The New Sudoku Players' Forum

[SpAce]

SpAce, as the originator of GEM, I admire your perseverance in employing it manually and am pleased that you have been able to benefit from it.

Thanks, David, and good job for creating GEM! I'm a fan of your invention so I'm glad to hear from you. I guess I was biased to picking up GEM, because I'd wanted to create something similar to replace my old trial-and-error markers, especially after experimenting a bit with X-Colors. Then I found you had my vision already nailed perfectly so there was no need to reinvent the wheel, except for the manual mark-up details.

At first I tried but quickly ditched your spreadsheet approach, even though it's clearly more flexible with regards to multiple seeding points. It seemed tedious and hard-to-read for me, and I'm a pencil-and-paper purist anyway (at least for now). I also haven't found use for group markers, because they seem more confusing than helpful (my mark-up already highlights group-relationships so they'd be kinda redundant, too). With those minor tweaks, I find GEM very intuitive and quick to use, and it has nice synergy with my other mark-up which is designed to make it easy to find and follow various kinds of chains.

After a while the housekeeping involved in solving puzzles gets very tedious, so I designed a 'Sudoku Drudge' spreadsheet to highlight singles, doubles, etc so I could quickly get to the more challenging bits. I then extended its colouring capabilities to be able to follow alternating inference chains using the GEM equivalence marks.

Nice. For some crazy reason I've enjoyed the challenge of adding similar features to my pencil-and-paper system. Of course there's no avoiding the housekeeping and the time it takes when done manually, but at least my in-place bookkeeping system ensures that mistakes occur almost never, basic solving gets done almost automatically, and the advanced mark-up stays up-to-date all the time. It's also purely additive so there's no need for an eraser (unless one makes an actual mistake, which rarely happens). I'm sure one of these days I'll get tired and turn my system into software, but so far I'm quite happy to endure the pains There's just something nice about doing it with the simplest possible tools, and the time wasted on the initial mark-up and housekeeping is insignificant next to the thinking time in the more difficult puzzles.

However I discipline myself only to follow single, un-branched chains, so I do not grade-mark these candidates as that would amount to using a network approach.

I admire your discipline I may give that approach a try. Then again, nowadays I only use GEM when it seems that I may actually need a network approach or can't otherwise proceed, and in that case I freely take everything it's willing to give. Of course it typically reveals un-branched chains I've missed as well, and I prioritize those over possible netting results (which aren't normally necessary). I avoid taking advantage of netting unless I see no other way out.

Taken to completion, GEM marking will kill most published problems very easily, but will identify many insignificant eliminations in the process. Here the challenge is to firstly only to mark up the parts of a puzzle that appear to have openings and secondly try to keep the solution as short as possible by identifying and eliminating the significant candidates first.

I understand. I'm not yet in the level that I'd try to optimize or restrict the solving path too much, but I'll keep in mind those additional challenge options. My first priority is to find at least one working path, but especially with simpler puzzles I try to find some alternate ways as well. So far I've been aiming more for simplicity and repeatability than maximum efficiency or elegance. I'm sure priorities will change with improving skills.

As the level of difficulty of the puzzles increases though, it becomes necessary to look for patterns such as Unique Rectangles and Finned Fish that will provide further inferences that can be followed.

Yes, it seems that the power of GEM grows exponentially with one's general solving skills. That's probably one reason why it could now solve the difficult puzzle that got stuck earlier, because I got more candidates marked than before (all of them, actually). By the way, it got solved in a bit weird way that I hadn't seen with GEM before and didn't immediately even recognize as a solution:

GEM only gave me a few eliminations and one solved cell directly, which didn't help much, and it didn't provide any parity-wide contradictions either. At first glance I thought the result was useless. Then I looked at it again and noticed that every cell that didn't have two opposing par markers had one candidate with either a par (only a few) or a super marker (many) of the same parity -- and there was one for each number in each unit (the rest were obviously sub markers). Surprisingly the whole solution sat right there in those aligned super and par markers. It took me a minute to grasp and believe that but it was easily verified to be true. Basically it turned into a classic trial-and-error happy path, which I surely didn't expect or aim for. Lucky seeding point?

Used in that way it need not be the 'Dark Side of the Force' that you are making it out!

I wasn't insulting GEM -- I'm a fan of the Dark Side of the Force just like I'm a fan of GEM! I just see this similarity and its associated risks:

Luke: "Is the dark side stronger?"
Yoda: "No, no, no. Quicker, easier, more seductive."

What I mean is that it's quite easy to ditch discipline and use the full power without much thinking, which may hinder learning and enjoying other techniques. On the other hand, it may also help learning, as it has for me. When I was a complete beginner with patterns and chains, I used GEM to find eliminations first and then looked for logical reasons behind them. That's how I learned to recognize useful chains. Also, as you said, in the real difficult puzzles one needs those "light-side" techniques as well to boost GEM, so it's not a silver bullet alone.

[SpAce]

I ran your hard puzzle through Hodoku and it's solution was a real nightmare. Among it's many moves were 18 linear AIC's and three Forcing Chain moves that read like War and Peace.

Glad to know I wasn't battling an imagined monster! I guess I got lucky with it in the end.

Well worth downloading this free software. If you are having trouble solving a puzzle, check the Hodoku solution, and if it's no simpler than yours you can stop beating yourself up trying to find an easy solution that is just not there.

Thanks for the tip! I just downloaded it. I've studied Hodoku strategy materials quite a bit but never tried their software before. I've mostly used the SudokuWiki Solver to check what alternate solving paths I've missed. The only other software I've used (very little, mainly for grading) is the Sudoku Explainer. How does Hodoku compare to them?

[Leren]

The good things I like about Hodoku is that it has most, if not all, modern moves and a database of puzzles with particular moves in mind.

The really amazing thing about it is the method of loading a puzzle. You simply copy it into the past buffer, in any format, and paste it directly from there into Hodoku.

To date I haven't found a puzzle format that it doesn't read in correctly. Me think that mazing

Leren

[David P Bird]

SpAce, thanks for your kind comments. To a certain extent I envy you as you are at the start of a quite enjoyable and fulfilling path of discovery which will pose questions about what you find acceptable elimination methods, whereas I'm reaching the other end of mine.

As your experience grows you will start to recognise familiarities between puzzles and will develop an eye for the potential openings they offer, which will influence your line of attack – the first seed points to use in GEM terms. The colouring options on computer helpers will highlight where the native strong links in a puzzle exist through bivalue cells or bilocal digits in a house, and some manual solvers maintain 'b/b plots' on the side to keep track of them. These are helpful in identifying fruitful start points, however they must be kept up to date as the solution develops - something I leave to my spreadsheet.

In difficult puzzles the native strong links will be quite sparse and additional strong link sources must be found, for example, as provided by group nodes and the candidates in Almost Naked Sets (a common source). Recognising these is where experience will tell.

Enjoy your journey!

David
.

[tarek]

The good things I like about Hodoku is that it has most, if not all, modern moves and a database of puzzles with particular moves in mind.

The really amazing thing about it is the method of loading a puzzle. You simply copy it into the past buffer, in any format, and paste it directly from there into Hodoku.

To date I haven't found a puzzle format that it doesn't read in correctly. Me think that mazing

That is why credit should be given to hobiwan for developing that software. He was active in the UFG thread & has a very good fish catcher there. the command line batch solver / generator there is also good and has helped in the NoFish collection as well.

Well done hobiwan

tarek

[SpAce]

SpAce, thanks for your kind comments.

You're welcome.

As your experience grows you will start to recognise familiarities between puzzles and will develop an eye for the potential openings they offer, which will influence your line of attack – the first seed points to use in GEM terms.

I bet. That's why I designed an elaborate mark-up method to provide visual cues to compensate for my relative lack of experience. It wasn't *all* luck that I happened to pick a surprisingly fruitful seed point in the above mentioned puzzle (and found some complex chains before that). While still lucky, it was also a calculated decision based on my mark-up that let me predict how deep and wide GEM could slide its tentacles. Like I said, I can use only one seed point (easily) so I like to have the odds on my side before I commit to one.

The colouring options on computer helpers will highlight where the native strong links in a puzzle exist through bivalue cells or bilocal digits in a house,

That's what my mark-up does, but it also highlights more complex strong links, such as group-links, empty rectangles, and (other) "almost something" -links I spot and deem potentially useful. All with the same pencil gray.

and some manual solvers maintain 'b/b plots' on the side to keep track of them.

I don't. The mark-up on my main grid keeps track of all strong links, including advanced types, and it's my main tool for spotting AICs. I may use one or two helper plots, though: one for single digits and another for bivalue cells. They can reveal many simpler patterns and chains directly and also support with AICs. The obvious drawback is that there's possibly three different things to maintain, but with difficult puzzles it's ok because they advance slowly anyway. In less difficult puzzles not all (or any) of them are needed. My system scales pretty well with the difficulty level (even if unknown at the start), which minimizes unnecessary overhead.

BTW, I've tried but failed to create a useful b/b plot. Where could I find an example of such a thing? I've seen it mentioned in many places, and I think I understand the general idea, but I can't find any sample images (looks like they were removed from a discussion I found here: Nice loops for advanced level players - b/b plot). Anyway, if I've understood anything from the descriptions, I have a feeling that it would typically turn into a mother of spaghetti-monsters. I don't think I would find that very helpful, and I've felt the same way with some software chaining aids.

These are helpful in identifying fruitful start points, however they must be kept up to date as the solution develops - something I leave to my spreadsheet.

I understand, and I wouldn't mind some level of automation myself. Then again, too much automation can make one miss certain developments on the grid. That's why I have, for example, a multi-phase candidate elimination process which ensures that no relevant information is lost before its effects are calculated and marked-up. Software can do all that in one step and really speed things up but, I'm wondering, does the player get disoriented if the board changes drastically all at once after a big move? I kinda like it that I'm fully aware when and where new strong links etc are born when a longer chain reaction is taking place.

In difficult puzzles the native strong links will be quite sparse and additional strong link sources must be found, for example, as provided by group nodes and the candidates in Almost Naked Sets (a common source). Recognising these is where experience will tell.

Yes. I've used ANS links quite often, especially when solving the mentioned puzzle (both before and while applying GEM). I think I used AHS in some chains as well. They're easy enough. I've yet to spot opportunities to chain more complex structures like almost-fishes or almost-unique-rectangles, but I understand the principle.

Enjoy your journey!

Thanks! You too -- even if you feel you're already there

[David P Bird]

SpAce, it's clear that you have done more research than I first gave you credit for!

On b/b plots there is no simple answer as either they get too elaborate or they only provide part of the picture. Mine uses a small side grid where only the bilocal digits are shown in each of the cells. As I change the focus digit, the cells where it is bilocal are highlighted in one colour and where it is part of a bivalue in another colour. When I survey the sources of additional strong links for that digit I can then refer to this plot to check the prospects for chain building from that link. I look on this as a basic memory aid as doing this in the full puzzle grid is a simple but time consuming exercise. Indeed, as a solution progresses familiarity with a puzzle's structure naturally develops and its b/b plot becomes less useful.

Apart from group nodes and ANS/AHS combinations, the patterns that produce other strong links are relatively restricted and I rely on memory to note where these exist. I then check the group nodes and ALSs that are available to connect potentially useful clusters of linked cells. This procedure has strengths and weaknesses though and is liable to miss some patterns, but I only check these when my basic approach reaches a dead end. This may also mean that any solution found without reaching an impasse might have taken a longer route than necessary.

Now this is the fun part. As you investigate additional methods and develop your own solving style, you will have to decide how and where to include them in your solving procedure.

David
.

[SpAce]

On b/b plots there is no simple answer as either they get too elaborate or they only provide part of the picture.

Ok. So my intuition wasn't entirely wrong? Spotting complex chains in a repeatable and human-friendly way seems like a problem that hasn't yet been solved completely. My main grid mark-up does have the full picture as far as strong links go, and it remains compact and readable. However, it lacks weak link indicators, which means it takes some mental visualization when building chains and loops. I haven't found that to be a big problem, though, as connecting the dots is quite easy. I'd still like to figure out a way to create visual aids that would make it more intuitive to see complete chains and loops.

Mine uses a small side grid where only the bilocal digits are shown in each of the cells. As I change the focus digit, the cells where it is bilocal are highlighted in one colour and where it is part of a bivalue in another colour.

Seems like a pretty good compromise. I may try something like that, although it's harder to implement with paper. Currently my main helper tool is the side grid with the single-digit plots, and it also has the relevant bivalue cells highlighted. It's very helpful and makes finding X-Chains/Cycles really easy (also helps with fishes, but I rarely look for them). I'm not yet quite happy with my other helper that has the bivalue cells and their relationships plotted. It usually turns into a spaghetti monster if there are lots of bivalue cells. That's why I suck at finding XY-Chains. It's easier for me to find complex AICs than simple XY-Chains and even Y-Wings.

[StrmCkr]

000900030004700600081054002005000000000020308000090060000070800017000000400106050

indeed this is a tough nut to crack: hodoku and xsudokus solutions path are defiantly nasty

my solution involves: { zero forcing chains as seen in hodoku mine also has a lot less steps but some of them aren't exactly easy to use/spot }
basics
BLR
size 2 fish
M-wing,
S-wing,
H-wing,
L-wing,
Bent Almost restricted naked subset {xy,xyz,wxyz -> size 8 }
Als-xz {dual link rule}
Als-xy,
Disjointed Distributed subset
Almost D.D.S,

the following isn't in anyone's solver except mine{ that i'm aware of}, its my own concept the basic concept derived from the daily sudoku forum that uses transporting a single digit via line of site back onto a pattern to extend eliminations or perform an elimination on an otherwise "dead" pattern

http://forum.enjoysudoku.com/fin-transport-irregular-xy-wings-aka-kraken-fish-t33596.html for reference and applied to more complex scenarios

(Fin) Transport asl-xz
(Fin) Transport als-xy
(Fin) Transport D.D.S
(Fin) Transport A.D.D.S {hardest step used} an example shown below

Code: Select all

+----------------------+-------------------+----------------+
| 2567   2567   (26)   | 9      1(6)   8   | 14    3    145 |
| 359    359    4      | 7      13     2   | 6     8    15  |
| 36     8      1      | (36)   5      4   | 79    79   2   |
+----------------------+-------------------+----------------+
| 1378   347-6  5      | (68)   34(6)  137 | 1247  12   9   |
| 1679   4679   (69)   | 45-6   2      157 | 3     147  8   |
| 1237   2347   (38)   | (348)  9      137 | 5     6    147 |
+----------------------+-------------------+----------------+
| (256)  (256)  (36)   | (24)   7      9   | 8     124  134 |
| 38     1      7      | 2345   348    35  | 249   49   6   |
| 4      29     (2389) | 1      38     6   | 27    5    37  |
+----------------------+-------------------+----------------+

Code: Select all

Two  [31,139] 29 Candidates,
     12 Truths = {6C5 7N1 7N2 15679N3 3467N4}
     16 Links = {2r7 6r145 2389c3 34c4 5b7 6b2457 8b5}
     2 Eliminations --> r4c2<>6, r5c4<>6 


(CELLS BASED ON 0-80 NUMBER ORDER)
Als a) 23689 @ 2,38,47,74
x => 3
aLS B) 2356 @ 54,55,56
y=> 2
aLS c)23468 @ 21,30,48,57
z => 6 Between A & C

Fin transport Digit 6 @ 4 ,31
=>> 39,28 <> 6

[champagne]

Hi StrmCkr,

I did not work for long (more than one year) on the solver, but for your puzzle, i have this

Code: Select all

PM map

2567    2567   26   |9     168   128  |145    3      145b   
2359    2359   4    |7     13    123  |6      8      15b   
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 |12457t 6      1457 
--------------------------------------------------------
23569   23569  2369 |2345  7     359  |8      1249t  13469
235689  1      7    |23458 348   3589 |249    249    3469 
4       239    2389 |1     38    6    |279    5      379   



success in expanded exocet
Exocet Image
base r1c9r2c9
targets r6c7r7c8


So a kind of exocet with digit 5 forced and contradiction on digit 4

[eleven]

SpAce,

guess you see now, that if you want to solve hard puzzles, you have to decide, which helpers you accept.
If you stick to paper&pencil, you will spend much time, which could be done in milli seconds - but spoiling the fun to find it.

The bad news i have is, that programs are better. So you can be proud of solving a puzzle after many hours, and then see, there had been a shorter or more elegant way.

[ghfick]

Hi champagne,
You refer to an 'expanded Exocet'. I am reasonable with Junior Exocet [JE] and this expanded Exocet is clearly not Junior. If one can exclude 4 from the base cells, then the base cells become a naked pair [1,5] which then gives the target cells with 1 and 5. Perhaps you are suggesting a way to exclude 4 from the base cells. Could you elaborate on this expanded method or point to a place in the forum where this matter is discussed?
Gordon

[champagne]

Hi champagne,
You refer to an 'expanded Exocet'. I am reasonable with Junior Exocet [JE] and this expanded Exocet is clearly not Junior. If one can exclude 4 from the base cells, then the base cells become a naked pair [1,5] which then gives the target cells with 1 and 5. Perhaps you are suggesting a way to exclude 4 from the base cells. Could you elaborate on this expanded method or point to a place in the forum where this matter is discussed?
Gordon

The idea of "extended exocet" has been discussed in one of the thread dedicated to exocets and Junior exocets.

It refers to pattern that could have been exocet but fail to be for one digit.

Here, we have an heavily downgraded form of potential exocet for the base r12c9 target r6c7 r7c8

1 in the base => 1r7c8
5 in the base => 5r6c7

if you can prove that 4 in the base => 4 (r6c7,r7c8) you have an exocet.

Junior exocet in the most common pattern to prove it and is there in most cases.
In other cases "classical AICs" can establish it
I used the expression "extended exocet" after some discussions on cases where the proof was worked out showing that a pm with the candidate in the base but not in the target was not valid through complex contradictions

So here you have to express why that pm

Code: Select all

2567   2567  26   |9     168   128  |145   3     4   
2359   2359  4    |7     13    123  |6     8     15   
36     8     1    |36    5     4    |79    79    2     
------------------------------------------------------
136789 34679 5    |3468  13468 1378 |12479 12479 1479 
1679   4679  69   |456   2     157  |3     1479  8     
12378  2347  238  |348   9     1378 |15   6     1457 
------------------------------------------------------
23569  23569 2369 |2345  7     359  |8     1    13469
235689 1     7    |23458 348   3589 |249   249   3469 
4      239   2389 |1     38    6    |279   5     379 

is not valid

Unhappily, in this specific case, the proof is not "elegant". the corresponding proof would be rated 9.xx by sudoku explainer.
The puzzle is rated 8.4, This means that the puzzle can be solved with many but simpler moves in sudoku explainer ranking.

On the other side, I have seen that skill manual players often prefer a complex single move to many boring small eliminations.

Here, having applied the exocet eliminations, my solver still has many simpler small eliminations, so nothing attractive for a manual player. But usually, manual players beat my solver.

[SpAce]

SpAce, guess you see now, that if you want to solve hard puzzles, you have to decide, which helpers you accept.
If you stick to paper&pencil, you will spend much time, which could be done in milli seconds - but spoiling the fun to find it. The bad news i have is, that programs are better. So you can be proud of solving a puzzle after many hours, and then see, there had been a shorter or more elegant way.

It doesn't spoil the fun for me if it turns out there's a shorter or more elegant way to solve something. At this point I'm happy if I can solve a difficult puzzle in some way, using my beloved paper&pencil method In fact, I don't mind if it takes a long time as the fun for me is in the process of solving. I like spotting as many chains and patterns as I can, even if they're not all necessary. I'm actually somewhat disappointed if I happen to spot a critical inference very early. I'll start worrying about efficiency and elegance once I get bored and need a new way to challenge myself.

Also, I want to fully understand what I'm doing. For example, the methods shown here by StrmCkr and champagne are really cool and interesting, but they go over my head at this point. Loops and forcing chains, on the other hand, are easy to understand, which I prefer at this point even if it leads to "many boring small eliminations". It seems that I can only motivate myself to learn more complex methods once I try puzzles that absolutely require them. Otherwise I'm inclined to take the path of least resistance even if it's much longer.

[SpAce]

S-wing, H-wing,

What are those? I can find information about M-wings and L-wings you also mentioned but not those two.