Logic Justifies Aligned Triple AIC Hinges

This post takes on a challenge puzzle 17 which follows the Figure 30.1 of the previous post, in Andrew Stuart’s The Logic of Sudoku.   A boomerang ANL shows why aligned triple candidates are eligible to be AIC hinge partners.

Logic 17 looked unlikely to continue after a bruising bypass round, gave up nothing else. My basic trace:

The opening advance is a remote pair.  Actually the 58 cells allow two, but I found no victim for one of them.

Then, as in 30.1, the bv scan yielded nothing, in spite of a much more generous bv field. No gifts from the X-panel either.



So when two clusters stalled as well, I added AIC hinges and started doodling. This time I included aligned triple partners as possible targets for a hinged ANL wink.

In the exploration of  the r9c4 hinge, an aligned triple hinge, you can start at the slink terminal and arrive at either  triple partner  at the other slink chain terminal, for a boomerang. The ANL takes an XY node and a 2-chain.



The hinged ANL from r4c5 requires a reversed bv and 2-chain. If you can get back to the cell of the other hinge terminal, on a candidate of that cell, you have it.


I’m checking the X-panel of the victim on each elimination. A new slink comes with this one.

In the analysis of the r1 hinges, the r1c4 hinge is not dependent on the aligned triple partnership, because 2 is a slink partner. Starting from 2r4c4, you would use r4c2 as an XY node until you see the opportunity to re-use the r4c6 hinge above. To keep the AIC going, you can go through one discontinuity, the pair of winks.


Or going the other way, you come upon the r78c5 ALS 167 as the connecting node.

The destruction of the 25 naked pair adds a 58 bv and another remote pair, wrapping green for the collapse.

In The Logic, Andrew described the 17 challenge as requiring “some fancy footwork with the strategies discussed in these lfew chapters”.



More specifically, it can serve in the Guide as a clarifying example on human exploration of AIC hinges.

Next, we begin the review of Will Shortz’s Hard Sudoku v.1 to cover “Beware! Very Challenging” 105, 115, . . . , 195. In case you still haven’t ordered your copy, here’s Beware 105, which Will certifies to be very challenging.

The next Guide page will be on Sysudoku pattern analysis.

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Fleshing Out Stuart’s ALS Node Figure 30.1

Andrew Stuart’s The Logic of Sudoku, in a chapter on Almost Locked Sets, presents an example of an ALS node in a confirming Almost Nice Loop, as Figure 30.1. This post fills in the solution, before and after the series of four grids in the AIC Building page of the Sysudoku Guide, that illustrate the flexibility of the ALS node in AIC.

As is the case throughout The Logic of Sudoku,  solving to Figure 30.1 starts with candidates  scanned directly from the given clues. Sysudoku Basic usually gets to advanced in a more entertaining way, and with more information.

When basic uncovers no clues, as in this case, there’s as many candidates.

Needing to account for a few candidates missing, and I went through the bv scan with the same level of success: none.

But next, on the 1-panel, a finned swordfish succeeded. The three kraken victims escaped.

Then on the 4-panel, a skyscraper triggered a Nc6 boxline, accounting for the remaining missing candidates in Figure 30.1.





Getting to the 8-panel, there is a kraken 8-wing and a Cc4 boxline. These removals come before the AIC scan in Sysudoku, but  do not affect Andrew’s example.

X-chains and fish are best at cutting through sucn a sea of candidates, and the same disconnected bv field that frustrated the bv scan makes coloring ineffective.

So it’s time to add the hinges and search out some AIC. For the results, go to

Guide/Sysudoku Advanced/AIC Building, where, under the heading The ALS node, the page continues with Figure 30.1 and two more grids, in which the innocent looking r12c3 ALS 245 is wired to produce a  confirming ANL, a grouped elimination ANL, and a nice loop.

Coming back from  that display, one AIC hinge gets the last laugh, as one of the winks makes the decisive elimination.

This type of ANL, with an outside slink partner of a cell seeing another candidate in the cell, is an AIC boomerang.

After working through the puzzle of Andrew’s ALS node example, I was hoping for another one in his immediately following challenge puzzle 17.  Next post is a report on that one, in which I got more than enough challenge. If you want to get your discoveries before reading about them, here’s Logic 17.

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Funster Extreme 130 Falls in Line Marking

The funster Extreme collection review closes here, with the early departure of the last pre-selected puzzle, Extreme 130. Charles Timmerman’s funster Hard to Extreme Sudoku includes 134 Hard, 134 Very Hard and 134 Extreme puzzles.

Here is the Sysudoku review table for the funster Extreme collection. Every 14th puzzle was taken, arriving at 130 to finish.

Maybe 130 pulled strings to get a seat in the Extreme gallery. The collection exhibits pleasing variety of advanced methods, and plenty of highlights. These include a finned X-wing in line marking, some Sysudoku firsts in coloring, and several elimination victims by inference chain “seeing”.  I rate it “funster Advanced”, but not extreme. An appropriate level for funstering.

Not much left to do,  but display a basic trace of Extreme 130. Two naked singles on the same line trigger a quick collapse.

Next, and before starting the basic level review of Will Shortz’s Hard Sudoku, v. 1, is a report in two posts on my experiences in a return to Andrew Stuart’s treatment of the ALS node in AIC chains, in The Logic of Sudoku. I followed up his Figure 30.1 example by working the puzzle from the beginning.  The result is the more comprehensive view of the ALS node now in the Guide, as signaled by AIC hinges, and as it is re-used twice for further eliminations.

In case you would like to compare details as usual, and without looking at the first ALS node in Logic’s Figure 30.1, here’s the given grid.

In search of another example, I also worked through Andrew’s challenge puzzle 17 immediately following  Figure 30.1. It provided another ALS node example, but further insight into AIC hinges, for the Guide.


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A funster Extreme 116 Labor Day Special

An effective bypass, and a simple uniqueness rectangle, and three choices to close down funster Extreme 116 early. Charles Timmerman’s funster Extreme collection is less than  extreme, but a good introduction to advanced solving methods.

The basic work is easy, because the bypass does most of the heavy lifting.






Advanced 116 begins with a Type 1 unique rectangle.  Candidate 1r6c8 is required to prevent an obvious multiple solution. The two candidates seeing it must go.






After a follow up of


there is a choice of three triggers for the collapse:

You have a border hugging XY nice loop.










Or a deceptively decisive Almost Nice Loop.







Or, if you’re a snapshot collector, or always do XYZ wings first, a regular 489-wing with a far seeing victim.








Our final funster selected for the review is Extreme 130. Review table next tim. The next review collection is Will Shortz’s Hard Sudoku, v. 1. Find the previous Shortz collection reviews on the Titles page. The latest new Guide page is about AIC Hinges, a topic way beyond Shortz.


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Funster Extreme 102 Goes BOGO

Barely escaping the bypass, funster Extreme 102 offers a thematic example as inference chain seeing nets an extra victim for the collapse.

Close to a bypass victim, Extreme 102 finishes basic quietly.

On the line marked grid grid is a flashing sign, a a four cell remote pair chain. Actually, there is a a second one, but this this one has a victim. Well Actually, this one has a second victim, courtesy of a skyscraper 1-chain.

Well, actually, the X-chain can be replaced by a naked pair necklace. The victim sees one terminal directly and the other, by the r6np13  wink. The two removals collapse what’s left of funster Extreme 102.

The bypass and AIC wink clinic continues next week with funster Extreme 116.


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A Timely Finned Fish in funster Extreme 88

Continuing the review of Charles Timmerman’s funster Hard to Extreme Sudoku, with Extreme 88.

The basic compensates for a modest  bypass with a favorable line marking. A naked single early and a finned 2-wing late. Finned fish is a topic recently added to the Sysudoku Guide.

The finned X-wing is ordinarily spotted on the X-panel, but looking up from the 2-slink on r8, the presence of the victim in the box of the fin jumps out at you.





Following the regular order is a regular 237-wing.



After the follow up,

I try to enlist the naked pairs in coloring.

The cluster expands by trapping 2r2c8, and blue is wrapped in r5. Game over.









Next is Funster Extreme 102 which illustrates a Sysudoku theme in an unusual way.

Also, a Guide page on Coloring Fundamentals is now available, off of the Sudoku Advanced page

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Funster Extreme 60 and 74 Go Together

Two brief advanced appearances are reported in this post in review of the Extreme section of Charles Timmerman’s Funster Hard to Extreme Sudoku.

In Extreme 60, the bypass starts with a 3-fill and uses them to solve a big wedge. The remaining line slink marking is easy.


The rest is easy too.  A type 1 unique rectangle is enough for a collapse.






In funster Extreme 74, a less decisive bypass, . . .

. . . is aided by a 6-wing, a form of fish directly signaled by line marking. Regular fish of all sizes are now explained in the Guide as  X-panel  methods, but the X-wing is often spotted in line marking as an alignment of slink marks.

This fish has no victims now, but the fish icons are left in, to exclude 6 candidates from r46c3 and r4c7 in the remaining line marking.







As basic is completed,  this XY-wing and naked pair triggers a collapse









Next in the review is Charles Timmerman’s funster Extreme 88. Next in the Guide is Coloring.


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