## Hodoku’s Limited XYZ Wings

In this post reviewing the Hodoku Wings page linked under Techniques, we see how an expert programmer can go wrong in explaining how to recognize where a technique applies and why it works . The omission of irregular wings is another update challenge for the Hodoku project. For realistic solver training, it’s now required to include the possible employment of grouped AIC winks in any technique.

Did you step into the cage and take a swing at the “Extended Variation” Sue de Coq? It turns out to have a multi-cell ALS in each remainder, but still manages to do some damage. A little more than Hodoku marked up, in fact. The contents of SEc7 can be described as

7(2+8)(4+9)

The row remainder is responsible for 4 or 9, but it so happens that r5c7 is left holding the bag for 2 and 8, and the ALS in c7 must supply 1 as well as 4 or 9. That wasn’t very nice.

To cap off a bad day, the Hodoku Wing section steps out with “An XY-wing is really a short XY-chain”. That is true. So why not treat the XY-wing as a side comment in the discussion of XY-chains? It’s time to do it that way, and I will, in the next post.

After some nice XY-wing examples, the wing section continues with the XYZ-wing, calling it “an enhanced version of the XY-wing”, which it isn’t. The extra Z in the hinge is more handicap than enhancement.

That is followed by “Now the pivot contains not only X and Y, but Z as well”. Well, why is that important? Nowhere does Hodoku mention the fundamental fact that one of the three Z’s must be true. The reason he doesn’t is explained shortly, but therein lies the advantage of XY-chains over XYZ-wings, two candidates, instead of three, that a victim has to see, no matter how long or how short the chain.

Hodoku’s first XYZ-wing example offers a side demonstration of this advantage. In a generous field of bv, XY-chains, the generators of 2-candidate toxic sets, run wild with opportunity. Here, only a few 3-candidate hinges were available, but a regular 457-wing did appear. I use thick burnt orange arrows to mark the hinge and wings. But the XY railroad gives two XY-chains making the same elimination, one with a bonus elimination and clue.

More on the Hodoku chains to follow, but my job here is to evaluate what Hodoku’s example note is telling readers about the XYZ-wing . After identifying pivot(hinge) and pincers(wings), it’s this: .

“If r7c2=4, r2c2=7 => r9c2<>7; if r7c2=5, r7c1=7 => r9c2<>7; if r7c2=7 => r9c2<>7”.

There is a full explanation of the notation in another section, but to use actual words:

Try each value in r7c2. No matter what r7c2 is, r9c2 is not 7.

What is this? Is it the way an XYZ works? No, it’s not about seeing 7’s in both “pincers” and the hinge.

Is it how you spot an XYZ? No, it’s not about pivot and pincers sharing numbers and seeing each other.

Is it something you do with every three-candidate cell, to see if it is an XYZ pivot and what it’s victims are? Astoundingly, yes.

The Hodoku diagrams sorely need explanatory notes, but this one has nothing to do with the XYZ- wing as a human solving tool. It actually describes a computer search for XYZ-wings! The algorithm actually goes something like this:

Now if you want a practical way to describe this to nonprogrammers, just identify the pivot and pincer cells, and write the Hodoku note above.

But think about how impractical this is for human solving. Such notes are not telling you how a person could find the wing or how it works in this case.

My post on regular XYZ does provide these essentials. In the following one, on irregular XYZ, there is another major update project for Bernhard. It’s in inclusion of grouped AIC winks in the XYZ link structure. This introduces many more ways for the victim to strip the hinge.

And what about the other winks of the schematic, the ones connecting the “pincers” to the hinge? Yes, these can be forcing chains and ER’s.

A remarkable case from Sue de Coq’s original post is reported in my XY-chains post of December 2011.   Of course this insight applies to all applications of seeing, that is to say, all winks in technique structures. It led me to promote the concept of the toxic set, a set of candidates other than a unit, guaranteed to contain a true candidate of a number. Toxic sets are generated in many ways, but all are exploited via the same “seeing” methods. It is important to recognize the forcing chain as a wink, a way of seeing.

Here is an example from Paul Stephens Sudoku Addicts, puzzle 134. These wings don’t exist for most experts reviewed in Sysudoku, including Stephens and Hobiger.

Hodoku does grouped AIC winks. For example of grouped AIC winks in the XYZ, and in the fatal vision of the victim, have a look at the review solution of KrazyDad’s Insane v.4, b.3, n.5. Such cases are not nearly as hard as they look after the fact. The search is awesomely pre-filtered by having a given start and ending point, and is guided by bv and slink markers along the way. The initial spotting process, aided by a map of the bv cells, is simple for the human visual system.

Hodoku passes up on the WXYZ-wing, but covers a relative, the ALS Death Blossom, reviewed later. I think it should be included, along with  the BARN and BNS, in any Hodoku update.

The last wing of the Wings page is the W-wing, which Hodoku describes as “two bi-value cells with the same candidates, that are connected by a strong link on one of the candidates. Actually his two examples reveal an AIC wink between two of the bv candidates, and simultaneously, an AIC slink between the other two. The W-wing is an AIC almost nice loop. It is an eliminating ANL, but if one of the “Discontinuous” winks is a slink, the W-wing is an AIC confirming nice loop for one of the X-candidates.

One of the Hodoku W-wing examples has been added in Sysudoku notation to in my December 2011 post on XY-Chains. Two more found by Gordon Fick appeared in a recent revisit of Weekly Extreme 435 from the Competition review.

The next posts will be about Hodoku coverage of chains. Some topics are handled well and the examples are very worthwhile. Unfortunately, Hobiger’s notes continue to describe only an inner loop in the coding of Sudoku techniques.