Your methods of solving an "extreme" sudoku puzzle

Advanced methods and approaches for solving Sudoku puzzles

Your methods of solving an "extreme" sudoku puzzle

Postby andre43 » Fri Sep 14, 2007 8:36 am

I’d like to pose a topic in this forum, which I believe many will find interesting. For us all the “intermediate” to “advanced” players of sudoku, it would be very fascinating to hear from the players of the front-line, how they solve their own puzzles, the methods they prefer to use in every stage of the solving process and also how they treat each one of these methods. Which are their first thoughts when they are confronted with a new puzzle grid? Which are the methods they prefer? What’s the juxtaposition of their solving arsenal they follow on the puzzles? Which are the tools/tricks they use to come off when they sometimes stuck at any stage on route for the solving? After all these nice and…endless discussions we have made in this forum (and which they gave the most important methods of thinking and solving sudoku puzzles as we know them today!) I think that it’s time to hear from the “giants” of the forum how they personally apply all this stuff in the real world of solving sudoku! Also (and because I’m a dedicated manual solver) I’d like to hear which of all these methods are impossible (or extremely difficult) to be applied to the manual solving. Also, this kind of discussion serves the purpose of comparing our ways of solving and I’m sure it will help many of us to reconsider at least some things that have to do with our ways of thinking…
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Postby RW » Mon Sep 17, 2007 3:58 am

Hi Andre!

When I joined the forums I wrote this article about my solving techniques (please note that it was one of my first posts to these forums, and all of the sudoku terminology is not quite correct). Even though 18 months have passed and several new techniques have been introduced to me since then, I still solve puzzles the same way. I haven't incorporated any new techniques in my arsenal, because no new techniques that can be used without pencilmarks have been invented. All techniques discussed here rely on staring at the pencilmarks, tagging them, finding paterns in them etc. I do also often look for techniques like that, but that's when I'm answering "what's the next move" question or trying to find the easiest solution to some puzzle discussed here. When I take an unsolved grid in my hand and decide to solve it all the way, then I do it as described in the post. Unfortunately, I don't actually sit down to solve puzzles very often anymore, at the moment I'm more interested in solving the big sudoku mysteries than solving individual puzzles, so my techniques have become a bit rusty in the last year.

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Try this out

Postby drstephenkerr » Sat Sep 22, 2007 11:59 pm

I solve puzzles now exclusively using the system that I developed, and have now published as a book.
(book promotion removed from this post - moderator)
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Postby tarek » Sun Sep 23, 2007 12:32 am

Some top secret methods there drsphinkterr. Can't you share some of it with us. Are these new or copied from elsewhere:?:

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Not a "these"

Postby drstephenkerr » Sun Sep 23, 2007 4:11 am

This is not a collection of tricks, it is a simple, straightforward system, I looked in every sudoku book, on every sudoku website, everywhere I could before I published it, nothing even close to this.
Hint: Never pencil in more than 2 numbers in any cell, for the rest you have to get the book, but in reality, you can figure it out from what I have told you
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Postby andre43 » Sun Sep 23, 2007 8:25 am

Hi drsphinkterr…I have heard about your book, and I’d like to believe all these marvelous features you allege as one's reason to buy your book…But, you know, in the past years had appeared some “well-wishers”, some guys who thought that they had…rediscovered the world and proposed their books as the only one and revolutionary method of solving all sudokus, but at the end, we found that their methods had to do only with…the “naked” and “triple pairs”!!! So, forgive my disbelief, but before I decide to order your book from amazon, I’d like to ask you two things: 1) can you solve, through your method, ANY sudoku puzzle, e.g. can you solve a Ruud’s Nightmare puzzle of Sunday (to speak of one of the most difficult puzzles in the world)? And 2) I worry about the description of your book I read in amazon, that “…This is not to say that we have taken the logic or the challenge out of solving Sudoku puzzles, we have not! You must still be thoughtful, thorough and sometimes imaginative (…)”. My concern lies in the world “imaginative”: how much imaginative must the solver be? Maybe this imagination will finally goes out of the logic world, driving us to a kind of.. a fairy tale?! Thanks! Also, thank you RW for your note about your older article you call my attention to. I have read the article, but it seems not to be a piece of cake for me!
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Postby champagne » Sun Sep 23, 2007 5:06 pm

Hello Andre,

Not so many asnwers, As I just described my "full tagging" process, I didn't post any message here.

However, if the silence to my call for contribution means that nobody can bring a solution for the list of puzzles I settled, this "relatively" simple process could be one of the most efficient.

At least, it solves about 90% of gsf list.
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Re: Not a "these"

Postby DreamCH » Mon Sep 24, 2007 4:30 pm

drstephenkerr wrote:This is not a collection of tricks, it is a simple, straightforward system, I looked in every sudoku book, on every sudoku website, everywhere I could before I published it, nothing even close to this.
Hint: Never pencil in more than 2 numbers in any cell, for the rest you have to get the book, but in reality, you can figure it out from what I have told you
Dr. Sphinckter comes in my mind...however, the stuff you can buy on the net like
is NOT really new stuff so hopefully you`ve written the book that has all answers:)
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Re: Not a "these"

Postby RW » Mon Sep 24, 2007 5:17 pm

DreamCH wrote: comes in my mind...

Thank you for pointing me to that hilarious article, I had a really good laugh!
Dizzy Lizzy wrote:As an extra challenge, the spectator can even be instruction to lie and mis-write the puzzle on the grid at the beginning of the routine - not only will the magician be able to tell which digits are incorrect - but also what they should be!!!

Ehm... yeah, sure...

As for "sudoku success"...

FREE BONUS #1 Access to 4,000 Sudoku Puzzles of all levels of difficulty for you to practice your skills with
SOLUTIONS, FREE even at $0.10 USD a puzzle that is worth $400.00

Wow! If that's the price for a sudoku puzzle, then gsf's program can make me a millionaire in a few hours. Thanks gsf!

As sudoku has become such a hit all over the world, it's expected that a lot of people will try to profit from it, but I'd be careful with how I spend my money. At the moment I believe the most extensive source for sudoku solving techniques and other sudoku related research in the world is these forums, and access to all this information is free. Most commercial products that claim to teach the "ultimate secrets of sudoku" teach the techniques that we call basic techniques. I'd be very surprised if someone is actually selling some sudoku related information that cannot be found here. Dr. Sphinckter, if you really have found some new point of view that nobody has thought of before, then congratulations. However, I'm quite sure that something similar has been discussed in one of the 1000+ threads here in the "advanced solving techniques" forum.

Not saying that all commercial sudoku products are wrong. I also like to carry around a book with puzzles because in a bus or train it's more convenient than solving on a laptop. But if you want puzzles in digital form, there's several collections of puzzles here in the general/puzzle forum that are of a lot higher quality than most commercial puzzles.

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Re: Not a "these"

Postby Sudtyro » Mon Sep 24, 2007 11:16 pm

drstephenkerr wrote:This is not a collection of tricks, it is a simple, straightforward system...
Dr. Sphinckter

OK, I'll rise to the bait. In wild anticipation of the new system, my #1 "Sphinckter" is tightly closed. PLEASE....solve any one of champagne's puzzles here and release the flood! And...I'll buy your book!
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Postby Glyn » Tue Sep 25, 2007 2:16 am

Just checked out the review on Amazon, very positive, but one of the reviewers has a name I've seen somewhere before.:D
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Postby champagne » Tue Sep 25, 2007 5:38 am

Sudtyro wrote:
PLEASE....solve any one of champagne's puzzles here and release the flood! And...I'll buy your book!

Sudtyro let's set a target we are sure he should reach.

Here above two other puzzles extracted from the bottom list of GSF.

Code: Select all


The second one is easily solved by "full tagging" without using step three,
The first one is tougher with my process, still far from the most difficult solved in that list.

If he doesn't solve the second one, there is nothing to learn in that book. Solving the first one would be more promissing.
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Postby Max Beran » Thu Oct 04, 2007 12:16 pm

Andre: shame that your original intention got a bit highjacked by a different topic but perhaps it was always a bit hopeful to expect the “great and the good” to respond to your invitation. They are all very busy pushing back the frontiers and it is also possible that they are not the best people to explain how they solve puzzles – it is not always the theoretician who is best able to apply the theory or judge its value in the real world of those of us sitting at our armchair pencil and paper in hand.

So if you’d allow an ordinary mortal to have his say, here are a few thoughts.

My first reaction is that much depends on personal characteristics. For example, I discovered the other day that my wife is totally bamboozled by the sight of all those candidates crowded into a cell, which is what I end up with. She uses positional dots, and to me, her grid looks like a game of dominos gone mad – I doubt I would find a naked pair in her presentation, let alone an advanced pattern.

Another difference is that some people can filter out required features in their mind, others need to have the feature highlighted before they can use the technique. Take empty rectangles as a case in point. There you need to first recognize that the candidate of interest occupies places in no more than one column and one row in the box of interest; then you locate the hinge where that row and column cross, then you mentally draw in a horizontal and vertical lines through the hinge, then you look along one of the hinge lines to find other cells with the candidate, then you check the line perpendicular to that to see if the candidate occurs as a bilocation, then you project back to the other hinge line from the far end of the bilocation and check if it contains the original candidate, and if so, you eliminate it. Not to blow my own trumpet as I suspect there are many out there that can do the same, I can cope with that quite easily with the fully candidated grid whereas others might only be able to cope if they had a a filtered version of the grid in front of them that just showed that one candidate.

Another example is xyz-wings which I’ve noticed is generally included as an advanced technique. To me that sems nonsensical. How difficult is it, say I, to find a box with a three and a two in it and to look along the row or column seen by the “three” to check if there’s another “two” fulfilling the necessary criteria of shared candidates? Similar considerations apply to aligned pairs and sue de coq though admittedly they involve a bit more staring. Anyway, the fact is (I assume) that a lot of solvers do not find that process simple but perhaps they do something that I find hard – for example finding fishy shapes and cases where n candidates are in n rows of n columns (x-wing, swordfish etc) where n>2 even with the filtered grid.

Then there’s the important issue of motivation that makes person A different to person B. Some of the methods require a lot of study and scriutiny and may even require that the grid is drawn and re-drawn. This is clearly off-putting to many so they will eschew these “kosher” procedures in favour of Araidne’s Thread, bifurcation, etc etc, often computer aided. For these the motivation is the final result, not the process of solving it. This came over to me very strongly in a spirited debate on the Mepham site about a marking scheme for a competition where clearly the setter had it in mind that solvers use logical procedures (as commonly understood) but this was not reflected in the marking scheme, and noone wanted it to be otherwise. In fact the pressure came from the other direction where some were pressing for key issues like correctness and timeliness to be sidelined so that late entries and typos were forgiven. This was all rationalised by the usual stuff like inclusiveness, not being judgemental, and the final solution being the central issue. Speaking pesonally, I would feel that solving the puzzle using one of these sure-fire techniques is about as satisfying as waiting for the solution to be posted next week and filling in the blanks from that!

It may be that some techniques are harder to program, and that is the reason why they are bracketed with the “advanced” techniques. And this brings me (sorry this is getting a bit extended) to a difference between theoreticians and the players – most theoreticians are also in the business of programming techniques, partly to test their generality relative to other techniques, partly for the fun of programming them. They may also claim that their program emulates the thought process of the player. But this claim, I doubt.

In particular, we can see that most of the pattern-based techniques like xy-chains, fishy cycles, and empty rectangles (at least the way I do it) are concerned with cells joined up by links. They have to obey certain rules in terms of what cells connect and what linkages you can place next to other linkages. And that seems natural to us. But it is not the natural way for the programmers or the theoretical discussions that look for common features of techniques in terms of their fundamental desiderata see it. If you can think of cells as molecules and links as forces between molecules that have to obey certain macro-level rules, then the theoretician looks at atoms, being the candidates, and the logical connection between candidates (using logical in its mathematical formal sense).

Perhaps an example will make this clearer. The armchair solver will look at xy-chains as a mental dance around the grid (having first highlighted the bivalues) in a way that fulfils stated pattern rules. The theoretician sees things differently (and more rigorously) as at their level you first arrive at a candidate in a cell via a logical step from the same candidate in another cell, then you interpose a logical step within the cell, then you proceed to a candidate in another cell. This way the integrity of the alternating inference chain of weak-strong-weak-strong etc is maintained. When we solve using nice loops, the notation we would use to express the loop will “offend” those theoretically inclined who will wish to parse the chain into its atomic components – natural enough from their perspective as it is these components that are what appear in the algorithm. They don't have four different types of loop, four different ways of propagating, four different inference possibilities, they just have the one which all the manual solver's options collapse to if the loop is parsed to its full expanded extent.

What this is coming round to is that players play by rules that appear natural and handlable to their way of seeing a sudoku grid and their motivations; there will always be a user-gap between that and the reductionist approach of those who are leading the way looking for fresh insights. Players may be disappointed by the lack of interest in the equivalent of technical widgets that we players may develop to help us apply those insights.

Anyway, I’ve wittered long enough and perhaps others will come up with a different perspective.
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Postby andre43 » Fri Oct 05, 2007 3:38 pm

Hi, Max Beran, yes I have disappointed by the fact that, while I was waiting for an answer in my invitation…. a different topic has taken place here, so I stopped the attempt. Perhaps you are right, maybe the great theoreticians “are not the best able to apply the theory”, as you say…I'm not criticize them saying this-on the contrary, I admire all these guys who have gave us all these great methods, but the applying of these methods is a horse of another colour... I have read your interesting thoughts about solving sudoku and the differences between “mortal solvers” and theoreticians... I'm a faithful manual solver and I can only write down my personal way to solve a puzzle. After the elementary work and the pencilling, I proceed with the following steps:
1) I search for “Pointing Pairs” in every number of every cell. I usually find more than one of them.
2) I search for “box/box reduction” eliminations..Unlike pointing pairs, this technique only seldom bring any eliminations to the grid.
3) Now is the hour of a more relaxed searching, a mentally enjoyable (I dare to say) process of finding the relations between the numbers in every row, column or box. I almost always find there in some naked or hidden pairs, triples and quads. So, by now, the grid has already disencumbered itself of the many numbers it might have in the start... Also, this is the end of the first set of my solving arsenal,

Now, I proceed with the second stage, which contains three parts again:
1) the Unique Rectangles and the Hidden Unique Rectangles, the latter is the new and subtle method by Andrew Stuart (it’s included in his excellent book THE LOGIC OF SUDOKU).
2) the hunting of any fishy pattern, particularly of the well known X-Wings, XY-Wings, XYZ-Wings etc. (At this point I must say that usually I don't go for X-Wings. I prefer to spot them within the Nice Loops - see next solving phase. It’s more convenient for me. The only exception, I think, is the case of Finned X-Wings, which is a pattern it may be traced by the discovery only of that pattern. Also, I don’t search out for Swordfish. It is also included, in Nice Loops, , but I think this happens in the case we have only two and not three strong links in all three rows or columns. ).
3) Then, if I have a grid with quite a few bivalue cells, I proceed with the Empty Rectangles, a misunderstood technique (to which you also refer to) which I suspect that no many solvers use, I don’t know why, because it’s a valuable method which usually gives me from 1 up to 3 or 4 eliminations- but this happens usually if I apply it twice, the second time at a later stage of solving.

Now, if the puzzle has not yet been solved (and this is the most usual case) the things have become more serious and it's time to get in the world of chains...This phase has two parts:
1) the first is the applying of the XY Chains, if we have now a quite enough number of bivalue cells. And then…the fun time is over! Because if I want to bring the puzzle to an end,I have to go to
2) the Nice Loops/AICs, which is “the nearest thing sudoku has to “theory of everything””, as someone said, and I agree with him. Though Nice Loops often need patience of Job, the truth is that they can bring us eliminations impossible by any other means! After the simple (and grooped) Nice Loops I try to find ALS in chains,following of course the rules of NL and AICs, which usually gives also 2 or 3 cases of eliminations. I found that this stage is generally the last one before the definite unlocking of the puzzle. (Needless to say that, in between the NL/AICs eliminations we can apply any of all the other methods is proper to get more eliminations. Also, on occasion I resort to some techniques not often used, at least by me, such is the Forcing Chain and 2-String Kite).
As an afterword, permit me please to express a complaint: although today we have many sources of nearly all techniques of sudoku, I find that there is a poor coverage of the theme of ALS Chains! There is a tutorial by SirDave in -but it isn’t enough…I’d like e.g. to learn more about the combination of two ALS in creating a nice loop…Is there any volunteer??!
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Postby champagne » Fri Oct 05, 2007 7:18 pm

andre43 wrote

As an afterword, permit me please to express a complaint:
although today we have many sources of nearly all techniques of sudoku, I find that there is a poor coverage of the theme of ALS Chains!
There is a tutorial by SirDave in -but it isn’t enough…
I’d like e.g. to learn more about the combination of two ALS in creating a nice loop…Is there any volunteer??!

By chance, I got to post recently in a thread of Denis Berthier the solution for a puzzle.
Part of it was (sorry, this is in chess notation)

and this extraordinary efficient loop :

__ A______ B____ C____ |D_____ E_____ F_____ |G_______ H_______ I
1||2357___ 2357_ 2m5M_ |35ê6b_ ______ 1a2T6B |________ 1A37
2||4c9C___ _____ _____ |4C9c__ 2u3y5Ë ______ |2358d___ 3d8D____ 2X35l
3||2345789 23578 24æ89 |3459__ 1p235_ 124è9_ |1Q2u35Ë7 137

4||16e789_ 178__ _____ |______ 14Ç7__ 148k9_ |4e6E____ ________ 179
5||12f579_ _____ 2F59_ |3z5ì79 ______ 1n9N__ |178D____ 1Q3Å78d9 1379
6||156789_ 1578_ 56i89 |34579_ 13Â5Î7 148K9_ |4E6e____ ________ 13z79

7||1g3À45_ _____ 245__ |46B7__ 247___ 2w46b_ |1G235í7_ 347
8||23468__ 23Á8_ 246I8 |______ 2479j_ ______ |237_____ 346h79__ 2379
9||12456h_ 1o25_ _____ |______ 249J__ ______ |125_____ 46H9____ 1R25L9

[]9H5/9(A5C5D5)_9(F5H5I5)/9C5_9(C3C6)B/5(C6C7)|*C3C6C7C8 _5(C1C5)/5C7_5(A7G7)/3(A7G7)|*A7G7_3H7/3(H1H2H3H5)_3(H7H8)/9(H8H9)|*H7H8H9

This is a classical alternate chain. |*C3C6C7C8 means:
"weak link within the 'almost cell' C3C6C7C8".

The complementary cells of an almost cell are forming an ALS. As a matter of fact, it is exactly the logic you are looking for.

Sorry but in that example, we have three ALS, and not two as expected. With some more time, I can give you examples sticking to your specifications.
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