## 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:

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.

It 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.

So 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.

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

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:

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.

“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.

This 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.

The 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.