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.


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


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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Completing CLEF for Unsolvable 197

This post notes how base candidate combinations of an exocet can be reduced in additional ways, then continues the exocet trials of Unsolvable 197 by means of Sysudoku Chute Lettering Exocet Filter.  This technique is, in part, a systematic way to exploit the crossing line constraints of the Junior Exocet approach reported on the EnjoySudoku forum by David P. Bird.

Unsv 197  chute letHere again is the grid with non-base candidates removed by chute lettering.

Unsolvable 197 illustrates other  interesting possibilities for trial reduction.  The  Single Alternate Sue de Coq describes the contents of as  either 8(2+7)(5+9),  or the naked pair np59.  The Sue de Coq term confirms 13c4 and the np term, 1r3c6. That trial is deferred here, but with either term, or either 1 being true, both bases contain  (2+7)(5+9), i.e. 27 and 59 are not possible.  We missed that one.  The details remind us that base digit restrictions can also come from APE.

Unsv 197 29 57 row sitesPicking up on the failure of double exocets blue 2&7and green 5&9 last week, next up is blue 2&9 and green 5&7. This set is a bit simpler because, with a base digit of 7, target 1 cannot be 2.


The single color combination tables:

Unsv 197 3 one colors

Both green target placementsUnsv 197 two 9257 exocets are set up for trial:



Unsv 197 remote pairThe left one reveals the core slipperiness  of Unsolvable 197 with a tight little clique of 348 candidates, but a remote pair exposes its contradiction in a collapse.

Unsolvable 197 doesn’t much care which green targets you choose, bringing you the same cast of characters.




Unsv 197 wing and ANLBut this time, a 384-wing with a forcing chain victim, plus a simple 8-chain almost nice loop gives up the solution.

How did it go for you?

Next time, we peer over David P. Bird’s shoulder at his comment length Junior Exocet 197 solution, explain what his JE rules are really doing, and suggest how these rules, and the Exocet itself, could be more clearly expressed as a trial.



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CLEF-ing Unsolvable 197

This post is a completely traced report of a solving of Unsolvable 197 by Sysudoku Chute Lettering Exocet Filtering.  The Unsolvable 197 double exocet is in the North band, in contrast to the earlier CLEF solved Unsolvable 190, with the double exocet in a stack.  CLEF tables are therefore shaped differently. The CLEF solution here is preliminary to a comparison with David P. Bird’s JE solution of 197 on Andrew Stuart’s Unsolvables page, and general comments on exocets, to follow in later posts.

Unsv 197 LM gridWe begin with the line marked 197 grid. Fill strings are attached, conveying something of the effort already invested in the puzzle when the exocets are recognized.




Several box slinks and a single clue, N6, were found in basic marking.

Unsv 197 basic tr

My X-panels found no X-chains, fish, or pattern constraints to cut though the candidate fog.  JC Van Hay and David P. spotted the blue and green double exocet  on 2579 in the North band.

Unsv 197 nonbaseOf the possible four placements of nonbase digits 3 and 4 in the North row chutes, chute lettering reveals only one allowing the double exocet  with complemetary base digits in the target cells.


Unsv 197 chute let

We will label targets t1 and t2 left to right in both exocets.

In this placement, bv 27r1c4 prohibits the green base 2 and 7, and combinations

(blue 2t1, green base 7),  (blue 7t1,  green base 2),  blue 2t1, green 7t2, and blue 7t1, green 2t2.

Similarly, 279r2c9 bans blue 2t2, green 7&9, and blue 7t2, green 2&9.

Finally, if the green base does not contain 5, the blue base exocet has to have t2 =5.

Unsv 197 xline tablesTo prepare for the remaining exocet trials, we tabulate for each base digit, its candidate locations in each of the crossing columns in both exocets. Then starting with blue 2&5, we set out to try each combination as necessary.

In 2&5, 7&9, bv27 bans 1t2 and the 279 bans 2t2.  For 2&7, 5&9, the row sites on crossing columns are taken from the columns of the crossline tables above.

Unsv 197 27 59 row sitesPlacement for each target pair can be posted to two dimensional  blue/green combination tables directly, but  I do it more reliably by first filling out row placement tables for each target placement. Then I fill combination tables one color at a time,  before combining them.

Unsv 197 27 59 combos

Two combinations conflict, leaving two exocets viable for trials.

Unsv 197 2795 setupHere is the first trial setup, with marks dragged into the cell center for clues.  It collapses to a contradiction quickly.  The contradiction you get depends on the order you follow.






Unsv 197 2759 contradictionWith green targets reversed,  the second 2759 combination reaches a contradiction as cell r4c3 is emptied.

Next, we  move on to … But wait, why should I have all of the fun?  Let’s make it  a team sport.  For next week, decide which combination(s) come(s) next, and perhaps, push on to the solution.



After that, we’ll be in a good position to appreciate how David P. sorts out the abcd of the solution in a more compact fashion.

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Jacobs’ Sudoku for the Brave

Coming back to basics, this post reviews Charlie Jacobs’ collection of basic puzzles, Sudoku for the Brave. The book has no commentary at all.  Just puzzles and solutions.

jacobs review tableCharlie labels his 200 puzzles “Extreme”, but they don’t come close to that.  I did find them challenging enough for the commute or airlines flight.

I was able to leave the advanced techniques  bv count columns out of the review table, because none of the 10 puzzles I worked through actually got that far.  Review table conventions are on the page linked above.  Preselected were Brave 6 and every 20th thereafter.

Two collapsed (—) in box marking.  One of these, Brave 146, brought something I’d never seen, a naked septuple (7 locked numbers).

Of course, these results assume you are starting with the slink marking bypass, finding all unit slinks in line marking, then finding all remaining clues and candidates in line marking.  Otherwise, you might happen upon all kinds of fish, chains, loops, and ALS.  Here we seek to find these only when they are needed.

For highlights, below are two grids from Sudoku for the Brave.  You could recover the givens and see if your counts and line marking are better than mine. That’s quite possible.  Or better yet, get a copy of Charlie’s book and have a completely independent look.

In Brave 26, the naked triple strikes on the last row of line marking, which is tough enough to leave your pencil marked copy an unholy mess.

Brave 26ntThe triple leaves a naked pair, giving N5, which  triggers the collapse.  I wouldn’t want  to wade through the sea of number scanned candidates that Brave 26 generates.

Brave 146 septupleNext is the grid of Brave 146, just as the  septuple develops in the SE box.

No clues in the box and the candidates of 8 numbers are present by virtue of slinks. Two candidates of the ninth number, 6, are required in r89c7. 6 can be placed nowhere else in SE, therefore the 7 cells are occupied by 7 numbers.  Two clues, a naked pair, and an immediate collapse are the results.

You can own this septuple by building up to it. The bypass and box marking traces are given below, as a checkpoint.

Brave 146 trace

Next week, I  return to exocets with Unsolvable 197, to properly absorb and acknowledge David P. Bird’s application of his Junior Exocet rules to this puzzle, and to apply another form of Chute Lettering to 197. Bird’s solution of 197, and 190, in comments to the Unsolvables page convinces me that I misinterpreted his compendium conditions and rules on JE’s.

My adventures with the exocet Unsolvables is bringing welcome attention, and hopefully, some good human solving insights, from EnjoySudoku  contributors.  I regret that I am not able to join in on the forum itself, while keeping to my weekly posting schedule at the same time. Maybe later.

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CLEF Homework on Unsolvable 190

Here is a checkpoint Sysudoku reader’s homework on the Sysudoku Cross Line Exocet Filter introduced in the previous post.

Was it hard?  I stumbled many times on the 3467 case of the last week, and I may need corrections on this homework checkpoint.  If you sailed through it, you may be close to doing it mentally.

First, the 3&7, 4&6 table. From the grid, blue base digits 3 and 7 force 4 in green target 2. Both 3,7 placements are viable with those green targets.

Unsv 190 3764 tables

Unsv 190 3764 trial gridWe can do a single trial with 3 and 7 in either target, and the green target clues.  The trial stalls with the targets unresolved.  The earlier encountered  remote pair and the 125-wing push it a little further.

Then we try 3 in blue target  1, arriving at the inconsistent coloring seen earlier in the orange 8-pattern trial. On 190, the pattern trials were just as decisive as the exocet solution trials.  Then 7 in blue target 1 goes all the way to the solution.

You would have little reason to follow up after getting to the solution, but if you want to check me out on the remaining trial reductions:

The 4&6 with 3&7 trial would start with a naked pair 46 in the blue targets, 3 in green 1 and 7 in green2.

Unsv 190 4637 trials

Two of four target arrangements are accepted for the 4&7, 3&6 trials. A single trial with  naked pair 47 in blue and t1=3, t2=6 in green, might suffice.

Unsv 190 4736 trials

Finally, for 6&7 with 3 & 4, the grid requires 4 in green target 4. A single trial with 67 in the blue targets,  and 3 and 4 clues in the green.

Unsv 190 6734 trials

To recap the two posts, CLEF is demonstrated here as a systematic procedure to make exocet trials in puzzles like Unsolvable 190 more humanly practical. Finally, we can let Unsolvable 190 RIP, with our thanks to Andrew Stuart.

Next, we catch our breath with Charlie Jacobs’s Sudoku for the Brave, a very tough, but basic solving collection.  Down the road, more Unsolvables.  Among them  a direct comparison of CLEF with Bird’s compendium technique.  And if you want to get there first, to CLEF the first monster of my blog, the Golden Nugget.  I knew that would get your attention.

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The Sysudoku Cross Line Exocet Filter

This post introduces a human engineered filtering method for reducing  exocet trials, in number and complexity.  The method is designed to follow the Sysudoku Chute Lettering  technique  introduced previously in this series of posts on the Andrew Stuart Unsolvables .  Here the method is explained and illustrated.  Readers are challenged to apply the method to remaining trials of the double exocet of Unsolvable 190.  The following post will be a checkpoint on this sysudokie homework, which does include the puzzle solution.

My recent project to demonstrate logic based human solving  methods for Andrew Stuart’s Unsolvables  has me considering monster-killing exocet  trials more seriously.  UnSolvable after Unsovable, these unbalanced puzzles include exocets more often than not, many doubled in a single band or stack. For that reason, and at the nudge of my chief scout,  Gordon Fick, I returned to the EnjoySudoku forum to catch up on how these worthies have resolved the problem.  The bad news is, they haven’t.  The good news is the extensive compilation of what they have accomplished, by senior contributor David P Bird.

Consider the solution of the exocet cells as distinct from the solution of the puzzle containing the exocet.  Two digits of the base cells are repeated in the targets.  Bird’s compendium clearly reflects expert opinion that one of these exocet  solutions is very likely to match the puzzle solution – likely  enough to justify using the exocet solutions in trials.  In a double exocet such as Unsolvable 190, the two exocets each contain a different pair of the identical base cell digits in their base and target cells.

There are 6 combinations of two target digits out of four base digits.  Some of these trials require either a single trial with both base digits in the target cells or two trials on the two possible placements of base digits.

In the Bird compendium, two variations of the exocet are considered.  These two are represented in the panels below, with base cells (B) and target cells(T), shown here  in their Unsolvable 190 positions.  Requirements are placed on base (B) digit candidates in companion cells(C) and crossing line remainders(S), to guarantee that a base set solution can solve to an exocet solution.

exocet juniors

In the Junior Exocet, or JE, there is a companion cell (C) for each target.  In the Junior Exocet Plus, or JE+, those cells contain a naked pair with one of the base digits, and a non-base digit. Two such pairs are present.

In JE and JE+, the TC, CT, QQ and RR pairs of cells in crossing line are called object pairs.  Bird’s requirement for JE object pairs is that “base digits only appear as a candidate in one (the target )cell and not in the other(the companion).

In my original post,  I interpreted this to disqualify the Unsolvable exocets  of my review series as JE’s, because, at the point where exocet trials would be useful, they have all four base digits as candidates in almost all object pairs.  Bird responded by starting an EnjoySudoku forum thread entitled Sysudoku Exocet, reporting that I had misinterpreted his Junior Exocet definition.  I’m grateful for David’s introducing the blog to the forum, and pleased to learn that Unsolvable Exocets do qualify as JE’s.

My problem was that I took the target’s companion in the quote above to be the companion in its object pair, in the same chute(mini-line).  It is actually the C cell in the other object pair.  The JE condition 2 goes beyond requiring the two targets to resolve to two base digits.  It bans other base digits from the object pairs, guaranteeing the targets resolve to two different base digits.  The added Requirement #2 sets up the JE elimination rules on true base digits in S cells which are enforced by the CLEF filter.

Requirement #2 has another profound role not explicitly addressed in Bird’s description.  It is the basis for selection of the target cells, at least in the cases I’ve examined.  The chutes selected among Unsolvable alternatives appear to be the ones meeting this requirement.  The requirement, and the resulting selection of targets, goes beyond champaigne’s Exocet to a more specific trial, more likely to succeed.

In this revision of the original post, I’m withdrawing my speculation on the effect of chute lettering on JE+ exocets.  Considering who’s watching,  better wait for evidence.

Bird’s study of the Junior exocets has the objective of bypassing the more specific trials with single base digits in the targets.  Unfiltered, this could amount to 12 trials: six selected pairs, and two ways to place them in targets.  By limiting to the Junior format in which target and companion can hold only one of the selected digits, then one can say that each target digit appears twice in the three crossing lines. The result is a host of rules for eliminations.  Bird acknowledges the difficulty of spotting cases adhering to these rules, and recommends recognition software for this task.

Since the JE conditions are not met by most of the Unsolvable exocets encountered so far, I was pressed in the Unsovable series project to use the forum’s insights about the crossing lines in a more specific way. I expect the resulting method will work very well for the JE’s as well.

Unsv 190 exocet setupAdapting Bird’s crossing line spotting technique into a constructive filtering procedure for exocet trials, here is the Sysudoku Cross Line Exocet Filter.  For this demonstration, return with me to the line marked 190 grid, after placement of extra digits 2 and 8 in the West chutes, by Exocet Chute Lettering.

We can already see that 3&6 is impossible for the blue exocet, because of the bv 36r7c3. Also, a blue exocet without 7 will require a green exocet with target 7r8c3.

Unsv 190 target fillsWe start by filling two target placement tables.  In each, we tabulate the possible placements of each digit in the crossing lines(S above). We do that for two cases: the digit in target 1 or in target 2. The base line of the blue exocet is r2.  In the green one, it’s r5.

The idea is that exocet digit placement in the base cells and targets impose fish like restrictions on crossing line placements.  In r5, 3 is a candidate in columns 1, 4 and 8. In the blue 3t1 column, the 1 is recorded because it accounts for the only 3 in the row.  But in the 3t2 column, it isn’t recorded, because that possible occurrence cannot cause a conflict with another digit on the r5 crossing line.  The 4 isn’t recorded, because column 4 is taken by the r2 line in the base line r2 in the 3t2 case.

On the other hand, the same digit in more than one column of the same line is not a conflict. For example, 4,5 in two rows means 4 in one row and 5 in the other.  The 7 in the 6 target cases conflicts with the 7,8 in the 7 target cases only when 6 and 7 are targets together,  eliminating column 7 in the 7 placements.

The digit tabulations of the double exocet are done independently.  It’s done the same way for a single exocet, but in the double exocet case, the two exocets compete with each other on the columns to eliminate digit combinations. Check me out on the target cases in the green exocet.

The target placement tables make it much easier to assess the possible blue exocet solutions and associated green exocet solutions for trials.  Each solution pairs two digits for the blue solution and two complementary digits for the green solution. Here we proceed in order by increasing digits of the blue solutions.

Unsv 190 3467crossingFirst up is the blue exocet with 3 and 4 as targets and  the green exocet  we concluded above had only one placement – 6 in target 1, and 7 in target2.  In the cross line tables, we write the column locations of the target digits in the three crossing lines.  In double exocets,  do this for each target placement

An easy way to fill these tables is line by line, reading down the digit/target column in the target placement table.  For example, starting with the first line of the blue exocet, for 3 in target 1, go down the 3t1 column in the blue target placement table, recording the possible locations in the three crossing lines.  Then do the same for 4, using the 4t2 column.

Unsv 190 4t1 crossingActually, this is what we first copy into the first blue line, but imagining how it looks on the grid, 4 is forced into column 5 in r2, and consequently, column4 in r5. When it is not possible to make such adjustments, the target placement is rejected by the conflict.

In the crossing line tables, it helps to  record 3 and 4 in their target positions, just to account for them in the table. This avoids distracting concern that digits do have to be in all three lines.

Unsv 190 3467comboThe third step in a double exocet is to tabulate the combined crossing line placements for eliminations and conflicts in small double combination tables.  The crossing lines of blue 3 and 4 with green 6 and 7 reveal a conflict in one of the blue target placements.

Normally the four combinations of target placements would require two trials, each with a bv in four target cells, and extra clues in the exocet digits.  The third step reduces this combination to one trial with clues in the target cells.

Unsv 190 3467 tr The resulting trial is much simpler than the pattern analysis trials of the recent 190 posts.


Unsv 190 3467 conflictThe conflict would have come earlier had we done that 8-pattern analysis earlier by coloring the 8-candidates.  The C8 on the third line erases a blue 8 after the NW blue 8 is confirmed, and a guilty verdict can be pronounced forthwith.

Note how the exocet trial’s conflict can be graphically recorded.

Previously oppressed Sudoku readers have to love it.

It may be a good time to point out, that the sequential filling of three tables for the Cross Line Exocet Filter is not strictly necessary for the Sudoku talented.  It’s just a mechanism that permits more typical solvers like me to concentrate on one operation at a time.  It’s a systematic way of tackling a less limited version of the  problem that David P. advised that human solvers not attempt.  As for you, dear reader, you get that problem on your  Unsolvable 190 homework.  Wouldn’t it be fun to discover, before next week, which 190 double exocet trials are rejected by CLEF, and how tough the 190 solution is?

The target placement tables are already in place for all complementary pairs of double exocet digits.  For the homework, you might make some copies  of the crossing line and double combination tables, and work on through the 190 double exocet trials.  I’ll be adding a presentation file with all three tables to the ©PowerPoint solving templates available by request from  sysudoku@gmail.com.  Tell your Sudoku friends, after announcing you solved Unsolvable 190 straight up, with nary an arbitrary guess.

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