A Little Harder Ardson v2. 358

Next to last, and getting beyond the XY railway, is A.D. Ardson Very Hard, v.2 358. Here is the basic trace, including an X-wing in the close of line marking.

The column 6-wing  was found in line marking closure, when the column 2 6-slink matched the column 9 6-slink from the bypass:

Persistence results in an XY elimination that seems less decisive than it turns out to be.








Moving on to the X-panels, the first one yields a 1-chain ANL (almost nice loop), and the N box removals create a new slink and a slink elimination in the South box. Elsewhere, this is described as a type of box/line interaction.




More decisive action comes on the 5-panel.  My habit is to look for fish before X-chains on a panel. Here I get a kraken 5-wing, where one of the finned fish targets sees the fin via a five link 5-chain. Simpler and better is the 5-chain removing the kraken victim and one more.





The trace runs until there are only two cells of three values holding off a BUG.




Coloring brings an easy wrap of green in r9, and its done.

The review of A.D. Ardson’s Very Hard v.2 closes next time with Ardv2 398. It is the most challenging of the puzzles pre-selected for the review.

Following that, we’ll double back on my miscopied version of Ardv2 38. Is your comment ready?



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Ardson Very Hard v.2 318

The review continues the pattern with Ardv2 318.

Ignore the pencil marks and pick out the givens if you have to, but try the bypass.  It gets close to the edge, leaving three 3-fill lines for box marking.







The full basic trace leaves a Type 2 unique rectangle.







A Type 2 is a form of box/line. The candidate that would remove the single extra value in two corners must go. The regular box/line removes the other 7’s in the North box.






But again, the bv playground allows the XY rail to romp, and a decisive XY chain just happens.

Hang in there, we’ll move on to 358 next week










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Ardson Very Hard v.2 278, Plus 38 Comments

A conversation about multiple solution puzzles and coloring may be developing, as the A.D. Ardson review plods on.  On Ardv2 278, hidden pairs (naked triples) compensate for a weak bypass.  The puzzle falls to yet another XY chain.

Two regulars commented on my last post, about my travails with Ardv2 38. Dov Mittelman raised an issue on coloring cluster extensions by AIC slinks.  Guenter Todt, with a sprinkling of fairy dust, uncovered a basic solving error that may have ushered me over multiple solution barriers.  Before the follow up as the review closes, perhaps you have something to add.

Going forward with 278, an anemic bypass is balanced by a naked triples (or hidden pairs) in line marking.

For DIY without your v.2 copy, lift the givens from the grid at the first naked triple.









The strong bv field supports a long, and  decisive, XY chain. The collapse is swift, generating a steep trace, with many resources untapped.

Next, we advance 40 puzzles to 318.

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Another Look at Ardson Very Hard v.2 38

This post brings up an interesting question about the multiple solution puzzle: Does its ambiguity prevent strictly logical solving from reaching a solution?

Introducing the first selected review puzzle of the A.D. Ardson Very Hard v.2 collection on April 11, I accidentally omitted a given.  Ardv2 38 should have a given 7r7c6.  The post of April 18, traced the resolution, with missing given, to a match of the Ardson solution,  with  given.

A diligent reader, Gerald Asp, who checks his transcription by running the puzzle through Andrew Stuart’s solver, got the unexpected report that my version of Ardv2 38, missing 7r7c6, has 63 solutions! In my trace, 7r7c6 is determined on the final color wrap. So either my resolution transgressed strict logic at some earlier point, making an unwarranted assumption about the truth of a candidate, or I was mistaken in the review of Denis Berthier’s The Hidden Logic of Sudoku when I said, in the post THLS vs.Unique Rectangle of 12/13/16, that uniqueness is proved when a solution is reached with no assumption having been made about the truth of any candidate.

Inherent in that statement is the belief that resolution between the multiple solutions cannot be achieved without such an assumption. But in the traced resolution of April 18, where is that assumption? A coloring cluster does not make such an assumption. It relies on the fact that in the slink network of the cluster, candidates of one color are true, and those of the other are false.  Hopefully, one color will be found to violate the rules of Sudoku, a color wrap.

Is such an assumption made when I  use an AIC to constitute a strong link, extending the cluster? This form of slink fulfills the definition of a strong link between candidates.

The question in play here has nothing to do with my disputing Denis Berthier’s claim that UR methods assume uniqueness. These methods do make a much more limited assumption. They assume only that multiple placements of the simple rectangular form will not be allowed by a professional puzzle composer. This has nothing to do with the composer’s willingness to run his solver long enough to be sure that no multiple solutions of any form exist.

Well, help me out here.  Next post, we will move on to resolve Ardv2 278, but do look for comments on this post in the coming weeks. Perhaps one of them will be yours.

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Ardson Very Hard v.2 198 and 238

The review of A.D. Ardson Very Hard Puzzles v.2 continues with Ardv2 198 and 238. The sysudokie resolution to 198 is a rerun of 158, but 238 is a classic remote pair example.

Ardv2 198 barely escapes the bypass, but still manages to get to the bv scan.







It arrives with a large, well connected bv field, which promises an extensive XY Railway.  The first XY  I happen upon, . . .







proves to be decisive.

That makes Ardv2 198 very much like Ardv2 158.




The next review puzzle, Ardv2 238, follows an entirely different advanced sysudokie path. Basic solving leads to .  .  .



. . . a grid dominated by 78 bv and 578 cells.  The easiest prey in this patch is the remote pair chains.







End cells of chains of even length are conjugate pairs, containing true candidates of each number!

Here we have two, a 4-cell (black), extended (red) to a 6-cell remote pair. The combined remote pair removals leave a naked pair 45 in c6, removing two 5’s.


The resulting 5-wing in columns 2 and 6 removes two of three 5’s in c5, leaving a decisive clue and naked triple.

Next in the review is Ardv2 278, but you get two weeks to get your solution ready.

That’s because next post will explore a curious situation arising from  Gerald Asp’s comment on Ardv2 38, on which a Sysudoku innovation is brought into question, because I left out a given!




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Ardson Very Hard v.2 158

After a one week pause, we continue the A.D. Ardson v.2 review with puzzle 158.

If you don’t have your copy, just load one from the Calibri font givens here, and do your own solving. Then compare with this checkpoint. It arrives with line marking almost done along the rows, and a productive 4-wing.

The basic trace, gets us to the next grid.

The ample bv field yields no UR’s or XYZ-wings for me, but there is a completely decisive XY chain.

Next is Ardv2 198, from A.D. Ardson Very Hard Puzzles, v.2

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Ardson Not So Hard Ardv2 118

Ardson Very Hard v.2 118 shows off the basic steps, but can’t quite dodge the consequences. A good Sudoku basic workout, and reminding us of the joys of basic solving.

Here is the basic trace, completing box marking with a naked quad.


The grid completes the checkpoint.









The column 6 marking completes a naked triple in r1, which restricts r1c8 enough for the naked pair 26 in the c8 marking, and clues NE9 and SE3, folding up Ardv2 118.

Next time, we move on to Ardson Very Hard v.2 158. That will be in two weeks, May 16, because of unforseen difficulties.

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