AIC Slinks Finish Only Extreme 3

This post continues the finishing coloring cluster expansion in Castillo’s Only Extreme 3, via not-both testing of AIC slinks.  After extending the blue/green cluster in the North bank via AIC slink, we continue with a second AIC slink adjoining the cluster, shown below.

If 1r5c5 and 2r5c8 both true, we could declare green false, blue candidates true, and be almost home. If not, the burgundy slink is also a coloring link, and blue/green expands.

The both-true combination forces two 3’s into c6.

The cluster expansion traps 67r5c4, but more importantly, it enables a third AIC slink to apply for a coloring license.

In the olive AIC slink 2288, if both terminals 2r5c4 and 8r4c7 are true, blue is confirmed, but along with that,  all three 8’s are removed from the South box. So 8r4c7 is green, and coloring makes a leap.






Traps along c8 and r5 are first, then the 8 removal in r5c6 creates a naked triple. In the North box, only the 5 sees all of its peers in the triple. The 6 and 7 candidates do not, because the triple is defined in the c6 column, not the N box.

After  a brief marking,





The blue confirmation finishes Manuel Castillo’s Only Extreme 3.

Certainly a puzzle requiring three not-both extensions of the coloring network (and two posts) deserves the extreme grade.




I will review the Only Extreme collection by preselecting these 10:   3, 46, 89, . . ., 385 in case you want to get there first. 

Before that, however,  let’s look at Only Hard Sudoku, Manuel’s earlier collection of basic Sudoku, that came out in 2014. Next week,  we’ll have the review table, and Only Hard 128, an unusual case of a box marking collapse triggered by hidden pair not accompanied by a naked triple.  Can you do the  Sysudoku basic without letting the hidden pair slip by?

 Next Monday, I’m doing an introduction to Sudoku for the Fairlawn Ohio Senior Club. I’ll report what I did and how it went, in case you might consider doing that. 




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Cluster Extension by Not-Both Trials

In this post and the next, the first puzzle of the Manuel Castillo Only Extreme Sudoku review, Only Extreme 3,  is taken ahead of the review of his Only Hard Sudoku. The reason is in the title. Rounding out the discussion of AIC slink, here they expand a coloring cluster. It requires the confirmation of their not-both conditions. This turns out to be a task suited to the trial trace developed for Sysudoku monster slaying.

To checkpoint your head start on Only Extreme 3, here is the basic trace and line marked grid. The trace is short because it reflects the help you’re given in basic, which isn’t much.

It’s enough to signal that this review is going to be tough. If you didn’t already try it, maybe you’d like to survey the line marked grid to see if you can find something more basic than the bv scan stretch I have for you below.



The bv field being limited and uncoordinated for XY-chains, I worked extra hard for XYZ-wings, and found this i786-wing:  one wing is attached to the hinge by a grouped 8-chain wink. The victim sees that wing’s Z=6 by forcing chain, or if you prefer, ER.





The X-panels were very imbalanced, but I closed one side of a skyscraper with a 1-slink for a productive AIC nice loop.



These removals allowed me two more nibbles, a finned 5-wing and a 4-chain ANL.









Even better action comes with an old friend I seldom get to use, the Sue de Coq.  In this one, the contents of chute Wr4 is described as 2(4+5)(6+7).

Within the West box, the bv 67 must supply the missing 6 or 7, so the extra 7 has to go.

Now there seems to be enough coloring action among the 1’s, and the dead 4-wing to get something going. Two AIC slinks are in position to expand the blue/green cluster.  In each case, the uncolored slink partner colors differently, depending on the not-both condition.

Testing the not-both for the aqua slink, the trial trace reveals that if 8r2c3 and 1r2c5 are both true, no only is green confirmed, but two 5’s are forced into r1. The arrows show the direct paths to this conflict. With not-both the cluster expands, trapping 5r2c8.



After the cluster expands to the 8’s of the North bank, 8r9c3 traps itself by  finding a way to see the green 8r5c5, as well as the newly colored blue 8 in c3.







After the naked pair c3np45, there is a 5-wing, and some further cluster expansion to do.

Want to take charge? Take over with the  not-both test of the burgundy AIC slink, and compare with my continuation next week.

This post is long enough.







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Badger’s Advanced Sudoku

This post highlights David Badger’s two advance puzzles in the Sudoku 1001 Hard Puzzles sysudokie review, both starting with the almost nice loops to be found along the XY railway.

In 301, the black XY ANL removes two 7’s, and the red extension ANL, two more.


The extra bv allow the XY railway to expand. Coloring extends along a (red) spur in the North box.





The cluster traps 4’s in N and C boxes, and the extension coloring wraps green, confirming blue for the collapse.  



Turning to 101, there’s a weak bypass, and relatively difficult box and line markings, with columns heavily favored over rows.


An indecisive ALS/XZ turns up in the bv scan, but I found nothing else.







On the X-panels, a 4-chain organized the 4’s of the North bank by box/line interaction.








The removal of 4r2c6 enables a 361-wing with an i-wink  victim. It sees the third 1 of the wing by forcing chain.








Plenty of bv for coloring. But the slinks are divided among three clusters. Fortunately in the red/orange cluster, 5r7c5 is found guilty of generating two more 16 bv in the Center box, to go along with the one already in place. The 5r7c5 removal would be decisive in itself, but with the coloring it wraps orange, which, as shown by the arrows, confirms green and violet.

The bottom line on David Badger’s huge collection, his foray into “ordinary Sudoku”, is a constantly entertaining basic level, and a challenging advanced level, if you have the patience to get there.

You never know what the next puzzle is going to be. Kinda’ like the Arabian 1001 nights.

Next time, I jump ahead of myself to preview a review, by taking on Manuel Castillo’s Only Extreme 3. It’s an opportunity to say one more thing about the AIC slink. You may find a way to skirt the trials featured in this post.

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David Badger’s 1001 Hard Sudoki

David Badger, a prolific composer of giant grid Sudoku puzzles, now has a giant book of 1001 standard size puzzles, self rated as “hard”. The publication date, listed in the back,  is June 17, 2017. Here is the standard Sysudoku review of this collection, pre-selecting puzzles 1 to 1001  in steps of 100.

David does many things a little differently, besides grid sizes of 12 x 12, 16 x 16, and 25 x 25 cells and box sizes of 3 x 4, 4 x 4 and 5 x 5.  Instead of extending fill symbols by alphabet, such as the hexadecimal number system {1, 2, …, E,F}, David uses two digit decimal numbers as filling symbols. That must make pencil marking a challenge. His 1001 Hard book carries no copyright notice. Like many of today’s collection books, there is no text of any kind.  Pages are large enough for four grids, with answers at the bottom of each page. The puzzles themselves are formatted in the customary way.

For an overview of the Sysudoku difficulty level, here is the review table:

Two reached advanced, one bypass victim, one box marking victim, and eight collapsing in line marking.  Anything can happen. 

I did 11 pre-selections because puzzle 1001 had a full page rendering, which I took as possibly significant. Turns out, it wasn’t. On 701, the bypass victory depended upon a two 3-fills, and finishes with another.

Here is the grid where the trace ends. Mop up is freestyle.










The advanced track of David’s 301 wasn’t typical .  You might like to examine these three potential UR’s, Dr. Holmes, and ferret out why they fail to eliminate any suspects

From there, investigate the XY railway of his beast, and find an ANL and extension ANL that eliminate a bunch of 7’s.




The extra bv will expand the railway into a  serpentine maize, to which you are to apply Medusa coloring, for a glorious finish.

I’ll checkpoint you on this next time, along with a play-by-play of 101, shown here. You can check me out on the above 101review table report, and find its advanced goodies.


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A Bifurcated Coloring of the AIC Slink

In this post, the AIC slink produces an alternative solution of a puzzle originally solved by a rather extreme pattern coloring analysis. This solution demonstrates how the AIC Slink enhances the already powerful technique of Medusa coloring. The July 11 post introducing the AIC slink has been revised.  It now identifies the condition allowing coloring to be extended via the AIC slink, and names it the not-both condition.

Going back to the KrazyDad Insane review of July 2013,  I thought to have another look at my earlier reliance on the more advanced to extreme methods in that review. Have any innovations or experience since then made any difference?  I was shaken up a little by this data point. I may need to do more.

You have the givens grid, and possibly tried out the bypass route with it.  Anyway, here’s my basic trace.

The bypass makes it look a little different, but the result is the same.

This time, the 5-wing is detected earlier. The icons prevent the addition of 5 candidates in rows 3 and 7 as columns are marked.

Newbies, the font changed when Microsoft changed the definition of the font encoded into four years of slides. In the blog, you’re looking at pictures of those slides.


That earlier attempt amounted to a color trial which I now consider a “last resort”. There are only two possible 5 patterns, and the symmetric slink network of the 5’s allows a 4 candidate into the cluster. The bv slink in that cell is the terminal link for two XY chain slinks between the green 5 and each of the 3 and 7 candidates

Remarkably, the respective 4 candidates are false regardless of the not-both status of the two XY slinks. Take the 5447 slink. If 5 and 7 are both true, 4r9c2 is false. But if 5 or 7 is false (not-both), coloring extends to the slink and 4r9c2 becomes green.  This traps 4r8c3, asserting blue, and removing 4r9c2 anyway.

The same argument applies to the 5443 slink, removing  4r8c3. Thus blue candidates are confirmed.

Note that not-both is decisive in this case, whether it holds or not.


After a modest XY removal at right,




a coloring of the remaining candidates wraps with two orange 3-s in r9.

The red army mops up.



It was startling  to see this sudden collapse of an otherwise intransigent Sudoku, and to wonder how widely the coloring bifurcation of the AIC slink applies.




Next, a review of David Badger’s Sudoku 1001 Hard Puzzles, with preselected puzzles 1, 101, 201, . . . , 1001. The first checkpoint is 701, the only one that falls to the bypass. It’s not a pushover.


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Two of Rebecca Bean’s Less Extreme

Here the Rebecca Bean Extremely Hard review closes with a line marking finish and an easy coloring. The collection is far from extremely hard, if the sample of 12 pre-selected for this review is typical.

On the way to line marking, 9-6 of the previous post gives up an unremarkable bypass, but does offer an unusual box marking.


In line marking, the  c4 creates a naked pair in r9, suddenly reducing 5 to one place in the SE box, a hidden single.






The trace pattern of the collapse is kind’a remarkable as well.

Puzzle 11-6 is less flamboyant, but illustrates well the idea of jumping into Medusa coloring when the bv field is generous.

A vigorous bypass runs out of 3-fills, but leaves pairs. Box marking is tame. In line marking, a naked triple calls attention to the hidden single NE6.






The rows finish up. Going directly to coloring, traps add bv and the cluster expands.








In the second round, an uncommon trap, as 2r3c7 is dispatched by blue or green. As 2r4c7 turns green, 8r4c7 is trapped, turning 8r1c7 green to banish the entire green army. That’s enough to finish 11-6.

Even though Rebecca’s collection doesn’t live up to the extreme label, you can certainly  enjoy the 588 other puzzles. You won’t know when the bypass will prevail, or exactly what advanced technique might be required, but some interesting turns can be expected.

Next, I have another example of the AIC slink. It’s a redo of the first puzzle pre-selected for the KrazyDad Insane review, the volume 4, book 1 #5. You’ll find it on the post of 7/16/13. I still consider the KrazyDad Insanes my most challenging collection.

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Bean’s Extremely Hard I

A review of Rebecca Bean’s 600 Extremely Hard Sudoku Puzzles with Answers begins with the review table and two puzzles, 7-6 and 12-6.

The collection is mostly basic, with the half of them solved by the slink marking bypass.

Puzzle 6 is selected from each of the 12 sections. Two of 12 sections reach the advanced level, loaded with bv.


In 7-6, a productive bypass leaves a simple box marking, and …




In 7-6, a productive bypass leaves a simple box marking, and …

The (46) bv shout out, and one string of four define a remote pair(red). Then an XY wing(black) and a longer XY chain (green) start a steep collapse:







Or, without the long XY chain, coloring brings a wrap of green, and blue wins.









On the second puzzle, 12-6, no graphics but a trace with multiple instances of the 3-fill recently added to Sysudoku Basic. The wide, flat trace profile is a typical result.

Next week, the Bean Extremely Hard review closes with puzzles 9-6 left and 11-6 right, below. Try them out.

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