Hard Beware 125 Bypass

This post continues the review of 10 pre-selected Beware! Very Challenging puzzles from Will Shortz’ volume 1 of Hard Sudoku, with Beware 125. The review is a Sysudoku Basic Clinic, all being solved before candidates are completed and advanced methods begin.

The basic trace is one long bypass collapse, requiring a restart at the left to stay on the screen.

After that first leg down to S6, we see a characteristic of this collection, a large number of naked pairs, some claiming box space to create others.

The first one, SE56, is easy to miss. The steep run from there demonstrates sharp bypass action and 3-fill power.

A chain of pair resolutions comes at the end.

Our next Basic challenge is Beware 135. It is another chute filler, requiring accurate box and line marking.

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Chute Filling Beware 115

The second selection for the review of Will Shortz’ Hard Sudoku v.1 is Beware! Very Challenging 115. After a checkpoint on the Sysudoku Basic solution path, there is a brief report on the Guide’s Pattern Analysis page, now published in part

Hopefully, you are using this series for Sysudoku Basic practice, and have already spotted a distinguishing feature, the 3-fill claiming of a chute by slinks and aligned triples, implying further fills and clues in the box. For new readers, my “chute” is the row/column intersection of three cells.

This type of 3-fill is frequent in the bypass. In the diagram of the completed bypass, how did the 6 digit fill string on c4 get there?

The claim on c5 for 1,2 and 6 is obvious, and it implies that Sc4 must contain 7, 8 and 9, which claims a 3-fill on c4 for 126. That last claim may have produced a naked pair and clue for the diagram, to raise some eyebrows.

All of that is well documented in the bypass trace, with the help of the explicit 3-fill brackets added to Sysudoku Basic last year. Here is the bypass trace getting us to the diagram above.

There are ten 3-fills in the bypass, marked by the square brackets.

Box marking fills in the claims and mental slinks.

Line marking a column creates a hidden single on a row.

Here’s the grid at the point of collapse. The hidden single occurs in r8 as the naked pair in c8 removes the only other 1 in r8.







The collapse includes another chute fill, as 8 marks claim the third cell in SEc7 to force 3r9c9.


Next we take up Hard Beware 125 from Will Shortz’ Hard Sudoku v.1.  It’s a natural for coloring, but here we want to know if it survives Sudoku Basic. Have your rating ready.

Meanwhile, part of the Guide page on pattern analysis is up. It is about tools for analysis, freeforms and lettering, and fundamentals of applying them to X-Panel Pattern Analysis (XPA) and Limited Pattern Overlay (LPO). The remainder of the page, to be added soon, combines patterns and coloring.

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A Challenging Exercise in Sysudoku Basic

This post begins a review of Will Shortz’ Hard Sudoku, v.1.  The review details the solution of a pre-selected 10 puzzles from the “Beware! Very Challenging” section of that book. Nearly all Shortz puzzles reviewed in Sysudoku are solved in the Sysudoku Basic stage, and Hard Sudoku is consistent with that.  The review therefore offers participants an opportunity to observe the efficiency and entertainment inherent in Sysudoku Basic.

If you haven’t attempted Beware 105, or have solved it in a different manner, make a copy from the previous post and walk through each move in the trace, accounting for exactly where and exactly why it is made. You may have to go back to the Traces page on the menu bar to resolve some questions, but the essential facts are:

  • that effects are indented in the line below their causes, and
  • that all effects of a cause are posted on the grid before the next effect to the right on the list becomes a cause.

Do participate. It will be easy for most, but hard for experts. To gain any perspective on Sysudoku basic, they will have to suspend their own preferences. This means dealing with    boxes named as compass points, explicit strong links, calling them “slinks”, and limiting objectives to the stage at hand. In the bypass (one list) you’re only getting clues and candidates of subsets. In box marking (one list per value), you’re denoting the remaining strong links of each value. In Sysudoku grids, box defined slink candidates are at the top, row slink candidates in the southwest corner, and column slink candidates in the southeast corner. In line marking, you’re filling in all other candidates, with those remaining unslinked listed from the middle left side.

Each review post starts with the basic trace, and one or more grids at points of interest. The commentary will be about the advantages of Sysudoku basic that are illustrated in the review puzzles.

As to the relative difficulty of the Hard Sudoku Beware collection, it is basic level.

Ready? Copy of Beware 105 in hand? Here is the basic trace.

The bypass has three unresolved 3-fills.  A modest result.

Beware 105 has two naked pairs, and a near collapse in box marking.

The final collapse starts in line marking on the sixth line, getting to a line of five unfilled cells. The cause is a naked quad.

Compare the compactness and relevant detail of this trace with any other Sudoku trace you have actually tried to read. The reason it is possible is that you, the reader, provide so much of the detail. You have the currently updated grid to specify the effect. The why you can figure out.

If I’ve made a mistake or missed a move, you can write me a comment for a correction. Believe me, I use traces to correct oversights all the time.

Here is the Sysudoku grid as the quad is posted.

The sequence of line markings is reported in the trace. Of course 7 is a hidden single as well.

Next we checkpoint your Sysudoku basic on Hard Beware 115.

The post will also report on the new Guide page on pattern(template) analysis.

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The Logic of Aligned Triple AIC Hinges

This post takes on a challenge puzzle17 which follows the Figure 30.1 of the previous post, in Andrew Stuart’s The Logic of Sudoku.   That puzzle illustrated again the type of ANL in which the AIC hinge becomes one of the two winks marking a victim of the ANL – a AIC type to be known here as a hinged ANL. This challenge puzzle illustrates how hinged ANL are found, and why aligned triple candidates are eligible to be 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 a triple partner of the other terminal. Or you might have put in the hinge only because 2r9c4 has a triple partner that is a slink partner, intending to look for an AIC back to 3r9c6.

The hinged 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 Hinges 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 Hinges, 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 the victim seeing a toxic set member with a hinge wink,  deserves a distinct name,

and I propose the “hinged ANL”.

The hinged ANL is generated naturally in the effort to keep a hinge initiated chain going until something happens.

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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