The New Sudoku Players' Forum

[SpAce]

I've been solving sub-9 puzzles consistently without problems, so I finally decided to take a stab at the next level. I picked a low 9.x puzzle randomly from the patterns game, and well, my feeble skills weren't any kind of a match for it I got exactly two placements with horrible nets before I gave up. I expected it to be a different game but not this different.

What surprised me more, however, was that even Hodoku couldn't solve it without two brute force moves (I'm pretty sure I've turned on all of its techniques -- Edit: but I was wrong, see below). The SudokuWiki solver couldn't solve it at all. I didn't expect that since the rating was only 9.2. To be exact, it was ED=9.2/9.2/8.9, which might explain the overall difficulty (if I understand those latter numbers correctly), but still, shouldn't Hodoku be able to handle max-9.2-techniques without resorting to brute force?

Anyway, I was wondering if a skilled human (or program) can find some advanced patterns here that would make it solvable without crazy forcing nets (or at least fewer of them)? I know some only by name (JExocet, SK-Loop, etc) and their general principles but have never used any.

Code: Select all

. . 1 | . . . | . . 2
. . 2 | 3 1 . | . 4 .
5 6 . | . . 2 | 7 . .
------+-------+------
. 3 . | . . . | . . .
. 2 . | . . . | 5 . .
. . 7 | . . 1 | . 8 .
------+-------+------
. . 6 | . 5 . | . . 9
. 1 . | . . 4 | . . .
9 . . | . . . | 3 . 4  ED=9.2/9.2/8.9

http://forum.enjoysudoku.com/patterns-game-t6290-35775.html#p263656

Code: Select all

.-------------------.------------------------.--------------------.
| 3478   4789  1    | 456789   46789   56789 | 689    3569   2    |
| 78     789   2    | 3        1       56789 | 689    4      568  |
| 5      6     3489 | 489      489     2     | 7      139    138  |
:-------------------+------------------------+--------------------:
| 1468   3     4589 | 2456789  246789  56789 | 12469  12679  167  |
| 1468   2     489  | 46789    346789  36789 | 5      13679  1367 |
| 46     459   7    | 24569    23469   1     | 2469   8      36   |
:-------------------+------------------------+--------------------:
| 23478  478   6    | 1278     5       378   | 128    127    9    |
| 2378   1     358  | 26789    236789  4     | 268    2567   5678 |
| 9      578   58   | 12678    2678    678   | 3      12567  4    |
'-------------------'------------------------'--------------------'

[Leren]

Looks like a brute to me. Couldn't find any JExocets, SK Loops, Multifish or MSLS.

Leren

[champagne]

you can have a look at the way Sudoku Explainer solves it, nothing exciting for a manual player.
Many steps in the area 8.9 9.2.
The first steps say

7 r1c1 -> no '4' in box 1
8 r1c1 -> no '4' in box 1
6 r2c9 -> no 8 in column 9 ....

[200e200w]

Hi, SpAce!
I used Hodoku at maximal settings and got this result (only techniques used and their frequency + rating of puzzle):
1 x 2-String Kite
1 x Hidden UR
1 x Finned Swordfish
1 x XY-Chain
1 x AIC
1 x Discontinuous Nice Loop
2 x Grouped AIC
12 x Grouped Discontinuous Nice Loop
1 x Kraken Fish Type 1
12 x Kraken Fish Type 2
Score: 12718/10.3
So, it is solvable with only pure and human-friendly logic. Another thing to say, I said here that Hodoku at maximal settings can solve puzzles using only logic even up to ER=9.6.
If you want to try more puzzles with ER~9.0, try Andrew's Weekly Unsolvables or my Top 250. Most of Andrew's Unsolvables and hardest puzzles in my Top 250 are from ~9.0 level, so you will have some fun from solving them (if you will manage to do it...).

200e200w

[SpAce]

Thanks Leren and champagne for confirming that I wasn't totally imagining the puzzle's hellish nature. And 200e200w -- thanks for telling me that I sort of was anyway

Hi, SpAce!
I used Hodoku at maximal settings and got this result (only techniques used and their frequency + rating of puzzle):
...
1 x Kraken Fish Type 1
12 x Kraken Fish Type 2
Score: 12718/10.3

Thanks! Seems that I wasn't using high enough Hodoku options after all.

So, it is solvable with only pure and human-friendly logic.

Pure, yes, but I guess we have a bit different definition of human-friendly logic I'd really like to see a human actually solve it using those techniques without computer aids and call it human-friendly. The list would be a bit more descriptive if it showed what kind of kraken fishes were used. I'm not sure if things like Type 2 Kraken Franken Whales with 4 fins etc can be called exactly human-friendly, unless someone shows me how they can be found relatively easily using just pencil and paper. I guess anything can be called a fish if you just add enough fins, which makes finding the useful ones pretty tough, I would imagine.

Another thing to say, I said here that Hodoku at maximal settings can solve puzzles using only logic even up to ER=9.6.

I remembered that, which is why I was puzzled when Hodoku couldn't solve it without brute force. I thought I'd already turned on all options after that discussion, but it turns out I hadn't (or perhaps I'd turned something back off to save time). Thanks for letting me know (again). With untied hands Hodoku did indeed solve this without brute force, but it took a long time. If it takes software that long to solve using those kinds of techniques, how long does it take for a skilled human?

If you want to try more puzzles with ER~9.0, try Andrew's Weekly Unsolvables or my Top 250. Most of Andrew's Unsolvables and hardest puzzles in my Top 250 are from ~9.0 level, so you will have some fun from solving them (if you will manage to do it...).

Thanks for the tip! I will try them, at some point. This one wasn't a particularly encouraging first attempt, though I was wondering if there were any 9-level puzzle collections screened for human consumption? I'd still like to get some practice with the harder techniques, but with some milder examples. With my minimal experience it seems like the jump from 8 to 9 is quite huge compared to the gap between 7 and 8. Most of the time I couldn't tell the difference between ER 7.x and 8.x puzzles, but it seems the game changes radically at 9.x. Does that assumption have any merit?

[totuan]

Code: Select all

 *--------------------------------------------------------------------------------------*
 | 3478     4789     1        | 456789   46789    56789    | 689      3569     2        |
 | 78       789      2        | 3        1        56789    | 689      4        568      |
 | 5        6        3489     | 489      489      2        | 7        139      138      |
 |----------------------------+----------------------------+----------------------------|
 | 1468     3        4589     | 2456789  246789   56789    | 12469    12679    167      |
 | 1468     2        489      | 46789    346789   36789    | 5        13679    1367     |
 | 46       459      7        | 24569    23469    1        | 2469     8        36       |
 |----------------------------+----------------------------+----------------------------|
 | 23478    478      6        | 1278     5        378      | 128      127      9        |
 | 2378     1        358      | 26789    236789   4        | 268      2567     5678     |
 | 9        578      58       | 12678    2678     678      | 3        12567    4        |
 *--------------------------------------------------------------------------------------*

An urgly part for this one – hope a better from others:

01: Present as diagram: => r1c8<>9

Code: Select all

(7)r9c6-r2c6=r2c12—-----(7)r1c2
 ||                 |    ||
(8)r9c6-(58=7)r9c23-    (9)r1c2*
 ||                      ||
 ||                     (4)r1c2-r7c2=(4-2)r7c1=(2)r8c1-(2=689)r128c7*
 ||                      ||     
 ||                     (8)r1c2-(8=7)r2c1-(7)r8c1
 ||                                        ||
(6)r9c6-(6)r8c45                          (2)r8c1-(2=689)r12c7*
         ||                                ||
        (6)r8c7-(6=89)r12c7*              (3)r8c1-r1c1=r1c8* 
         ||                                ||   
        (6)r8c8-(5)r8c8                   (8)r8c1-r8c9=r23c9-(8=69)r12c7* 
         ||      ||
         ||     (5-3)r8c3=r3c3-r1c1=r1c8*
         ||      || 
         ||     (5-8)r8c9=r23c9-(8=69)r12c7*
         ||
        (6-8)r8c9=r23c9-(8=69)r12c7*

From here it’s not hard to downgrade the puzzle based on Almost X-wing 9’s on r68, I’m lazy to complete it

totuan

[SpAce]

Code: Select all

(7)r9c6-r2c6=r2c12—-----(7)r1c2
 ||                 |    ||
(8)r9c6-(58=7)r9c23-    (9)r1c2*
 ||                      ||
 ||                     (4)r1c2-r7c2=(4-2)r7c1=(2)r8c1-(2=689)r128c7*
 ||                      ||     
 ||                     (8)r1c2-(8=7)r2c1-(7)r8c1
 ||                                        ||
(6)r9c6-(6)r8c45                          (2)r8c1-(2=689)r12c7*
         ||                                ||
        (6)r8c7-(6=89)r12c7*              (3)r8c1-r1c1=r1c8* 
         ||                                ||   
        (6)r8c8-(5)r8c8                   (8)r8c1-r8c9=r23c9-(8=69)r12c7* 
         ||      ||
         ||     (5-3)r8c3=r3c3-r1c1=r1c8*
         ||      || 
         ||     (5-8)r8c9=r23c9-(8=69)r12c7*
         ||
        (6-8)r8c9=r23c9-(8=69)r12c7*

Wow! That's a pretty cool net With your notation it's surprisingly understandable, too! I'm just wondering... how do you actually find such beasts? I've understood that you're a master of these kinds of net solutions, so I guess you must have a method for it.

Btw, is there an 8 missing here: (2)r8c1-(2=689)r128c7* ?

[200e200w]

Good news to you, SpAce!
There are 9.x puzzles for which the hardest required techniques according to Hodoku are AIC's. These are 2 examples of them, with SE rating at the end of the line:
.4..1.2.......9.7..1..........43.6..8......5....2.....7.5..8......6..3..9........ (ER=9.2)
....4...1.3.6.....8........1.9..5.........87....2......7....26.5...94.........3.. (ER=9.0)
Try them - with your skills I'm sure you'll solve them.

200e200w

[SpAce]

Thanks, 200e200w! I appreciate it, and it will be interesting to see what happens (when I have time to try them). My confidence level just dropped a bit, as I got stuck with your Weekly Extreme #3, even though it was only 8.1. It seems that my earlier claim about sub-nine puzzles was premature. Now I'm left wondering if there might be even 7.x puzzles that could beat me :/ The ER doesn't seem like an exact indicator of perceived difficulty.

[200e200w]

About your problems with my WE #3, this is the pencilmark grid in the puzzle's most difficult moment:

Code: Select all

.-----------------.-----------------.---------------.
| 4579  489  1    | 589  3589  2    | 3479  6    39 |
| 279   3    279  | 4    6     79   | 8     5    1  |
| 6     489  579  | 1    3589  3579 | 3479  349  2  |
:-----------------+-----------------+---------------:
| 239   5    6    | 7    239   1    | 39    8    4  |
| 479   1    3479 | 89   3489  349  | 5     2    6  |
| 8     249  349  | 259  3459  6    | 1     39   7  |
:-----------------+-----------------+---------------:
| 3459  249  3459 | 259  7     8    | 6     1    39 |
| 239   7    8    | 6    1     49   | 234   349  5  |
| 1     6    259  | 3    2459  459  | 249   7    8  |
'-----------------'-----------------'---------------'


Just use this Kraken Cell:

Code: Select all

Kraken Cell r7c2.
(2)r7c2
||
(4)r7c2 - (4=98)r13c2 - 9r2c13 = r2c6 - (9=4)r8c6 - (4=239)b9p345
||
(9)r7c2 - (9=3)r7c9 - r7c13 = r8c1
=> -2 r8c1


Then, you should be able to solve the puzzle.
Was it helpful for you?

200e200w

[SpAce]

Thanks, I'll try that! I have to admit that I got stuck two moves earlier. I missed the eliminations of 3r5c1 and 4r3c3. I'm especially pissed about the latter, because it was findable with a simple Grouped AIC (although for some reason Hodoku shows it as a huge ALS-XZ move). I should have seen that at least. I got to that point with four relatively easy moves (1. AIC-Loop, 2. AIC, 3. X-Wing, 4. XYZ-Wing).

[JasonLion]

The ER doesn't seem like an exact indicator of perceived difficulty.

No it isn't. Most people agree that there isn't any existing rating system that gives perceived difficulty It is an open question if such a rating system in even possible in principal.

[StrmCkr]

It is an open question if such a rating system in even possible in principal.

agreed

i purposed such as system years ago to give a more generalized human difficulty grading system as a three pronged approach

simplicity, complexity and comparison Rating
outlined in this post

however:
writing a program that finds every single technique type and variation at each step and track the total count of each that has eliminations and without eliminations
further complicated by allowing it to have a mutable solving sequence {selecting only 0-N of each technique at each step {where n is the move count with eliminations} }

that way we can compare solving paths, number of steps and possible number of moves at each step and technique type.
to generalized how difficult each step is at finding a valid advancing move.

this task alone would be more difficult and time consuming not to mention each puzzle could take exponential time to compute the three rating

ultimately probably not feasible compared to writing a fixed sequence solver based on some agreed steeping system that's currently in ER. {which does need a massive overhaul, to include more modern system}

my own project can do the first sections relatively easy as i coded it as a depth first search engine and reports both elimination steps and non elimination steps.
it can also do every technique at each step of the puzzle with out disturbing the grid.

I had a mutable selection of code at one point, and found out that some moves remove other techniques when the sequence changes which could actually make a puzzle harder
{even adding an early single can make a puzzle harder}

i've never went as far as adding a technique set rating, due to the following

my whole problem arrived when I scaled the search size of some technique set
ie:
my first fishing program
searching nxn+k for size N (1-7) where k=0,1,2 on digits 1-9 took 16.75 hours on 1 grid at each step. {current builds have it down to 3.25 hours}

that's just 1 of many techniques...

if its searching for all of them that could be days at each step.

meaning this whole task is another NP-{class} problem.

[SpAce]

I had a mutable selection of code at one point, and found out that some moves remove other techniques when the sequence changes which could actually make a puzzle harder
{even adding an early single can make a puzzle harder}

I'm interested in this, as it's really counter-intuitive. I've seen it mentioned elsewhere (including the thread you linked) but I'd like to see more examples. What kind of moves are affected? I've understood that at least uniqueness-based ones are, which is logical, but what else?

[StrmCkr]

It's deffintly not a documented objective.. most of the examples directly are uniqueness based as you mentioned and I Belive there is links in the thread I posted about a possible rating theory.

Alot of techniques are affected in theory... however direct examples don't exist to the best of my knowledge..
The idea behind it is:
Placing a single breaks a link in the same cell completing a shorter version of a move set, their could be a longer version still applicable, or it can completly dissolve all advancing techniques for that specific technique set.

since most solvers are hierarchy based with simplistic to difficulty grading this oddity is very often over looked.

The easiest way to self check is by opening a grid in Hodoku, and run a. Search on all techniques, place a single note the 20 cells affect for digit placed. The re run then the solver, and note how many techniques vanished that are not excluding those 20 cells.

Have fun.
Ps I know one of my grids a few years back was an example of this issue....
Adding an extra clue made the 8.4 puzzle jump to a 9.2
which one it was might take a while.. Pretty sure it was savage attacking monster (suggest a move)