 r1c6=9 r1c7<>9 r1c7=6 (r1c5<>6) r2c9<>6 r9c9=6 r9c5<>6 r4c5=6 r6c6<>6 r6c8=6
r6c8=6 r6c8=6
r8c8=6 (r9c9<>6 r9c5=6 r9c5<>9) (r8c8<>8 r2c8=8 r2c8<>9) r6c8<>6 r6c6=6 (r4c5<>6) r1c6<>6 r1c6=9 (r1c5<>9 r4c5=9 r4c2<>9 r9c2=9 r9c1<>9) (r1c5<>9 r4c5=9 r4c2<>9 r9c2=9 r7c1<>9) (r1c5<>9 r4c5=9 r5c4<>9) r2c4<>9 r2c9=9 (r7c9<>9) r5c9<>9 r5c1=9 r6c1<>9 r6c1=2 (r9c1<>2 r9c2=2 r9c2<>9) r7c1<>2 r7c1=1 r9c1<>1 r9c7=1 r9c7<>9 r9c9=9 (r9c9<>8 r8c8=8 r8c8<>6 r8c7=6 r4c7<>6) r5c9<>9 r5c9=2 r7c9<>2 r7c9=3 r1c9<>3 r1c7=3 r4c7<>3 r4c8=3 r4c8<>6 r4c4=6 r6c6<>6 r6c8=6

Love that last one - obvious when you think about it

Leren

[SpAce]

Andrew's solver has Kraken style forcing chain moves but not complex network varieties. Here are a few from the Hodoku solution.

But if you turn on "Allow ALS in chains" then Hodoku doesn't need any nets for this puzzle. Since Andrew's solver can handle ALSs in its "AICs" (nice loops really) and forcing chains, shouldn't it be able to solve this in theory? I'm guessing the problem is in the implementation and not in the technique-set per se.

PS. What kind of Hodoku settings did you use to get those Forcing Net examples? I only got one when I turned off the "Allow ALS in chains", and more if I turned off all ALS moves, but not exactly the same ones you showed.

PPS. Does anyone know how Hodoku decides whether to show the Contradiction or the Verity type of a forcing chain/net? If I understand correctly, those types are aliases for Nishios and Krakens. Either can be used to prove both eliminations and placements, so that's not a definite divider. It's a bit confusing when both types are unnecessarily mixed in the same solution. As they're (always or just mostly?) interchangeable, I'd like Hodoku to show only one or the other type for all forcing chains/nets in the same solution, or at least be able see their counterparts easily when applicable. Mostly I'd like it to show verities (Krakens) rather than contradictions (Nishios) when possible, but the default seems to be the other way around. (The way it outputs those chains/nets in text format is horrible anyway, but fortunately the graphics help.)

The second part to that question is when if ever is it not possible to turn a contradiction into a verity? The Hodoku documentation says it's always possible in the other direction: "For every Forcing Chain Verity a complementary Forcing Chain Contradiction exists." It doesn't say it always works the other way around, though.

[ghfick]

The users manual for HoDoKu is very useful. Chapters 3 and 5 should address the issues under consideration.
I have made some rather minor changes to the defaults. I place XY Chains in the 'Hard' category now [not the default 'Unfair'].
Also, at various stages, consulting the 'All Possible Steps' should help as well.

[SpAce]

The users manual for HoDoKu is very useful. Chapters 3 and 5 should address the issues under consideration.

Yes, it is in general, but I didn't find anything there concerning my questions. I know how to use "All Possible Steps" to create custom solutions with any steps I want, but I was asking about the standard solution Hodoku generates. I can't find anything that would allow me to choose to see only Forcing Chain/Net Verities instead of Contradictions (or vice versa). I can only do that by creating a custom solution and manually picking one or the other. By default Hodoku uses both types in its standard solutions using some internal logic (apparently mostly verities for placements and contradictions for eliminations) and I don't see any way to change that.

Hodoku has very detailed configuration options for some things, especially fishes, but not for chains. For example, I'd like to disable (Discontinuous) Nice Loops altogether and see only AICs (and continuous loops), but that's not possible because they're bundled.

I have made some rather minor changes to the defaults. I place XY Chains in the 'Hard' category now [not the default 'Unfair'].

It's a good thing Hodoku allows to configure those kinds of things, because different solvers see the relative difficulties of various techniques differently. Did you change the value of X-Chains too, or do you really think XY-Chains are easier than them? I find almost any other kind of AIC before I find a long XY-Chain. To me it's much easier to follow a chain when most of the strong links are bilocal instead of bivalued. That's why I don't understand Berthier's obsession with turning everything into XY-Chains.

I haven't touched the hierarchy ordering or difficulty categories, but I've changed the defaults in some other ways. The most important thing is checking "Allow ALS in chains", which for some reason is not enabled by default (thanks to 200e200w for pointing that out). I've also enabled Krakens (with reasonable sizes and fin counts, or finding any solution takes forever), Forcing Chains and Nets, and Death Blossoms. I've disabled both coloring moves. (Similarly in the SudokuWiki solver I've disabled Simple Coloring, 3D Medusa and APE, for example.)