Recovering From a Small Disaster


This post corrects an incorrect homework assignment, and announces some changes in Sysudoku due to a switch to a new computer and updated operating system.

Last week was not a good one. On Tuesday I posted an incorrect puzzle for homework on the bypass. When I dragged the given clues of Dave Green’s Saturday 9/3/16 4-Star into my puzzle template, I got one wrong. I must have forgotten my box-by-box check.  In preparing the post,  I somehow “solved” my version with the bypass. Like you, I never check  solutions unless I encounter a problem.  My apology to all readers who spent time on it.  Without access to a solution, you couldn’t know that clue 1r2c3 was out of place. It belongs in r1c3.

But I was amply rewarded for this transgression when my hard drive died the next day. Now I had to switch over to the new laptop I purchased some time ago in anticipation of this sad day.  And I have to rework everything not backed up, including checkpoint for this post.  That’s how I discovered the error.

That leaves us with a plausible looking puzzle that doesn’t have a solution. On which some readers have experience. Let’s consider it an opportunity to see if your bypass would have revealed the contradiction.

green-mis-trHere’s mine, with some accounting below on how unwritten aligned triples and a smidgen of line marking carried the contradiction along: 

 

N2t =>NW2, N5t => NW5 & E5m => NE5,   N4t => NW4,   NE8 is a 3f: trap.  

green-9-03-con-gridIt turns out that S8 conflicts with the now forced 4r9c5!

Hold on! This doesn’t look like a Sysudoku grid? You bet it doesn’t.

Unfortunately, the new ©MS Windows is without the Brush Script Font which represented solver input. So I learned that updated solvers can’t duplicate my blog pictures with their newer computers. The solution is to choose a new solver font from among currently available ones. This grid shows Bradley Hand ITC.

green-9-03-bradley-sampleI’m not so sure I want this one. The problem is, the 7 and 9 get a bit flamboyant. Here’s a little sample, along the way to the solution, that includes 7 and 9, and pencil marks.

lucinda-handwriting-sampleAn alternative is Lucinda Handwriting, less extreme and more bold. It’s not as distinguishable from the Calibri font of the given clues. Maybe a little too perfect for handwriting?

segoe-script-sampleA better option, perhaps, is Segoe Script. It is bolder, with more conventional hand lettering. I don’t care for the jumpiness in  vertical registration. Again, it’s harder to distinguish from given clues.

For now I’m sticking with Bradley Hand ICT.

All you have to do, to incorporate any of these fonts into your Sysudoku puzzle template, is to select the font for your script letters on the right. Some font size adjustment in the pencil mark text box may help with placement in the cell.

So consider all this an extension of the earlier basic clinic posts. My amended assignment is to move that 1 clue as shown above, and tackle the bypass on the real Green’s Saturday **** of 9/03/16. To follow up, I’ll interpret  the trace with the role of the unwritten aligned triples and slinks. In the bypass, I’m now including another useful tactic, the mental line marking of the lines as they are reduced to three free cells, the 3f:’s.  

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Dave’s Friday Labor Day Four-Star


This post traces basic solving on the first of three Labor Day puzzles by Dave Green.  The series is an opportunity to highlight the efficient and uncluttered basic level Sudoku solving with the slink marking bypass.

In keeping with the adoption of the slink marking bypass into Sysudoku basic solving, I’m the tour guide on three in a row that showed up in my Beacon Journal just before Labor Day, from King Features, Inc.  Dave Green gets my Oscar for basic level puzzles every year.  If you haven’t asked for free ©PowerPoint and ©Word  templates, and don’t have your own,  look over the Tools page and send an email request for them.  Try out the puzzle template by dragging in last posts grid of Green’s 4-star of 9/2/16, and filling it as you read the bypass trace.  The grid with the completed bypass is below.  Account for every event in the bypass.  The grid may help.

green-9-02-basic-tr

green-9-02-bypass-gridThe bypass leaves the grid with only 28 blank cells, and hopefully, it leaves you with an added source of adventure for basic solving.

From here, slink marking is easy and line marking easier than it would have been.

By its nature, the bypass can be done on the original copy of the puzzle.

In this case, there was no line marking, just a deep collapse.

I said deep, not steep.  My traces are sometimes described as too complicated.  Landscapes are complicated because nature is complicated. Sudoku solving, taken all together, is complicated.  I take it as a compliment.

green-9-03For an immediate follow up, try to duplicate next week’s bypass trace on Green’s Saturday 9/03/16 4-star.  I call the NSEW box patterns wells.  Before starting, I saw clues in two of them, while looking for naked pairs in all four of them.  That’s the way to react to a well, isn’t it?

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Adopting the Slink Marking Bypass


This post reviews the origins of the slink marking bypass, now adopted for Sysudoku basic solving. A bypass trace on Very Hard 28 illustrates the challenge available in a basic level puzzle.   It also kicks off a series of  Dave Green’s Labor Day  weekend puzzles  that show off the bypass.

Working through the Beginner’s page and the early posts on basic solving, I came to realize how inevitable it was for me to adopt the slink marking bypass as the way to begin puzzles of any level.  After all, Sysudoku was started when I realized, with due diligence, that human solvers needed a better way to begin.

For a time before that I had wondered what I might be missing, because Sudoku advisers devoted so little attention to finding candidates.  So much effort went into generating candidates, then removing so many of them. There wasn’t even a name for what seemed to be the default starting method.  Tom Sheldon in his Master Class, called it the “completion strategy”.  Not wanting to dignify it that much, I called it “number scanning”.

I was ready to begin when I was convinced that box marking with dublex and crosshatch, then finding the remaining candidates with line marking,  finds all remaining candidates more efficiently with much less distraction.  I’ll tell you how it started, but first, you may have more work to do on Very Hard 28.

vh-28-basic-trYour assignment is to inspect this Very Hard #28 basic checkpoint trace.  Unless your trace looks better, you must read through it, marking your copy of the grid, and decide exactly what each move is and exactly why it is possible.

For navigation hints, see the traces page.

 

 

The slink marking bypass originated in my review of Peter Gordon’s basic solving advice in his Guide to Sudoku Solving.  His basic solving I recognized as box marking with clues only, with limited line marking.  While definitely not enough, it was a positive step toward minimizing clutter.  Although he did not explain them explicitly, Peter was evidently tracking some slink effects and naked pair claims on cells.  I decided to try this as a first stage of box marking, with pencil marking for naked pairs only.  I called it the dublex bypass, and recommended it for speed tournaments, in October 2014.

Shortly afterwards, I was doing  basic clinic posts, reviewing some Dave Green puzzles.  So  I compared traces with the bypass and without.  The bypass did surprisingly well, finding almost all clues and replacing some slinks with clues.  Slink marking was easier to  accomplish, after the enjoyably challenging bypass.

Next I reviewed Wayne Gould’s Train Your Brain with Su Doku, Fiendish collection . Wayne advocated no pencil marks at all. He doesn’t give any instruction on basic solving, but his basic level puzzles do require taking slinks into account.  See the review table and quotes in the 11/04/14 post.   I worked through them while trying to track naked pairs mentally, but gave up on this memory exercise.   Not because they don’t work.  I just don’t like to do them, even though I should.

Since November 2014 I’ve been using the bypass effectively.  It definitely takes slink marking further in minimizing distracting clutter of less than relevant candidates.  I think it also adds the challenge Wayne had in mind.

Clues are discovered in line marking, often the triggering a collapse.  But clues found in my box marking all too frequently reveal something overlooked in the bypass.  Keep that in mind when you read a bypass trace in Sysudoku.  After a tough-to-diagnose effect, you might wonder how you could have seen it.  Well, I probably didn’t.  However, discovering what I’m missing in the bypass, I believe I’m seeing more.  Thanks, Peter and Wayne!

Next we’ll  checkpoint our way through the Dave Green Labor Day weekend trio.  I think it will show you another side of Dave’s excellent basic series.  I was sure one of these would cross the Wizard Green’s line into advanced solving.  But it didn’t happen.   Dave knows what he’s doing.

green-9-02Here is Green’s **** of Friday, September 03, 2016. The bypass starts in the NE.  I’m counting on you to figure out why and where, and to go on from there.  Enjoy!

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Mike Peterson’s Very Hard Sudoku, v.1


Resuming posts after a quiet summer, this review identifies the title book as a basic level collection, offering an interesting challenge for the slink marking bypass, and little else.  The brief  introduction offers interesting historical facts, but is another example of ineffective solving advice.

Through my occasional Amazon scan, I picked up one of Mike Peterson’s Sudoku puzzle books, Volume 1 of an apparent series of “Very Hard” books.  The back cover pictures six levels of these books, ranging from “Very Easy” through “Very Hard”, then “Extreme”.  My magnifying glass reveals that volume 9 of each of these levels is pictured on this volume 1 book.  Except for Very Easy Sudoku, only on volume 6.  The review book has a publication date of April 1, 2016, written on the last page, and carries no copyright notice.  Seriously?

veryhard ex 1Among the historical and mathematical data in his three page introduction, Mike drops in a one paragraph prescription for Sudoku solving, which I just have to quote, along with his example grid:

“The process known as ‘scanning’ involves analyzing cell for possible values, and filling cells where one number is possible. Scanning alone will solve most simple Sudoku puzzles.  In the grid above, x = 1.  Harder grids require the ‘forcing chains’ technique.  Above, any value of a forces f=2, since

a=1 => b=8 => c=7 => f=2

a=2 => d=9 => e=7 => f=2.”

Did you follow that?  If you did, it was only by finding the candidates first.  Mike’s “scanning” assumes the number scanning  I’ve constantly called out as inefficient and a generator of distracting clutter. After that, Mike’s  advice is to pick a cell and follow the chains for each of its possible values, looking for a cell registering the same value for all chains.  If you’re a computer, this trial & error is practical.  If you’re not, it’s not. Not in real puzzles, that is.

veryhard ex 2After line marking,  the final step in Sysudoku basic solving, the above chains are much easier to follow. Sysudokies don’t follow forcing chains. They take  them  as winks in advanced solving techniques.

veryhard ex xyzAs an example right here, a forcing chain enables 1r9c4 to “see” the third Z=1 candidate in the 891-wing.

 

 

veryhard ex xyOr if you prefer, how about completing an XY chain to eliminate 8r3c4, setting up a Snp19 to eliminate 1r9c4? In either case, the immediate collapse confirms 2r6c8, no T&E and no problem.

very hard review tableGetting to actual puzzles, my review selection provides no evidence that forcing chains, or XYZ-wings, or XY chains, are necessary for  Peterson’s Very Hard collection.   I took Very Hard 1 and every ninth puzzle, the series being  1, 10, 19, 28, . . ., 82. Starting with the slink marking bypass on each puzzle, I had 7 of 10 collapse in the bypass, and three in box marking.  The consistent 17 givens suggests that the puzzles may come from the Royle collection that Mike cites in his introduction.

Green 9-02

 

Very Hard Sudoku provides a good workout on the slink marking bypass. I enjoyed the book recently on some long airline flights, and shared it with  grandson  Daniel , who was equally successful.  For your bypass homework, here is Very Hard 28, one of Daniel’s impressive victories, with a 2-D trace checkpoint to follow in the next post.

 

The  mini-clinic on the slink marking bypass will continue with puzzles from Dave Green, the composer I follow daily in the Akron Beacon Journal.  I’ve been modifying earlier Sysudoku posts to adopt the bypass fully. Last week, in the Friday, Saturday and Sunday paper, Dave posted two 4-stars and a 5-star that demonstrate especially well the techniques and value of the bypass.  I’ll be checkpointing them with detailed traces to show the enhanced clutter fighting power of slink marking.  And to clue you in on the pleasurable challenge of beginning efficient solving of basic level puzzles with the bypass.  Don’t miss it, and do your homework!

 

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What I did this Summer


The previous post of June 7 let you out for three months. No homework.  Welcome  back to school . This is your notice that Tuesday posts resume on September 6.

Over the summer  I  got in a trip to Sidney and Port Douglas, Australia and to the highlands of Malaysia, and ran a muggy half marathon in Akron, Ohio, my home town.  That’s fine, but what you really want to know is, what about Sysudoku?

Well, for one thing, I started my long intended review of Denis Berthier’s The Hidden Logic of Sudoku .  I have the first part in the can, for release this fall. The issue of this part is whether or not Denis’ account of the hidden properties of Sudoku logic, as exploited in his rule based AI solver, has practical value for the enterprise of human solving.  Later, after allowing readers a breather, I want to look at specific strategies that Denis has advocated, starting in THLS.

Later still, when there’s time, I do want to come back to my Exocet skirmish with David P. Bird, who believes he is not conducting a trial when he certainly appears to be.  David began a thread on Sysudoku, but dismisses the blog as “homespun” and devoid of any value for forum devotees.  He’s probably right, but that’s not about Sysudoku.

Getting to my main excuse for taking the summer off, it was to think about how to revise and update the Sysudoku posts, going back five years.  The first year, of late 2011 and 2012, is the most in need of updating and the most important.  Unless I start over, the pages and these posts are the resources for new readers to learn about the systematic basic and advanced strategies I enjoy and recommend.

I didn’t do much revision this summer, but now I do have a plan. It’s not to start over.  Instead, I’ll revise and link the posts and pages to preserve the chronological emergence of ideas by post date, but superimpose a path through the material in the recommended solving order flowcharted for reference on the Order of Battle page above.   Learners start with the beginning posts, and expert browsers go top down through the Find It pages.

My immediate revision projects are to integrate the slink marking bypass into the basic solving posts, and to replace all 1-D traces and all grids with multiple candidates of the same number.  I’m revising the Traces page this week.

My first normal post will be a review of Mike Peterson’s   Very Hard Sudoku, v.1 .  This review is very much related to the bypass.

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A Quiet Sysudokie Summer


Welcome to Systematic Sudoku!

The weekly posts are suspended for the summer,  to be resumed September 6.  I’m leaving this overview post for those who may be encountering Sysudoku.com for the first time.  It’s to let you know what this blog is about, and what you might find among its 250 posts and 20 pages.

It’s about methods by which humans can solve difficult Sudoku  puzzles, with the office software that comes with every laptop, but without programs known as solvers.  The blog is a narrative following the discoveries made week by week over five years.  Thanks to experience before starting, and some good luck, the principles I began with have held up to produce a system of solving that is good for puzzles of every difficulty, from newspaper  single – stars to monster  “unsolvables”.

Over a five year period,  my outlook  and writing tools have naturally evolved, though the principles have not.  At this point, I’m taking a posting holiday to update existing posts, add links between posts, and improve navigation pages.

Post Topics

Early posts deal with the basic task of finding all candidates, and marking them.  The sysudokie approach incorporates the solving of easier puzzles, and avoids flooding the grid with hundreds of candidates that could have been more easily eliminated on a less cluttered grid.  The marking of all candidates necessary for advanced methods is done in a manner unique among Sudoku writers.  Once comfortable with this basic technique, solvers are able to do part of it mentally, adding another pleasurable challenge to Sudoku solving.

Most of the 2012 posts, are  about advanced solving, which exploits logical relationships between candidates.  Then the blog turns to evaluating collections of puzzles, and the writings of other authors on human solving techniques.  This process continues today, as new collections and writings emerge.

Also continuing is the gradual introduction of “extreme” methods for exceptionally tough puzzles.  Most of these puzzles swamp the solver with too many  candidates, concealing the relationships accessible to human vision.  But even these puzzles can be solved “by hand” by extreme methods based on trials.  A trial is conducted by assembling a set of candidates that are true or false together in the puzzle solution.  The puzzle is much more solvable, once the trial set is found to be true or false.

More experienced new readers may agree with me that much of the available Sudoku solving advice is more suited to computer solving than human solving and will discover human engineered methods here that are  found nowhere else.  Among them, a trial version of Sue de Coq called Single Alternate SdC,  a scratchpad algorithm for locked and almost locked sets and fish, finned or not.  Also new forms of wings and wing eliminations by forcing chains, a railway graphics tool for finding all XY-chain eliminations,  bent naked sets, nice loop coloring, and new forms of pattern analysis. They may want to join me in a currently ongoing discussion of exocets.  Also you may be pleased to know that the work of Denis Berthier is on the Fall 2016 Sysdudoku agenda.

Sysudoku Template Tools

The puzzle grids you see on this blog are made by dragging numbers of the “given” font into a ©PowerPoint presentation slide, then dragging in clues and pencil marks of a different font as the puzzle is solved.  Slides are saved at significant stages to make a presentation file record of the solving.  Graphic lines, curves and icons are added.

This template is available to readers, for installing puzzles in the same way.  It enables you to follow the solving process step by step from a blog trace. The trace tells exactly what is done, but the reader, looking at her own detailed grid at that point, supplies the reason why it is done.  There is no better way to learn Sudoku at any level.

Other templates are available to represent the logical relationships between candidates in various ways, to support advanced and extreme techniques.  Fish, chains and wings are more easily spotted on these templates.  Any template you see in a blog post can be obtained  free by email.

Sysudoku Pages

The blog is accessible in several ways, via an extensive set of linked pages.  Following the blog chronologically, you can “drop in” by simply scrolling down the screen, or by using the month by month link roll along the right side.  Each link brings a page with the first lines of the post description of the month’s posts.  Click for the full post, with comments section.

A bar menu across the top accesses the following pages:

Beginner’s Page

For a Sudoku beginner, or a beginning Sysudoku reader wanting a quick overview  of Sysudoku basic principles.

Sysudoku Speak

A glossary explaining terms used in the blog, and often citing terms used elsewhere for the same concept.

Order of Battle

A set of flowcharts recommending an order in which to use Sysudoku techniques.

Sysudoku Traces

Explanations of how to read, and write the two types of Sysudoku marking traces.  Trace rules prescribe which new clue or locked set  to follow up next.  The regular trace is depth first, following up all effects of one cause, before taking up the next one.  The trial trace is breadth first, following up each cause on a new list for one step, then repeating the list for one step.  Besides being a tool for learning, traces enable you to analyze exactly where your human solver circuits went wrong.   A special trace for trials allows trial contradictions to be documented graphically.

Find It

A breakdown of topics into pages linking to posts and more detailed pages, guiding you to posts for explanations and examples.

Solving Tools

Illustrations of the solving templates and links to posts introducing them.

About

Background on the blog, and Sudent, its author. That’s me.

You’re welcome to send in a comment.  I appreciate them all, but only publish those that would interest other readers.

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Bird’s JE Solution of Unsolvable 197


This post comments on David P. Bird’s Junior Exocet soutions of Unsolvables 190 and 197, posted in comments on Andrew Stuart’s Weekly Unsolvables page.  Bird describes his JE definition as a means of spotting exocet patterns.  However, it can  be regarded as a trial strategy, not of champagne’s Exocet,  but of a specialized exocet more likely to succeed .  Bird’s exocet ”spotting” rules incorporate naturally into an enhanced version of the Chute Lettering Exocet Filter, limiting the number of target trials, and reducing the complexity of the necessary ones, much more effectively than the CLEF of my recent posts.  Unsolvable 197 provides an example here.  The original post of April 26 introducing CLEF,  has been revised to correct my misreading  of Bird’s Junior Exocet definition, and to explain where I went wrong.  I’m sure mayor David will patch that pothole.

In his introduction of the Junior Exocet  in July 2012, Bird quotes  champagne’s  definition this way:

Unsv 197 bird quote

There is a lot to miss in this definition.  For one thing, champagne’s Exocet is a lettered pattern.  It is about all possible combinations of the base cells.  By this definition, there is no exocet unless the ‘reducing’ condition holds for all possible combinations.

The fourth word of this definition, “when” acknowledges that an Exocet is subject to trial. Champagne could be sure about the conclusions only after the condition is shown to hold.  The unique solution of a Sudoku allowing the base and target pattern does not have to include an exocet base and target pattern.  But if you know that the puzzle forces every combination of base digits into the targets,  then you can be certain the puzzle solution does contain one of the exocet’s solutions, simply because it must contain a base solution.  That is the more consequential result above.  The characterization of the exocet as an elimination method is incidental, and has needlessly confused the issue.

In my posts on the exocets of the Golden Nugget and Fata Morgana (Find It , Monsters) I reported on a direct method of showing champagne’s sufficient condition.

gn exotrial 1It is to find AIC nice loops enabled by the base candidates and threading the identical target candidates, for each combination of base candidates.

The first combination I came across is shown here. Fortunately, it turned out that the X-chain components of each candidate were identical in every combination in which it appeared.

 

After demonstrating GN exocet, I was justified in direct trial of each case, having proved  that the monster was cornered. Showing the champagne condition for Fata Morgana’s three combinations was easier.  So were the trials.

Now years later, the incentives of the Unsolvable challenge and Bird’s monumental compendium have brought me back to the exocet, and as David pointed out, only to misunderstand his elimination rules for Junor Exocets.  When reading the rules, object pairs contain a target and a companion, but the target and companion are in different object pairs.  That makes a big difference.

I did understand enough to appreciate Bird’s conclusions about limited placements of base digits in crossing line cells, and I realized how they can disqualify base digit combinations.  In fact, that led to  the crossing line tabulations that I’ve combined with chute lettering in the CLEF of Unsolvables 190 and 197. The combination tests limit the number of base digit combination trials necessary to conclude that an exocet pattern combination solves the puzzle, or doesn’t.  They do not verify that the lettered pattern is an Exocet, by champaign’s definition.  That is, they do not show that every base combination forces like contents of the target cells.

And neither does Bird’s Junior Exocet elimination rules.  In the JE reports, David abandons the champaigne Exocet test, and acts directly on the unproven hypothesis that the puzzle solution will contain an exocet solution.  Candidates that contradict that possibility are eliminated.

But it is not champagne’s Exocet that is on trial.  It is one with interfering JE band candidates removed, and targets selected by Bird’s requirement #2.     I can’t say its specific enough to guarantee a puzzle solution, but it could be a remarkable instance similar to the BARN, where a set of cells are selected by a simple rule defines a toxic set.

Yes, this is another success of the general concept of a trial, and the construction of a trial setup by logic consistent with the rules of Sudoku.  Resistance of the trial concept is pervasive.  It accounts for the overly cautious requirement embedded in champaigne’s definition of the Exocet.  The JE Exocet meets an additional condition that definitely makes two of its qualifying base candidates more likely to be true. It would not be surprising to learn that this condition, perhaps with minor refinements , makes that a certainty.

Unsv 197 bird 1So now, let’s liberate David’s quick solution of Unsolvable 197 from the confines of an Unsolvables comment.  His first step is to remove non-base digits from the targets.  Is there any bolder action on the above mentioned hypothesis?

Next, David duplicates chute lettering results by eliminating base candidates that “see” both bases and targets.

Unsv 197 bird 2The harvest includes a naked pair Nnp34. The question this raises is,  “Does this step always leap over chute lettering?”

Unsv 197 bird 3

Next is the first base digit elimination from a target cell.  In the comment , Bird only has room for “base digit is absent in the mirror node”, but going back to his JE definition in the compendium, the full rule is:

Unsv 197 bird 3b

Acknowledging what he is actually doing, David could put it this way:   “5 in blue target 1 forces 5 in blue target 2 as well.”  Bird had to work carefully to formulate a spotting rule that covers this.  I’m  agreeing with him in saying that a long checklist of rules can only be applied by computer, not by human solvers.

David now turns to the cross line eliminations, but I’m putting that aside, along with the study of David’s continuing  JE eliminations, because he is already in position to collect much lower hanging fruit.

Unsv 197 bird 4“Singles” follow up on the 5r1c5 removal yields  5r1c8 in the green base, with its removal from the blue base as well. Then the removal of 2r1c8, consistent with the exocet.

Unsv 197 bird 5This leaves only three possible solutions, under the exocet hypothesis, namely

green 7t1, 5t2 and

blue 9t1,2t2

or

green 9t1, 5t2 and

blue 2&7, either way.

 

 

 

Unsv 197 bird 6The trial of the latter two are combined with naked pairs 2,7 and it is “all singles”:

When it fails, we have only to verify the solution exocet of the previous post.

Have you learned the Sysudoku trial trace yet?

Bottom line here is that only the briefest and most obvious application of the exocet hypothesis was required to expose Unsolvable 197.  By looking beyond the grid induced restrictions of the previous post, and into David’s hypothesis testing rules,  we will probably seldom need the CLEF tabulations. They are, however,  a systematic  way to implement the JE cross line rules.

To be prepared for tougher exocets, I plan to become  familiar with all of David’s rules, but not in the form of a list of searchable causes.  That is for computer codes.  Instead, human solvers can better utilize them to visualize the completion of a base/target pattern, or its failure.   With experience, I expect to be able to spot a rule violation by its effect on the visualized pattern.  This may be what David is already doing on the Unsolvables.

This long-running blog on human Sudoku solving is approaching an ending point.  No, no, don’t get upset!  I welcome suggestions on what else can be explored, but for the most part, my package has been delivered.  To have some time to tie it up gracefully, I’m  suspending weekly posts through the summer.

I’ll be at work updating existing posts and pages, adding forward links and navigation pages.  Along with that, I plan to have a print and e-book reader’s guide to the  Sysudoku blog published when the blog is concluded.

Next week’s post is a mini-guide for those who encounter the blog for the first time this summer.  It gives a brief summary of the intent and accomplishments of the blog, some component themes, and navigation features.

Regular posts will resume on September 6, 2016 at the latest, with puzzle collection reviews, and the long promised commentary on Denis Berthier’s Sudoku by artificial intelligence.  At least Denis comes right out front with it.

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