Longo’s Nastiest Ever After

This post finishes the illustrative review of Frank Longo’s The Nastiest Sudoku Book Ever, with review puzzles 673, 684, 695 and 706. The bv scan and occasional easy coloring continue to be enough for what Frank claimed to be the toughest part of this not so nasty, but entertaining, collection.

nastiest 673 UR 1 and 2Nastiest 673 catches a nasty case of Type4 Unique Rectangle. One of the worst I’ve ever seen.

On the left, the 3-slink prevents any UR partner 4 from its corners, bringing in two more bv.

In the middle, the 5-slink throws out the only two 6’s in c4 outside of the N box, for a boxline removing two more.


nastiest 673 UR 3, nice loopThen as the dust settles, another UR emerges, obviously requiring the presence of 9r1c8. I include the magic top hat nice loop that I thought would be important, but now it only marks the raging path of the collapse.

See a doctor about that nasty UR infection, Frank.




nastiest 684 easy extended UROut of line marking, Nastiest 684 only needs 7r7c8 to prevent an extended unique rectangle and collapse the puzzle.








nastiest 695 sasdcNastiest 695 followed the recipe closely. An X-wing in line marking, and a definitely obvious Single Alternate Sue de Coq.

A regular 485-wing triggers a boxline for two more removals.


nastiest 695 fin fish XY ANLThen an XY ANL and the review’s only finned fish with a fin box removal.










nastiest 695 coloringWhen a large bv field brings out the crayons, two clusters are laid out. Two blue candidates land in the same cell, and get their clan ejected. Green then implies red and 695 is history.

On the battle field, you can see it all from here.





nastiest 706 259 wingThe party ends with Nastiest 706 with two Single Alternate Sue de Coq’s archived. A 259 wing enables . . .








nastiest 706 XY ANL. . . an XY chain ANL (black)to remove 1’s.  A 12-wing (purple)removes 9r3c7, but not before another victim sees a wing of the 12-wing by forcing chain(red) through it. The collapse follows promptly.

From this pre- selected set of puzzles from Frank Longo’s The Nastiest Sudoku Book Ever , its fair to say that the book falls a bit short of the title.

However, that’s what we have come to expect from Frank, a ringmaster of the Sudoku circus. At least all of the reviewed nasties get into advanced technique, and with entertaining results, and basic solving is not difficult. This may be just what you want.

Next post, I return to the bent N-set methods to revisit the remarkable BARN, and tell how it was constructed by the equally remarkable StrmCkr, from timber cut by the Sudoku sage, Andrew Stuart.

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Tough, But Not So Nasty

Continuing with the review of Frank Longo’s The Nastiest Sudoku Book Ever, a sysudokie faces another hard judgement on a Single Alternate Sue de Coq, in Nastiest 662. If the trial is archived, the puzzle withstands major blows before giving up, and delivers much needed WXYZ-wing along the way.

Or so I thought. No sooner had I posted my “gem”, when two of my backup buds, Gordon and StrmCkr, alerted me to a flock of X-wings overlooked in line marking. Sad to say, the WXYZ got squeezed out. Not to be completely outdone, however, I duck taped it to the end of this revised post.

nastiest 662 LM wingHere is the grid at the first 1-wing in the basic solving trace below, right after the naked triple in c4.

You, too, can join my backup/ mortification team by copying the Calibri scripted givens on an early grid. Or just point out the gross error at any stage. You don’t have to pin down how I got there.

nastiest 662 basic trLooking at the whole basic trace, Nastiest 662 starts off generously, then turns a little stingy.

Right after the 1-wing, the 4-wing r68c29 clears out 3r1c2, 4r7c2 and 4r7c9. Follow up marking does a box/line wipe out of 6r1c2.



nastiest 662 sasdcLine marking is followed by the Single Alternate Sue de Coq

SWc2 = 6(2+4)(1+9) +  196.

The trial of SWc2 =196 results in an “obvious” forcing of two 4’s in c8.

This verifies the

Sue de Coq


The removals bring an immediate collapse, beginning:

nastiest 662 collapse trIf we archive the SASdC, however,

we get to see, not the WXYZ wing I got with sloppy line marking, but . . .


nastiest 662 nice loopA very productive nice loop, or two stacked nice loops, if you prefer.


Remarkably, in view of the quick SA Sue de Coq collapse, Nastiest 662 hangs on.


The naked pair r3np19 is going to remove 9r3c6, but I peeked at the 9-panel , and said, “Not so fast!


nastiest 662 9-panelBefore you go, your presence is required in a swordfish.” Of course, if 9r3c6 departs first, the 9-wing that remains will confirm 9r9c6 and the swordfish victim is doomed anyway, but I like to look at a swordfish when I get the chance.

Well, that did it. After a nice loop coloring,

nastiest 662 last tr




nastiest 662 coloringthe cluster extends out to where the blue army contradicts itself in c2, and the green army takes over. You can see it from here.


Nastiest 662 is done, but don’t you want to see that misbegotten WXYZ-wing I wanted so badly?




nastiest 662 1294 wingHere it is, a 1294 wing with an irregular victim. It is not a BARN or BNS, because it reaches outside of any bent region. The significance of that was explained in Please Give WXYZ Some Space last August, and will be explored in an upcoming post on the BARN.

The victim sees the hinge, and one of the wings, by forcing chains. Too bad it didn’t really happen.

Next time, we finish the review of The Nastiest Sudoku Book Ever, with snapshots from the final four preselected puzzles.

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The Nastiest Ever Party II

This post displays some sysudokie snapshots from Nastiest 618, 640 and 651, The bv scan rules, with line marked fish, unique rectangles, Sue de Coq, XYZ-wings, and XY-chains.  A  Sysudoku technique formerly rated extreme gets to stop for a drink.

nastiest 618 LM 9 wingIn Nastiest 618, a 9-wing popped out in line marking. The removal and scattered 9’s prompted me to look at the 9-panel ahead of the bv scan.






nastiest 618 9 panelI found no other live fish, but did notice the right angle slinks that promise LPO pattern slinks and orphans. This kind of observation on the X-panels I am now accepting early in the Order of Battle. In this case, East to West freeforms show that patterns are limited to one blue and two green. On the main grid, the healthy cluster extends into the bv field to a trap, but since I had bypassed the bv scan, . . .



nastiest 618 sdcI came back to find a classic ALS aided Sue de Coq

NWc2=8(1+2)(6+9) ,

sharing one removal with the coloring trap and making an additional removal.






nastiest 618 452 wingThere is also a 425-wing to extend the cluster, but more additionally, . . .



nastiest 618 nice loop. . . a nice loop to start the collapse.




nastiest 640 sdcLongo’s Nastiests continued to make the Sysudoku bv scan look good, as Nastiest 640 falls prey to the classic Sue de Coq Sc4 = 9(3+4)(5+8) ,







nastiest 640 i891 wingthen a grouped i891-wing,







nastiest 640 XY ANL, NLand finally, three XY-chain ANL and a nice loop along the XY rails.









nastiest 651 169-wing, extended URThe party continues, as Nastiest 651 gifts the bv scan with a regular 169-wing and an extended unique rectangle with an easy removal.







nastiest 651 coloringWhat’s left is almost a BUG, but that makes for quick wrap of blue on a single cluster, without traps. The solution is green.

Next post will review the toughest of the Nastiest Ever review puzzles,

651 + 11 = 662.









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Longo’s Nastiest Ever Collection

This post begins the review of Frank Longo’s The Nastiest Sudoku Book Ever with a  review table and  solving highlights of two review puzzles, Nastiest 607 and 629. The original post was revised to correct errors found by my backup team, Gordon Fick and Strmckr.

Recalling the fun I had reviewing Frank Longo’s Absolute Nasty IV, and having gotten over my disappointment Frank’s supplying puzzles for Peter Gordon’s Guide, I thought that his compilation of the Absolute Nasties would be a good test of my progress over four years of the blog. Since Frank, in his introduction, says “the 706 puzzles generally increase in difficulty, from ‘very hard’ to ‘insane,’ as the book progresses, I tried to capture the flavor of the last 100, being careful to avoid duplication with the IV review. I went from 607 to 706 in steps of 11.

nastiest review table

In the next few posts, we’ll look at the advanced techniques that seem to be required, with some attention to areas that could have been overlooked in earlier reviews. Frank is generous with givens. The basic solving data includes the bypass, which is generally successful. The table shows the number of committed cells in clues and locked sets.

nastiest 607 LMThe first puzzle I looked at, Nastiest 607, had a lot to say. I was closing out line marking when I came across two locked sets.

The 4r4c4 removal triggers a 4-wing r24c59.






nastiest 607 ht148 I missed a hidden triple after the 4-wing but my backup reader, Gordon Fick, sent me word about it.

nastiest 607 UR18The prodigious removals create a naked pair r8np18, and a unique rectangle demanding 4r4c5 and an immediate collapse, beginning


(NE4, E4, N4, NE4, C1, E5, N8)



I skipped Nastiest 618 to get to what I thought was another WXYZ-wing outside of the bent family, but two friends I’ve mentioned before, Strmckr and yes, Gordon Fick, pointed out a small detail I had overlooked, the primrose path of Nastiest 629, lined with X-wings, to a collapse in line marking. So I’ve revised the post to tell the story of the basic solving of 629 and where I failed to follow the Sysudoku line marking process that would have solved it easily.

nastiest 629 8 wing 1The first removal occurs on the first fill line of line marking. The 8-wing is noticed as I move the 8 mark from the middle line to the bottom left corner to indicate the line slink in r1. In that process, I’m supposed to scan for any matching slinks on other rows. I mark the removal and copy the slide, but leave the “fishes” in place to guard against accidentally adding an 8 as I fill other rows.

nastiest 629 basic trIf you’ve not looked into how sysudokies populate the grid with candidates, you can start with the givens on this grid, and follow the 2-D trace. The first part is the bypass of pencil marking, very generous in this case.


The second part is box marking, with no 6: list, since all 6’s have been placed.

By taking the givens from the grid above, or your copy of The Nastiest Ever Sudoku Book, and with reference to the traces page, you can follow the story exactly. As you do that, compare the actual effort and engagement involved in the way you normally do it by hand.

Line marking (3f:)starts with a fresh slide, after bv cells have been bordered. The smallest number of free cells is three, the minimum, and the follow up of the 8-wing runs down the page, and across the list.

nastiest 629 wing 2A second 2-wing is encountered in marking the last row, r3. I saw the naked pair in c7, and should have scanned the other columns, looking among the bottom right corners of cells for a matching slink. Then , in removing the victim, I would have seen the third wing, and been off into the collapse.

Failing that, I should have spotted that second wing in line marking closure. With the rows filled, you check each column with no fill string for a column slink created by the row fills. That’s when many bottom right corners are filled. When I got to c7, and placed a 2 mark in the corner by the 7, all I had to do is scan the columns for a match. But I didn’t.

The point is that the Sysudoku basic marking procedure, much more efficient and secure that the scanning for candidates that most solvers do, was not at fault in this case. If you solve by brain, you should try it.

The next post continues this Nastiest review, with Nastiest 618, the skipped one.

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Hodoku ALS Death Blossoms

This post finishes the review of Bernhard Hobinger’s Hodoku, with his Death Blossom page, featuring two insightful examples. The Sysudoku diagrams are followed by a summary of the site evaluations and Sysudoku lessons learned from this extensive site.

I began this review saying it would be an occasion to look back on the advanced methods illustrated in over four years of the Sysudoku blog. That has certainly been the case, with the Death Blossom a very suitable last look.

To quote from The ALS Petaled Death Blossom of July 2012:

death blossom“In this schematic of a death blossom, each candidate of a cell, the stem, sees all matching candidates in an ALS (including bv). The matching ALS, the petals, have at least one number in common among them. The ALS candidates of the common number form a toxic set.”

In the XYZ map scan, I suggest Death Blossom Lite(11/22/11), a version of the Death Blossom with bv petals, and came up with an three candidate stem in which the victim required a forcing chain to see all members of the toxic set.

Hodoku’s two examples of ALS Death Blossoms also illustrate that a stem of two or three candidates is about all you can expect. They also show that, compared to bv, ALS petals can generate more toxic set opportunities. In fact, a bv or triple with common linked ALS may be the most likely DB scenario. DB is another reason to scan for ALS. The stem cell can focus attention on two or three ALS among so many.

Hodoku DB 1Here I only show the one victim noted by Hodoku, but my sysudokie readers may have noticed the removal of all of the 7 candidates seen by the 7 common in c4 and the North box. An ALS common is toxic because one of the connected ALS must ultimately get the true candidate.

But this is just part of it.


Hodoku DB nice loopThe Hodoku Death Blossom 1 is also an AIC nice loop! This example shows how the ALS grouping and slink can form a nice loop, with more concentrated and powerful toxic sets.

The additional removals are especially welcome here, because the batting cage puzzle qualifies as a monster, if it has a solution.




Hodoku’s second example is also surprising, and in a very instructive way:

Hodoku DB 2

The three ALS are severely overlapped! It sure makes it easier for the victim to see the 5’s in all three, but is this legal? By the Death Blossom removal rational, yes. It’s all between the stem and petals. The victim sees all the fives, and if it is true, takes them all. Then each ALS takes its unique common candidate from the stem, leaving nothing . It doesn’t matter if commons overlap, as long as the petals covered by the victim include all candidates of the stem. Permitted overlap is another reason to consider Death Blossoms seriously in human solving.

Now to conclude the review with parting thoughts.

Regarding the Hodoku contribution to Sudoku solving, I believe it is primarily in the many excellent examples, to the extent readers can interpret them. Hobiger’s range of advanced puzzles is a superior achievement in itself. Perhaps I should have gotten into the batting cage for more Hodoku examples, but I fear your patience may not stretch any further.

However, while some techniques are adequately explained, Hodoku is not the place to discover why techniques work, or how or when, to spot them.

Anyone valuing their time must reject the Hodoku claim that productive chains are the product of arbitrary premises. For computers they are the result of millions of blind operations, premises included, with each chain starting with a premise related to the one among many searches that the software is currently on. For humans, chains must be the result of patient and knowledgeable chain construction, recognizing the construction goals and the chain results. Hodoku joins many other Sudoku writers in making the damaging error – or the intentional misrepresentation – of advising humans to mimic computer codes.

I began the review believing Berhard Hobiger had somehow devised Hodoku algorithms to create puzzles exhibiting advanced techniques on demand, by name, immediately after basic solving. Now I find that too hard to accept. Much more likely is that large numbers of puzzles were custom generated and filtered to derive a set for each demand category, ready for display when demanded. I’m not taking the time to confirm this suspicion. I could spend a lot more time to do that, and to solve delicious puzzles from the collections I have only sampled in review. But for now, that weekly deadline holds me to the next possible blog topic.

I feel that the effort that went into interpreting Bernhard Hobiger’s Hodoku site was well rewarded. It led to a satisfying review of my four-year blog, and pushed me in some new directions. I plan to continue for at least one more year. Then it may be time to limit my attention to refining the blog and making its contents more accessible. Unless, of course, something entirely new in human solving turns up!

Next, I return to Frank Longo with his compilation of Absolutely Nasty and Gordon Guide puzzles, which he deems The Nastiest Sudoku Book Ever. I’m sampling only from the last 100 of his 706 puzzles that “generally increase in difficulty,” hoping to recapture the spirit of his Absolutely Nasty IV reviewed earlier.

My 2016 plans include a revisit of the Bent N-Set family of methods. In the meantime I’m revisiting reviews of the toughest collections to update them according to the new position of this family in the revised Sysudoku Order of Battle(bar above).


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Hodoku ALS Chains

This post explains the Hodoku ALS wing and chain as special ALS node AIC ANL with toxic set groups defined by ALS nodes. This is how they should be constructed, so as to leave the mind’s door open for more general AIC almost nice loops with ALS grouped toxic sets.

Hodoku starts with an AIC of three ALS nodes, which he therefore insists on calling a wing. If you label a three node XY chain an XY-wing, then it’s consistent to do that. I’ll quote Hobinger’s description of the ALS wing, but how about if I throw in a diagram to go with it?

Hodoku ALS wing schematic“An ALS-XY-Wing needs three ALS A, B, and C (it is an ALS Chain of length three: z- A -x- C -y- B -z). ALS A shares RCC X with ALS C, ALS B shares RCC Y with ALS C (X and Y must not be the same digit). Both ALS A and B have a common digit Z. Z can be eliminated from all cells, that see all instances of Z in A and B.”

RCC here means restricted common, and the victim indeed must have a grouped link with both ALS groups. One of these groups contains the true candidate. The internal slinks between ALS groups are included in the diagram, making it clear that what we are talking about is simply an AIC with grouped terminals and a grouped almost nice loop. Been there, and done that, but not exactly in this way. Right? ALS C can’t be replaced by a single candidate, but it could be any AIC chain with a terminating commons into A and B.

The distinguishing feature is that the terminal links are groups created within ALS. These being AIC, It’s not required that all nodes of the chain be ALS, as you might gather from the Hodoku descriptions.

Hodoku ALS wing 1Hodoku has two “wing” examples. If you do basic solving on the first, tell me how to get to the first wing grid. I almost made it by making 4r3c6 a given, then finding a naked triple in c4 and a naked quad in c3. This still leaves the shadowed candidates. One of them, 1r6c1 compromises the example.

Does the removal of these candidates leave a solution? I checked it out and it does, but this habit of deleting candidates without explanation is an annoying feature of the Hodoku batting cage.

I outlined only the terminal groups within the ALS. The RC’s function as winks in the AIC. The ALS provide the internal slinks between groups. The toxic set is made up of the like numbered groups defined by the ALS nodes.

Contrary to Hodoku batting cage expectations, it is not practical to look for such ALS chains, as entities. Without the context of the chain already in place, the 3 groups seem unrelated. Much more likely to find are the extensions from the red ALS terminals into the bordering ALS, where the 3-groups complete a grouped ANL.

Hodoku ALS wing 2The second example is also compromised with unexplained removals. One of them, 4r2c4, is necessary for the example.

Here again, the removal would only be found by stringing ALS nodes in an AIC and noticing a pair of like numbered ALS groups for the ANL. The best solving practice is to make the chain constructions at the right time, being open to the possibility of such grouped ANL occurring.

Hodoku ALS chain 1Moving to ALS chains, Hodoku’s first includes a bv, remaining technically a chain of ALS. The grouped wink notation applies as well as the restricted common notation.

Hodoku notes that this is really two ALS chains, one generating toxic 6’s, the other toxic 9’s. It actually demonstrates a AIC with ALS grouped pincers.


Hodoku ALS chain 2The last ALS chain example includes an XY chain, illustrating well that it only the terminal groups that distinguish ALS chains from AIC with ALS nodes. This time, the missing candidates have no effect on the example. W5 was added to the givens to get that close.

Hodoku mentions that the blue ALS and bv r2c7 are doubly linked, and a set of forum formulated rules governing a limit imposed on “adjacent” like-numbered commons in and out of an ALS in an ALS chain. I’ll have to look into that later, but the underlying AIC is certainly valid here.

Next time I’m in the AIC hunt, I’ll try to link up some ALS, and use those ALS boxing gloves at the terminals.

Happy New Year! We’ll conclude the Hodoku review with the next post, featuring the Hodoku Death Blossom examples, and general conclusions on this extensive and “ancient” site.

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Hodoku ALS-XZ

For your after Christmas Sudoku fix, this post is about Hodoku’s ALS-XZ, a label favored by most writers. I prefer the term ALS toxic sets, associating the method with others by the goal of identifying a set of candidates guaranteed to include the true one. Unfortunately, the first Hodoku ALS-XZ example is compromised in a way that many Hodoku batting cage pitches are. With the given clues, there are candidates missing from the example, a crucial one in the example.

Hodoku ALS-XZ 1It works only if 7r1c7 is removed, as in the Hodoku diagram. But how and when did it go.


Hodoku ALS-XZ 2We’re on firmer ground with the second example. All candidates are present, and the ALS partners in the toxic set come from two boxes. The question that arises often with ALS toxic sets is, “How on earth did you find it?”

One answer is, just relax and be on the lookout for ALS with single cell candidates and restricted commons. I can say it, but I seldom do it.

As to enumerating all ALS toxic sets, as an almost last resort, I’m pleased to have greatly improved my technique for this  very recently. Instead of attempting to enumerate ALS first and then finding pairs to generate toxic sets, I now advise that you enumerate promising primary ALS and search for a toxic set partner for each one. This mercifully ignores the way too numerous ALS pair combinations.

The process is illustrated in the revised post, Enumerating the ALS-XZ , of 7/24/12.

In the primary ALS you want single or boxed group number for the restricted common. You favor many cells and numbers for more possible toxic sets. That may mean using the suset enumerator to flush them out.

For partners look at nearby units. For primary lines, overlapping boxes or lines, or parallel lines crossing an overlapping box. For primary boxes, overlapping lines or aligned boxes, as in the example. ALS pairs cannot cover a unit. That would lock each number. Once a partner is found, check for forcing chain victims.

Adjacent lines are more prevalent than the example’s aligned boxes, so I start with primary lines, working down.

As an example of systematic ALS-XZ search, let’s walk through the one leading to Hodoku’s second example above, using susets. In r1, the suset list contains 5/12, 9/28, 59/128, 79/258 and four combinations of three cells, over 1258.

5/12 is locked with r2c5 in a naked pair

9/28 no ALS partners not filling the shared unit

59/128 no ALS partner

79/258 no ALS. NE167/23578 doesn’t qualify.

157/1258 (red)has two of each number, each in separate boxes

Hodoku XZ 2





Hodoku XZ 3159/1258 has one 5, and an RC with the bv r3c1, but it’s toxic set has no victims.



Hodoku XZ 4c1:39/578 is even harder to see.

179/1258 obviously has no victims

That gives some idea of the hordes of possibilities. It is clearly impractical to look that closely at all of them. With some practice, it may be possible to cover most of them with a reasonable scan.

For me, the technique has to stay at the back of the line, where an enumeration this extensive is justified.

Hodoku XZ 5Here I’ll just suggest a few of the more promising possibilities on the way to the example pair. Candidates isolated for restricted common terminals are circled.

Next post examines Hobinger’s examples of AIC chains exclusively constructed of ALS nodes. You wouldn’t want to look for them particularly, but only to be alert for them as you construct AIC .

Happy New Year!

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