Smooth Navigation in Rocky Terrain

This post reports a sysudokie attack on Alary’s More Extreme 84 with several highlight eliminations. A naked triple and a combination X-panel punch on the tightly linked numbers lead to a polarity ANL, color bridging and a surprising color wrap. Sounds good?

more 84 basic gridMore Extreme 84 is grudging, if not downright stingy, in basic solving.

An interesting event is the naked triple 459 in the West box . It forced 9 marks before the box was marked to produce them. The c2 removal came from the more 84 basic trresulting NWc2 boxline.

The basic trace:






more 84 finned sword anl

Once in a while an elimination can be credited to either of two advanced methods.

A finned swordfish and a 2-chain ANL share victims on the 2-panel. The swordfish eliminates the victim because it is in the fin box. There is even an alternate chain on the ANL.


More 84 freeformsNext, the 4-panel slinks call for 4 coloring. Winks in r3 and c9 limit the cluster. One of the colors is surely true, and freeforms drawn from the left through the cluster candidates identify only one blue and one green pattern, and orphan 4r3c9, extending the cluster over all 4-candidates.

A remarkably simple and effective application of pattern analysis to coloring.

There are two ways to explain what happens next, when the AIC hinges are marked.

More 84 two shct ANLThe hinges allow a blue and a green 4 to get on the 2 network. The slink between any blue and green candidates in the cluster completes the all black ANL removing cr3c6, and the red dashed ANL removing 2 r6c6. That’s my shortcut ANL.

Another interpretation is that each of the two candidates use forcing chains to see both a blue and a green candidate, one of which must be true. Since the Bob Hanson review, I’ve been calling that a polarity ANL.

more 84 bridgeElegant as that is, it does not solve More Extreme 84. Fortunately I have the slinks to add a red/orange cluster, and it produces some classic bridging.

Cells r1c9 and r3c5 assert

not(green and red), implying blue or orange,

Cell r9c2 then traps 1, 5 and 7 but also asserts

not (blue and orange), implying green or red.

So its (blue and red) or (green and orange).

My trial trace finds that (blue and red) wipes out all 9s from box C. That leaves (green and orange) to wipe out this gem.It looks like More Extreme 84 was custom composed for Sysudoku. I’d sure like to know how much of this analysis Antoine anticipated when he came up with it.

More Extreme 144Just one more review puzzle, More Extreme 144 shown here, and then we’ll do our version of Antoine’s challenge special, #200.

I hope you have your copy and are about ready to compare some sysudokie notes with me.

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Alary at His Stingiest

This post details the solving of the Antoine Alary review puzzle More Extreme 104, featuring a laborious line marking leading to a sea of candidates. Then the day is saved by Antoine’s escape hatch, maintaining a reasonably advanced level of the collection.

The bypass has some success, but Whew! The 2-D trace of line marking doesn’t remotely do justice to the effort involved.

more 104 basic trSo if you passed up the homework assignment, here is what you avoided:

more 104 BML gridBut even here, the efficiencies of Sysudoku line marking make it much less work than traditional number scanning. If you aren’t convinced, here are some line marking pointers: Go back through it, and this time, form the next long line string from the previous one, by deleting the new clue numbers, and typing back in the old ones. On really long strings (6f, 7f!, 8f!!), after copying the line string, delete the numbers seen from the cell before inserting the copy into the cell.

Oh, you’re doing this by hand? You’re not using my ©PowerPoint template? No wonder you’re thinking of tossing Alary’s book into the round file. Don’t do it, Pilgrim! Look at the Tools page. Send the email. Get the template file, it’s free. You can thank me later.

more 104 ANLYes, its horrible. But there’s the upside. It’s easy to dismiss the possibilities of Sue de Coq, APE, or UR rectangles. From line marking I remember marking more slinks for 6 than any other number, so I try fill in the 6-panel first, and notice an almost nice loop.




more 104 nt gridMarking from the NE6 clue, a slow collapse includes two naked triples.

The collapse continues without hesitation, undeterred by the large number of candidates in many cells.





more 104 collapse trMy impression is, that if this doesn’t happen in an Alary stingy, you have probably missed the advanced technique eliminations that Antoine built the puzzle around.





more 84OK, are you willing to stand up to another Alary stingy pants? This one, More Extreme 84, gets into some really extreme stuff, but basic solving is merely challenging. With the free template and your sysudokie technique, it’s a snap.

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A Little More Extreme

Here is a follow up on the advanced level More Extreme 4, with background looks at the bv map, XYZ map, and X-panel . There is a challenge to find a forcing chain XYZ alongside a regular one.

Entering the bv scan with the More Extreme 4 line marked grid of the last post, we were short of candidates or bv on every Sue de Coq or APE chute, but the XYZ map made up for it.

more 4 bvHere it is shown with several rejected hinges, and two live ones. There is a regular 347-wing and an irregular one constructed with a forcing chain. Both have victims. If you did not find them, jump back to the line marked grid, and take a shot, with the hinges and wings shown here. I’m placing the grid marking of these wings after the other eliminations, but don’t peek.

more 4 fishGoing to the 3-panel after the wings, we catch either a swordfish or a complementary jelly fish, depending on where your net landed. They have the same four victims.






more 4 XY railNow if you haven’t done it already, you can verify that the fish victims enable us to draw this XY rail, the first one available. On the grid, the slink ending 7-candidates are a toxic set, removing 7r5c3.

But neither that removal, nor the new bv it creates, seems to matter.


more 4 3slinksInstead, the more decisive result from the fish attack is the network of strong links among the remaining 3-candidates. The 3-chain analysis yields nothing more. Unfortunately, the octagonal loop is closed with two adjacent winks.

However the long slink chain is a strong asset in Medusa  coloring.



more 4 AICThe blue/green cluster produces nothing immediately, but when the AIC hinges are added,an AIC chain is found for a strong link between blue 3r5c8 and 3r4c5, extending the cluster by making 3r4c5 green.

Did that one get by you? It’s just putting together what we already know. The chain says that if 3r5c8 is false, then 3r6c7, 9r6c1, 5r4c1 and 3r4c5 are all true. That’s the definition of a strong link! And slinks are the building blocks of Medusa clusters.

Please note, T&E worry warts, there is no assertion here that 3r5c8 is false. Nor is there any test of its falseness. There’s only a demonstration that a remote slink exists. Fortunately, that slink extends the cluster into a wrap. Two green 3s wind up in c5 and in the C box. For that reason, the green army is false, and the blue army, including 3r5c8, is true. More Extreme 4 collapses in a heap.

more 4 XYZsOK, you didn’t peek and you found at least one of the XYZ-wings. Right?

The regular orange 347-wing hinged at r4c5 eliminates 7r4c6.

In the burnt orange 347-wing hinged at r1c1 is something else. The 37 wing is sees the hinge 3 by forcing chain. One victim sees the toxic set by unit winks, but 7r5c1 needs a grouped forcing chain to bow out.

Show this to your Sudoku friends. So far the forcing chain XYZ-wing is a Sysudoku exclusive despite numerous posts demonstrating it.

More 104That was fun, but I want you also to experience the misery of line marking one of Alary’s stingies. Not that number scanning is any easier. For this mission, should you accept it, the assignment is More Extreme 104. Your 17 clues have just arrived. In the sea of candidates, there is a lifeboat. If you lose it in the fog, I’ll send the Coast Guard next post.

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More Extreme?

Here we begin a review of the second collection of Antoine Alary’s Extreme series, with general comments, a review table, and a checkpoint on the Sysudoku solving on More Extreme 64, a puzzle that is typical of the “generous” variety of Alary puzzles.

Antoine Alary has published two puzzle books under his own name, claiming each to contain “200 of the toughest Sudoku puzzles known to man.” My review differs with this brash claim, but more importantly, it discloses Antoine’s rather unique approach to composing. It’s ambitious and unique, in keeping with the daring Antoine of the back cover, a mathematical logician electronic designer immersed in razor edge sports such as “snowboarding, wakeboarding and mushroom hunting”. You scare me, man.

As usual for the review, I preselected 10 of the 200 puzzles, tracing my solving process with 2-D traces and significant grids. My selection was every 20th puzzle, starting with More Extreme 4. I hope you were successfully introduced to the collection via More Extreme 64, which is represented in the review table. For conventions of the table, see the Reviews page.

More Extreme Table

The table makes clear that Antoine’s claim of “toughest known to man” is a bit overblown, but his puzzles are consistently advanced level. Two invoked a touch ofpattern analysis on my part, but no trials of any kind were required. Among my reviewed collections, KrazyDad’s Insane collection appears to be significantly tougher. And then there’s the established monsters, including two mounted in the Sysudoku trophy room.

This review table is the first featuring the bypass (DB) phase of box marking. I had solved the puzzles before adopting the bypass, and could therefore compare the numbers of box marking clues I found with and without it. In the table, box marking results without the bypass are written below with it. For sure I did better with it, making line marking easier. But in all cases, the final basic solving candidate field after line marking was the same. Only the line marking results with the bypass are included.

Sysudokie readers might be wondering why the number of given clues is omitted from the review table. It’s because it is always the same number, 17. Antoine’s mathematical logic professor may have required him to study the proof that 17 is the minimum number, and in scholarly daring, he has taken this on as a trademark of his puzzles. I can report that, as a composer, Alary consistently provides a route to the solution, which is no small accomplishment with this uniquely limited number of givens.

My bottom line is that my sysudokie readers can well invest in these books. I now have them both, on the strength of the second one, the subject of this review, entitled More Extreme Sudoku, © 2011. The first, Extreme Sudoku, apparently came out in 2010. I don’t understand how I missed it, so I’ll just blame it on Tom Sheldon, Andrew Stuart, Paul Stevens, Will Shortz, SudokuOne, KrazyDad, Max Pitkow, Bob Hanson and Wayne Gould.

In fact, when you get your copy, solve More Extreme 200, the puzzle Antoine singles out as the collection’s toughest. I didn’t want to include the standout toughest in the review, but I will post a checkpoint for you immediately after it. Be prepared for the worst, or best, depending on you.

More 64 DB trThe More 64 bypass trace is typical, with long chains of clues on two numbers. I’m quite pleased that the bypass experience. Miss the path and you are often overwhelmed with candidates.

Speaking of being overwhelmed with candidates, I was annoyed that Antoine includes all number scanned candidates in a keypad format on half of his puzzles. You have to wonder if any Sudoku publication outside of this blog will ever acknowledge the redundancy of keypad marking, and adopt something more useful.

Antoine is excused, though, because his Extreme Sudoku pre-dates the early Sysudoku posts on slink marking, but I do hope that his later editions and collections drop this “helpful” feature. It may be that a good part of the difficulty attributed to his puzzles is just having to get the basic solving done with a minimum of givens, and an inferior starting method. To my way of thinking, providing the candidates, or doing it by computer, is not the answer.

The DB and Box columns of the table divide the collection on basic solving. Puzzles 64 and 184 are especially generous in box marking, while 104, 144, and 164 are downright stingy. Not many clues are added in line marking. We’ll see how this plays out in several puzzles checkpointed in detail, first with the very generous More Extreme 64. The bypass hit two numbers 3 and 9 hard, and the run continued on 9 in slink marking.

More 64 BM tr

More 64 578 wingLine marking is easy, and the resulting grid is liberally populated with slinks and bv, strongly suggesting Medusa coloring . But if you go to your bv map, you are rewarded with a regular 578-wing. The more advanced part is that the victim sees one of the three toxic candidates by forcing chain.




More 64 coloringOr if you happen to miss the XYZ-wing forcing chain, when you get to coloring, you get an easy wrap with two green 8-candidates in c6. In either case, the collapse is immediate.

Let’s do another one.

In the review table, More Extreme 4 rivals a Frank Longo Absolute Nasty IV, or a CrazyDad SuperTough.



More 4 LMIt starts easily and is also basically generous, but it calls for some advanced artillery.  You can lift out the original clues, do box marking and line marking if you like. From here, see if your advanced solving confirms that review table line. I’ll checkpoint you next post.

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Guide 775 Concluded

Here we continue with Gordon Guide 775, going through Sysudoku advanced methods, but trying particularly to invoke those brought up in the Guide.

guide 775 ER-192Last week, we found a regular XYZ-wing, a 231-wing to be exact, generating 11 new clues and as many marks. Updating our XYZ and bv maps, there is a sysudokie ER 192-wing that cuts another wide swath. It’s outside of the Guide repertoire, because the victim needs “Empty Rectangle” vision to see both toxic 2’s. ER is shown here as a forcing chain.

There is one UR (Gordonian rectangle) opportunity, with corner cells on this grid. It requires both 5r2c7 and 9r3c7 to be removed. I tried several candidates before realizing that 5 and 9 cannot both be removed from NEc7, because cell r9c7 would then have to supply both.

guide 775 XY ANLAn XY-chain relates to Gordon’s bivalue graph, except here it results in almost nice loops, , not a nice one. The black chain makes the same elimination as the ER 231-wing, and the red branch adds more. The railroad bv map made these jump out at us.





guide 775 near Bug  trGuide 775 has a very interesting ending from here. The follow up trace .  .  .


guide 775 twisted BUGleaves a near BUG, with all bv except for 129r3c4. Coloring, a trap of 2r3c4 leaves an impossibly twisted BUG, and no solution, because the cluster proves both green and blue false.

That suicidal war means that 2r3c4 cannot be removed, and its installation as a clue, brings a solution, mixing blue and green candidates.

This is the situation Andrew Stuart had in mind with his BUG rule in The Logic of Sudoku, to promote the candidate appearing three times in a row.

The final trace is below

guide 775 final trIf you are among the readers enjoy my struggles with the hardest puzzles, you have to be disappointed with my selection of Longo puzzles for this review. Why not select from the last 100? I would turn around and do that, except that Frank has given me a better plan. His later puzzle book, The Nastiest Sudoku Book Ever, is replete with the inferno cover and the charming warning that “only the most skilled Sudoku Experts should try these mind-blowing puzzles”. I had to buy it, only to discover it is a mix of his Mensa Guide and Absolutely Nasty Sudoku IV puzzles. What would you do?

Here’s my plan: After the great stuff  already announced, I promise to review Nastiest. That’s relying on Frank to have picked the most wicked from his two hardest sets. I’ll exclude any Nastiest that I’ve already reviewed from the Guide and Absolutely Nasty IV collections. Maybe the Nastiest collection will get up to the KrazyDad Insane level. Another candidate collection is the consecutive string of Weekly Extremes coming up shortly.

more 64Next we review the More Extreme Sudoku collection of Antoine Alary. This collection book follows his Extreme Sudoku. I’m doing the second book, which Antoine says is identical in scope. More Extreme Sudoku does reach an extreme level occasionally, but the most interesting feature for me is how the puzzles react to the newly introduced two-stage version of box marking. The puzzles can be generous , or very stingy, in basic solving. You can get a feel for the generous side from More Extreme 64, but you may need touch of advanced technique to finish it off. Be sure and start with the bypass.

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Gordon Guide Puzzle Review

This post reviews the collection of 700 Frank Longo puzzles following the text in the Gordon Guide to Solving Sudoku. A review table summarizes the Sysudoku rating of 10 preselected puzzles, and one advanced puzzle is analyzed in detail.

The review table my preselected review puzzles suggests that the level of difficulty ramps up from #100 to #800. If you have this book, you may want to select a number range to suit your level of difficulty. In the table, the leftmost data column gives the number of clues/naked pairs produced by the bypass. Each naked pair is counted as two marks, to be consistent with marking counts in other columns. Four dashes mark the collapse.

gordon review table

Three were solved in the bypass, three more in box marking, two in line marking, and two by advanced methods. Of the advanced methods presented in the Guide, the reviewed puzzles offered three X-wings, but no other fish, and single XYZ-wing. I looked for Gordonian rectangles or polygons, and bilocation cycles, but none turned up in my preselected set.

If you go through the seven hundreds diligently, I’m sure you will find a more Gordonian events, but these results may be due to the Guide favoring rarely useful methods at the expense of frequently useful ones.

guide 775 bypass trMy track through #775 aligns with this opinion. My bypass trace is:

As expected, the bypass clues leave a very easy line marking

guide 775 BM tr



guide 775 LM 9-wingThis brings a moderately tough grid for line marking, which uncovers a 9-wing:

The wing markers are left in place to keep 9-candidates out of c4 and c7 as the remaining lines are marked.

Guide readers, line marking X-wings is routine for sysudokies.  You could pick up a lot of how-to information from the early Sysudoku posts.

guide 775 LM remainingThe remaining line marking goes


guide 775 finned 1-wingThe resulting candidate field is shown here, along with a finned 1-wing. The Guide doesn’t include finned fish, but its result in this puzzle is superseded anyway, so we’ll pretend it didn’t happen.

More news for guide readers: after line marking, sysudokies search for Sue de Coq and APE. The ample supplies of bv in Guide puzzles generate many of them.

guide 775 XYZ mapThe Gordon Guide does include XYZ-wings, but Guide readers should see what sysudokies use to find every XYZ, regular or constructed with forcing chains, and those with forcing chain victims. The crossed out hinges had the wings available, but not the connections and victims. That left one good one, a regular 231-wing.

Think maybe you should look this up? Click Find It! on the menu line.

guide 775 231-wingThe 231-wing removes one of two 1-candidates in c6, doing some damage. The trace of that damage is below. Update your grid first, then check it against the trace.

I’ll continue from here next time. We’ll search for Gordonian rectangles, polygons and bilocation cycles, and finish Gordon Guide 775. We’ll check out the X-panels, find some XY-chain ANL, do a little coloring , and step on a BUG.


guide 775 231  trAre you Gordonary solvers coming along? Please come on in, the waters fine!

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Cycling Blindfolded with the Guide

This post calls out Gordon Guide misguidance related to coloring, slink chains and the XY chain. AIC fundamentals are omitted in favor of ineffectual strategy and renaming of well known AIC formations.

gordon 32 LMFirst, lets checkpoint the basic solving of the Gordon Guide Example 32, through which we meet its “nonrepetitive bilocations”.

My bypass produced only N4, and box marking was similarly anemic. That left a demanding line marking. That must have been challenging for the Gordon guided.

A 7-wing was left in place, which eventually generated a naked pair 25 in r9, and NW2.

gordon 32 AICThis sets the stage for Gordon’s illustration of an AIC form he calls the nonrepetitive bilocation cycle. He calls it non repetitive, because two different numbers are members of the loop in all cells. We show the wink in each cell that makes this clearly an alternate inference chain. Its single AIC hinge is marked in the usual sysudokie way. The rest of the cycle is actually an AIC with winks connecting slinks of Gordon’s bilocation graph. Do you like my angry fish?

Gordon explains this elimination by going around the loop, which his way of making solving structures seem like procedures. He neglects to explain that the angry fish as a nice loop, making every adjacent pair of candidates a toxic set. The 57r7c1 pair is removed because the 5 and 7 see the toxic 4 and 9.

Gordon’s implied claim is that he found the angry fish with his bilocation graph. As always, he just points it out, implying that it’s quite obvious. If he showed what is actually involved, readers would have reason to complain about his Guide, rather than becoming discouraged about missing the obvious.

gordon 32 bilocation graphHere is the bilocation graph, which Gordon attributes to the web site of a Professor David Epstein. Take a moment . Do you see what it is? Now trace around it until you come upon the angry fish. Or don’t, if you value your sanity.

Those following this blog know that there is a much better way to represent this nest of slinks. Of course, Medusa coloring.


Unlike Gordon’s grid coloring, Medusa clusters are factual structures, not graphically supported guesses.  Coloring clusters are slink nets, organized into opposing armies, one side true, the other side false. And without the chicken scratches.

gordon 32 coloringIn this case, the candidates enlist in a blue/green cluster and most of those without connections to do that get into the red/orange cluster.

The green forces are proved false when two green 6’s are forced into r5. Then cell r1c5 shows that blue => not orange.

Blue and red candidates leave little else to decide.


The AIC is a fundamental concept of advanced solving, occurring constantly in many forms. The Gordon Guide conveys nothing about this important concept. Instead, in example after example, Gordon walks through the alternating strong and weak links, saying how this one is true, making that one false, making this one true, etc. That’s why those relying on the Guide may understand the turbo fish of the last post, but have no clue regarding X-chains in general, including the simple 9-chain ANL on the same grid. They also have no clue on where to start looking for another turbo fish.

In this blog, AIC were explained first as X-chains, their simplest form, followed by XY-chains, the automatically alternating and most frequently occurring form, with toxic set and nice loop eliminations working the same as X-chains. Then more rarely occurring general forms of AIC with inverted bv, mixed links and ALS nodes could be understood and constructed when needed.

gordon 32 railroadIn the Order of Battle, however, XY-chains come first, being more frequently occurring. They are made easy to find, even to exhaustively enumerate, by the use of a railroad diagram.

Here is a very  extensive railroad diagram from Guide Ex. 32. There are more connections to be made, but this enough to give us plenty of toxic sets to chew on.

gordon 32 ANL partyIn fact, we would have found a solution to Example 32 much easier with an XY-chain, and never had to look for a nonrepetitive bilocation cycle. Every repeat of numbers along the rail marks a toxic set.

A few of the decisive eliminations along these rails make the point.



gordon repetitive ANLGordon’s repetitive bilocation cycle, Example 33, has a single cell with one candidate in both slinks. The almost nice loop confirms that the candidate at the converging slinks is true.

It’s an AIC ANL, reversing the slinks and winks of an XY chain. It doesn’t actually require that the node cells be bv.


Either Peter doesn’t understand or conceals the AIC fundamentals of this example. I suspect the latter, as a means of pretending to publish methods that “experts don’t know”. I’m led to this opinion by the “Gordonian” claims which to this date Gordon seems to have escaped any censure from the Sudoku expert community.

gordon ex 34Gordon’s single example of the XY chain ends the chapter. It is not the frequently appearing ANL so prominent in Example 32 above, but the more rarely encountered nice loop. The XY ANL is a sad omission.

The last instruction chapter in the Gordon Guide is, appropriately enough, an apologetic defense of guessing. In an ridiculous final section, “To Guess Or Not To Guess” , Peter claims that Guide readers “now know everything”, and will be forced to guess only by “ridiculously hard puzzles written by someone who thinks guessing should be allowed”. This is an ironic “defense by offense” twist of logic that would make the most blatantly illusive politician proud. My respect for Frank Longo certainly dipped when I realized he had allowed his work to be promoted in the same paragraph.

mensa 775Speaking of Frank Longo, whom we awarded a superlative review for his Absolutely Nasty IV collection, our next task is to review his collection of 704 puzzles composed for Peter Gordon’s Guide. The 800 puzzles claimed on the cover include the sets of 12 puzzles following up each chapter of the Guide, which are, in effect, reviewed already.

I took every 75th puzzle, starting with 100. Only two of my preselected review puzzles reached the advanced level. To get in the mood, see what you can do with the only one I’m going to analyze in detail, number 775.

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