The New Sudoku Players' Forum

[Arajmahad]

i have been pondering over this one for hours and i have exhausted all conventional methods of extracting answers. so now it's time to move on to the more advanced techniques, which i am, as of yet, unclear on exactly how to employ.
would someone out there mind giving this one a shot and then maybe just tell me what technique to try next and then i can try to do it for myself? i don't want the straight up answers, but just help leading me to the way to get it done myself, to help me learn.
the numbers in parentheses, in case you haven't guessed, are the numbers i've not decided for certain are the ones that go there. also, i have only penciled in numbers where there are only 2 options per either block, line, or column. if a line has more than 2 possibilities for a number, i didn't write it in. i never do and usually i can finish them. if that should be my next step, then please let me know that as well.
i look forward to your responses. thanks a lot for reading

3 (5) . | 2 (1) 4 | . 7 (8)
(45) 7 (4) | (3) (13) 8 | . 2 .
. 2 (1) | 7 9 5 | (1) 4 3
------+-------+------
(5) (3) (3) | 4 (5) 1 | 2 9 7
2 (59) (9) | 8 7 3 | 4 (5) 1
1 4 7 | (59) 2 (9) | (8) 3 (8)
------+-------+------
(7) 1 2 | (3) (38) (7) | (9) (58) 4
(7) .5 | 1 4 (7) | 3 (8) 2
(4) (3) (34) | . (8) 2 | 7 1 (9)

[m_b_metcalf]

Sudoku Explainer tells me that your puzzle, better represented here:

Code: Select all

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

is very hard. You can try stepping through it with SE yourself to see why.

HTH

Mike Metcalf

[Leren]

It certainly is a hard puzzle for the casual solver. It looks to me like you may have made some mistakes. Just in case, here is the solution.

Code: Select all

*-----------------------*
| 3 9 8 | 2 1 4 | 5 7 6 |
| 5 7 4 | 6 3 8 | 1 2 9 |
| 6 2 1 | 7 9 5 | 8 4 3 |
|-------+-------+-------|
| 8 5 3 | 4 6 1 | 2 9 7 |
| 2 6 9 | 8 7 3 | 4 5 1 |
| 1 4 7 | 5 2 9 | 6 3 8 |
|-------+-------+-------|
| 7 1 2 | 3 5 6 | 9 8 4 |
| 9 8 5 | 1 4 7 | 3 6 2 |
| 4 3 6 | 9 8 2 | 7 1 5 |
*-----------------------*

Leren

[Leren]

You could also try putting your puzzle into Andrew Stuart's solver, which you can find here and step through the solution.

When you don't understand a move you can read up about it on the same site here.

Alternatively you could download Hodoku, a free solver, which you can find here.

All you have to do is paste your puzzle into it's main page and it automatically solves it. You can step through the solution and refer to its solving strategies page when you don't understand a move.

Hodoku's solution for this puzzle involved, apart from some basic moves, 2 uniqueness arguments, 7 AIC's and XYZ Wing and a Multicoloring move.

That's why Mike and I did not attempt to provide you with specific advice, the solution is just too long and arduous for any advice to be helpful.

Leren

[SpAce]

Sounded like fun so I had to do it. Yeah, it's not one for beginners, but not really worth its SE rating (8.4) either. Once again, I don't really understand those ratings. I've certainly solved harder puzzles with lower grades, while one with the same rating nearly killed me. This one I did on one sitting with no problems, using pencil and paper only as always. It took a few steps, alright, but all relatively basic and easily found (the same chain fragments could be reused multiple times). I had the same number of steps (11) as Hodoku, but three of those were unnecessary (so 8 relevant steps). SudokuWiki took 14.

My unedited manual solve path:

Hidden Text: Show

1. Grouped X-Chain (Kite): (5)r6c4 = r6c79 - r5c8 = (5)r7c8 => -5 r7c4
2. Grouped AIC: (5)r9c4 = r6c4 - (5=6)r4c5 - r12c5 = (6)r2c4 => -6 r9c4
3. Grouped AIC (ANS): (5)r9c4 = r6c4 - r79c4 = (5-6)r5c8 = r78c8 - (6=95)r9c49 => -5 r9c5
(4. Grouped AIC: (9=5)r9c4 - r6c4 = r4c5 - r4c12 = (5-9)r5c2 = (9)r5c3 => -9 r9c3)
5. AIC: (9=5)r9c4 - r6c4 = r4c5 - r4c1 = (5-4)r2c1 = (4)r9c1 => -9 r9c1
(6. Grouped AIC (AHS): (6)r2c4 = r12c5 - (6=5)r4c5 - r4c1 = HP:(54)r2c13 => -6 r2c13)
(7. AIC: (8=6)r9c5 - (6=5)r4c5 - r4c1 = (5-4)r2c1 = (4)r9c1 => -8 r9c1)
8. X-Chain: (5)r2c1 = r4c1 - r4c5 = r7c5 - r9c4 = (5)r9c9 => -5 r2c9
9. Grouped AIC: (5)r2c1 = r4c1 - (5=6)r4c5 - r12c5 = r2c4 - (6=9)r2c9 => -9 r2c1
10. UR Type 1 (79): r78c16 => -79 r7c6
11. UR Type 1 (68): r16c79 => -68 r1c7; stte

(unnecessary steps in brackets)

Hodoku path:

Hidden Text: Show

1. Hidden UR (36): -6 r7c5
2. Grouped DNL: -6 r2c1
3. Grouped DNL: -6 r2c3
4. Grouped DNL: -5 r7c4
5. Grouped DNL: -9 r9c9
6. Grouped DNL: -6 r9c4
7. Grouped DNL: -5 r7c7
8. Multi-Colors: -5 r2c9
9. DNL: -9 r2c1
10. XYZ-Wing (689): -6 r3c3
11. UR Type 1: -68 r1c7

SudokuWiki path:

Hidden Text: Show

1. Hidden UR (36): -6 r7c5
2. WXYZ-Wing (1689): -6 r2c3
3. Grouped X-Cycle (5): -5 r7c4
4. WXYZ-Wing (3679): -6 r9c4
5. AIC (DNL): -9 r9c1
6. AIC (DNL): -6 r2c1
7. AIC (DNL): -5 r7c7
8. X-Cycle: -5 r2c9
9. Grouped X-Cycle (5): -5 r9c5
10. AIC (DNL): -8 r9c1
11. AIC (DNL): -9 r9c3
12. AIC (DNL): -9 r2c1
13. XYZ-Wing (689): -6 r3c3
14. XY-Chain: -5 r1c2, r4c1

[200e200w]

Hi, SpAce!

I don't really understand those ratings.

These ratings are:
SudokuWiki - I don't understand Andrew's rating system.
Hodoku - sum of ratings of all steps. Also used by SudoCue.
Sudoku Explainer - rating of the hardest step required to solve the puzzle.

I had the same number of steps (11) as Hodoku...

Using Hodoku's "Find all steps" tool, powered by all techniques up to Kraken Fish, I managed to reduce the number of required steps to only 3. First is a Kraken Finned X-Wing, second is a Kraken Finned Franken X-Wing, third is UR Type 1. I'll post that solution later.

200e200w

[200e200w]

Ok, I'll now post the solution.

Step 1: Kraken Finned X-Wing.

Code: Select all

.---------------------.---------------------.---------------------.
| 3      5689   1689  | 2      16     4     | 15689  7      5689  |
| 4569   7      1469  | 36     136    8     | 1569   2      569   |
| 68     2      168   | 7      9      5     | 168    4      3     |
:---------------------+---------------------+---------------------:
| 568    3568   368   | 4      56     1     | 2      9      7     |
| 2      569    69    | 8      7      3     | 4      56     1     |
| 1      4      7     | 569    2      69    | 568    3      568   |
:---------------------+---------------------+---------------------:
| 6789   1      2     | 3569   3568   679   | 569    568    4     |
| 6789   689    5     | 1      4      679   | 3      68     2     |
| 4689   3689   34689 | 569    568    2     | 7      1      569   |
'---------------------'---------------------'---------------------'
Kraken Finned X-Wing.
Finned X-Wing: 8 r78/c18 fr7c5,r8c2
(8)r7c1 - (8=56)r34c1 - (5=136)r124c5 - 3r2c4
(8-3)r7c5 = r7c4 - r2c4
(8)r8c1 - (8=56)r34c1 - (5=136)r124c5 - 3r2c4
(8)r8c2 - (8=56)r58c8 - 5r5c2 = r4c12 - (5=136)r124c5 - 3r2c4
=> -3 r2c4

Step 2: Kraken Finned Franken X-Wing.

Code: Select all

.---------------------.---------------------.---------------------.
| 3      5689   689   | 2      1      4     | 5689   7      5689  |
| 459    7      149   | 6      3      8     | 159    2      59    |
| 68     2      168   | 7      9      5     | 168    4      3     |
:---------------------+---------------------+---------------------:
| 568    3568   368   | 4      56     1     | 2      9      7     |
| 2      569    69    | 8      7      3     | 4      56     1     |
| 1      4      7     | 59     2      69    | 568    3      568   |
:---------------------+---------------------+---------------------:
| 6789   1      2     | 3      568    679   | 569    568    4     |
| 6789   689    5     | 1      4      679   | 3      68     2     |
| 4689   3689   34689 | 59     568    2     | 7      1      569   |
'---------------------'---------------------'---------------------'
Kraken Finned Franken X-Wing.
Finned Franken X-Wing: 9 r69/c4b7 fr6c6,r9c9
(9-6)r6c6 = r6c79 - (6=5)r5c8 - r5c2
(9-4)r9c1 = (4-5)r2c1 = r4c1 - r5c2
(9)r9c2 - r789c1 = (9-5)r2c1 = r4c1 - r5c2
(9)r9c3 - r5c3 = (9-5)r5c2
(9)r9c9 - (9=5)r2c9 - r2c1 = r4c1 - r5c2
=> -5 r5c2

Step 3: UR Type 1.

Code: Select all

.---------------.---------------.---------------.
| 3    569  689 | 2    1    4   | 568  7    68  |
| 45   7    14  | 6    3    8   | 15   2    9   |
| 68   2    168 | 7    9    5   | 168  4    3   |
:---------------+---------------+---------------:
| 58   35   38  | 4    6    1   | 2    9    7   |
| 2    69   69  | 8    7    3   | 4    5    1   |
| 1    4    7   | 5    2    9   | 68   3    68  |
:---------------+---------------+---------------:
| 7    1    2   | 3    5    6   | 9    8    4   |
| 9    8    5   | 1    4    7   | 3    6    2   |
| 46   36   346 | 9    8    2   | 7    1    5   |
'---------------'---------------'---------------'
UR Type 1: (68)r16c79 => -68 r1c7; stte

200e200w

Edit: Corrected a typo in Step 2. Thanks to SpAce for sighting it.

[SpAce]

200e200w, thanks for your informative post!

I don't really understand those ratings.

These ratings are:
SudokuWiki - I don't understand Andrew's rating system.
Hodoku - sum of ratings of all steps. Also used by SudoCue.
Sudoku Explainer - rating of the hardest step required to solve the puzzle.

I think SudokuWiki has a summing point system similar to Hodoku's. At least their ratings are usually in step. Sudoku Explainer, however, has sometimes quite weird ratings from a manual solver's point of view. I think the perceived difficulty of a puzzle depends mainly on three variables: the most difficult technique required (which, of course, is somewhat subjective), the number of steps required (times their difficulty), and the narrowness of the solve path. The SE ratings apparently only count the first variable, though I'm not sure how exactly it calculates the result. Even that doesn't explain some things. For example, compare the puzzle above with this other puzzle that has the same SE rating of 8.4:

000900030004700600081054002005000000000020308000090060000070800017000000400106050

Code: Select all

+----------------------+-------------------+--------------------+
| 2567    2567   26    | 9     168   128   | 145   3     145    |
| 2359    2359   4     | 7     13    123   | 6     8     15     |
| 36      8      1     | 36    5     4     | 79    79    2      |
+----------------------+-------------------+--------------------+
| 1236789 234679 5     | 3468  13468 1378  | 12479 12479 1479   |
| 1679    4679   69    | 456   2     157   | 3     1479  8      |
| 12378   2347   238   | 348   9     1378  | 12457 6     1457   |
+----------------------+-------------------+--------------------+
| 23569   23569  2369  | 2345  7     359   | 8     1249  13469  |
| 235689  1      7     | 23458 348   3589  | 249   249   3469   |
| 4       239    2389  | 1     38    6     | 279   5     379    |
+----------------------+-------------------+--------------------+


I don't think their difference is just in the number of steps required! I'm pretty sure this latter puzzle requires not only many more but also much harder steps (both Hodoku and SudokuWiki seem to agree). On the other hand, the other puzzle is solvable with pretty basic AIC techniques: not even ALS-nodes are needed. The only "advanced" feature in my solution is group nodes. Still, both are SE 8.4.

I had the same number of steps (11) as Hodoku...

That was 11 unedited steps, meaning I took some steps that weren't necessary but recorded them anyway to demonstrate a human solving process. It's hard to calculate on the go which eliminations end up being important, even though I try to have some strategy. I guess the same is true for software solvers unless they analyze and optimize the full solve path before showing it. On the go they usually seem to pick the simplest step available (depending on how they're ordered) without much strategic planning.

Anyway, my relevant original path was 8 steps. Afterwards I managed to reduce it to 7 while also simplifying the steps (no more ALS-nodes) and making the progression more logical:

1. Grouped X-Chain (Kite): (5)r6c4 = r6c79 - r5c8 = (5)r7c8 => -5 r7c4
2. Grouped AIC: (5)r9c4 = r6c4 - (5=6)r4c5 - r12c5 = (6)r2c4 => -6 r9c4
3. Grouped AIC: (5)r7c8 = r5c8 - r6c79 = r6c4 - (5=9)r9c5 - r9c9 = (9)r7c7 => -5 r7c7
4. X-Chain: (5)r2c1 = r4c1 - r5c2 = r5c8 - r7c8 = (5)r9c9 => -5 r2c9
5. Grouped AIC: (5)r2c1 = r4c1 - (5=6)r4c5 - r12c5 = r2c4 - (6=9)r2c9 => -9 r2c1
6. AIC: (9=5)r9c4 - r6c4 = r4c5 - r4c1 = (5-4)r2c1 = (4)r9c1 => -9 r9c1
7. UR Type 1 (68): r16c79 => -68 r1c7; stte

I don't know if it can be made much shorter without resorting to more complicated steps. My point is: if that puzzle can be solved with six relatively simple chains and one UR of the simplest and most obvious kind, how can it have the same SE rating as the other one??? That part I don't understand at all.

Using Hodoku's "Find all steps" tool, powered by all techniques up to Kraken Fish, I managed to reduce the number of required steps to only 3. First is a Kraken Finned X-Wing, second is a Kraken Finned Franken X-Wing, third is UR Type 1. I'll post that solution later.

Thanks for showing that! Pretty cool. While I have no immediate plans to start fishing or using krakens, your example helped me understand those concepts better. Maybe one of these days. My current manual solving skill and tool sets support finding chains pretty well, but not so well other kinds of patterns including complex fishes. Therefore I don't consider them human-friendly solving techniques at this point.

Did Hodoku show you those kraken fishes directly or did you do something else to find them? I couldn't find them in the list but maybe I didn't look hard enough (there were about 200 kraken fishes listed). How did you know which ones would be the most productive?

[SpAce]

Ok, I'll now post the solution.

Thanks for these! Very interesting to me as I'm not proficient with either complex fishes or krakens. This definitely helped me get some grasp because these were pretty understandable examples.

PS. I think I spotted one typo (the 9 added):

Kraken Finned Franken X-Wing.
Finned Franken X-Wing: 9 r69/c4b7 fr6c6,r9c9
(9-6)r6c6 = r6c79 - (6=5)r5c8 - r5c2

[200e200w]

(9-6)r6c6 = r6c79 - (6=5)r5c8 - r5c2

Of course you were right, SpAce. Corrected.

200e200w

[200e200w]

Did Hodoku show you those kraken fishes directly or did you do something else to find them? I couldn't find them in the list but maybe I didn't look hard enough (there were about 200 kraken fishes listed). How did you know which ones would be the most productive?

Of course, all Kraken Fish were shown to me by Hodoku. I knew which ones are the most productive ones from the sorting machine of Hodoku's 'Find all steps' tool, that has 5 sortings:
1 - Sorting by the number of directly unlocked singles (ie. the singles that are unlocked using only this step and other singles).
2 - Sorting by the number of singles unlocked by this technique and all 'Progress' steps (for me, all basic steps and nothing else).
3 - Sorting by the cell in which the elimination/digit placement occurs.
4 - Sorting by number of eliminations.
5 - Sorting by technique used.
I use the sortings 1 and 2 - they give the moves that unlock most singles, and give most progress on the puzzle. I also use this tool to see if a potential Nightmare could be a Nightmare, a One-Trick Pony, or it should go out.

200e200w

[SpAce]

Did Hodoku show you those kraken fishes directly or did you do something else to find them? I couldn't find them in the list but maybe I didn't look hard enough (there were about 200 kraken fishes listed). How did you know which ones would be the most productive?

Of course, all Kraken Fish were shown to me by Hodoku. I knew which ones are the most productive ones from the sorting machine of Hodoku's 'Find all steps' tool, that has 5 sortings:
1 - Sorting by the number of directly unlocked singles (ie. the singles that are unlocked using only this step and other singles).
2 - Sorting by the number of singles unlocked by this technique and all 'Progress' steps (for me, all basic steps and nothing else).
3 - Sorting by the cell in which the elimination/digit placement occurs.
4 - Sorting by number of eliminations.
5 - Sorting by technique used.
I use the sortings 1 and 2 - they give the moves that unlock most singles, and give most progress on the puzzle. I also use this tool to see if a potential Nightmare could be a Nightmare, a One-Trick Pony, or it should go out.

Thanks for the tips! As can be seen, I haven't used Hodoku much. Those tips helped, but I still can't reproduce your process of finding those steps. For the first step I can find the elimination through sorting by the cells, but it only shows two Forcing Net solutions (no Krakens mentioned). For the second step I can find the Kraken solution using the cell sorting. However, I can't find anything about two those cells using sortings 1 or 2. I assumed they should be at the beginning of those lists if you thought they should be most productive? What am I doing wrong? (Btw, it's very tiresome to click open all those trees in sortings 1 and 2 -- is there a way to open them all at once?)

PS. Can you explain why Sudoku Explainer gives those two puzzles the same rating? I'm sure you agree that their difficulties are very different from a human solver's point of view?

[200e200w]

Hi, SpAce!

For the first step I can find the elimination through sorting by the cells, but it only shows two Forcing Net solutions (no Krakens mentioned).

If you want to see this Kraken Fish, you need to go to Edit -> Preferences -> Steps and tick 'Allow ALS in chains'. Then, you will be able to see my Kraken Finned X-Wing (it uses ALS nodes, which I have enabled to give Hodoku more power in solving sudokus - at best settings it can crush sudokus up to ER=9.6!)

PS. Can you explain why Sudoku Explainer gives those two puzzles the same rating? I'm sure you agree that their difficulties are very different from a human solver's point of view?

I cannot explain why SE gives both puzzles the same rating. But I agree that their difficulties are very different from a human solver's point of view. Hodoku also agrees:
Your puzzle:
SE: 8.4
Hodoku: 9198
My rating system (based on hardest technique as of Hodoku): 10.3
Puzzle from this thread:
SE: 8.4
Hodoku: 3864
My rating system: 7.9

200e200w

PS. I will publish my rating system when I'll end doing examples. I finished the first two, the third is still unfinished. But I can tell you why I decided to create it. That's because of eleven's complains about my Nightmare #6, which was too easy. He said that the puzzle can be solved using only W-Wings, XY-Wings and Single Digit Patterns (except from basic moves). More about that here.

[SpAce]

If you want to see this Kraken Fish, you need to go to Edit -> Preferences -> Steps and tick 'Allow ALS in chains'. Then, you will be able to see my Kraken Finned X-Wing (it uses ALS nodes, which I have enabled to give Hodoku more power in solving sudokus - at best settings it can crush sudokus up to ER=9.6!)

Thanks again! That helped. Now I can find it and understand your process.

I cannot explain why SE gives both puzzles the same rating. But I agree that their difficulties are very different from a human solver's point of view. Hodoku also agrees:
Your puzzle:
SE: 8.4
Hodoku: 9198
My rating system (based on hardest technique as of Hodoku): 10.3
Puzzle from this thread:
SE: 8.4
Hodoku: 3864
My rating system: 7.9

Thanks for that, too! Your and Hodoku's ratings seem much more logical in this case. For comparison, SudokuWiki grades them like this:

"My" puzzle (actually a SudokuWiki 3D-Medusa example): 1526 (Extreme)
Puzzle from this thread: 279 (Extreme)

Those points are not exactly logical either as the latter score seems too low now. I think it would get a higher score if it weren't partly completed. Nightmarish puzzles typically get a score between 600-900, which I guess depends more on the number of steps than the difficulty of them (which explains the low score here). For comparison, I've seen it give 898 points to a puzzle (SE 7.2) that it marked only "Diabolical" instead of "Extreme" (I guess that label only depends on the most difficult step). Then again, an SE 8.9 puzzle only got 814 (Extreme). I've also seen it give only 440 points (Extreme) to an SE 8.2 puzzle, while an SE 7.9 one got 1389 points (Extreme). So, it's a bit weird rating system, though not completely broken: those values did correspond relatively well (better than SE) with the perceived difficulty (or tediousness) of manual solving (at least for me).

PS. I will publish my rating system when I'll end doing examples. I finished the first two, the third is still unfinished. But I can tell you why I decided to create it. That's because of eleven's complains about my Nightmare #6, which was too easy. He said that the puzzle can be solved using only W-Wings, XY-Wings and Single Digit Patterns (except from basic moves). More about that here.

Sounds good! And good work in general -- glad to have you here!

[SpAce]

I found this thread about SE which mentioned, among other things, this:

for sure, using groups, we have a very simple chain.

SE does not recognize groups, so it will never generate such a chain and has no rating for it.

http://forum.enjoysudoku.com/oddities-of-sudoku-explainer-t6672-60.html#p211228

I was wondering if that might have something to do with the weird ratings on some puzzles? Could it be giving too high ratings for puzzles that are relatively simple to solve with grouped chains (like this one here)?

Is there good (or any) documentation available for the techniques SE uses? Some of the names it uses aren't quite standard, so it would be helpful to know their correspondence with more familiar names. For example, is a "dynamic forcing chain" basically equivalent to a forcing net? In the above thread (page 3) I also found this, which I interpreted as much:

When using a dynamic method in SE, after finding that a candidate of a cell cannot exist while searching for a chain (assuming some value is on or off to start with), that candidate value is removed from the cell when processed and the search for a contradiction continues

The term dynamic is for dynamic removal of candidates while searching contradiction

I found this list explaining a bit about how SE ratings are related to the various techniques:

http://english.log-it-ex.com/3.html

However, that list stops at SE 9.5 and Dynamic Forcing Chains. What techniques does SE use beyond 9.5 and how does it rate those? I see it also has Multiple Forcing Chains and Nested Forcing Chains available which are not on the list. Are those used for the hardest puzzles? Does the "chain" length and/or nesting depth determine the final score for them?