Weekly Extreme 426 Traces and Trials

We open the Weekly Extreme Competition review with #426. My selection for the review is simply the consecutive weeks, from here to #435. I’ll provide complete tracing to the point of guaranteed collapse.

I want to particularly welcome WEC players. I will do my best to enlist you into the sysudokie ranks, even as you continue making competition deadlines. My regular readers, please be patient when I sound like I’m talking to someone else, throwing in explanations and links to the familiar. When we’re done, and with added experience of the WEC review and WECer comments, we’ll all march on Fata Morgana. Let’s enjoy these Weekly Extremes in their fascinating detail.

wex 426 bypassWex 426 opened with a generous bypass and box marking. Then a routine line marking closes with a hidden pair.  WECers, if you go through #426 again, but follow the traces, you can  pick up the trace conventions without reading the traces page.


wex 426 basic trwex 426 basicOn the candidate grid the chute Wc3 can become a Sue de Coq 8(5+6)(3+4), (outlined in red) once we verify that the (5+6) alternative is not missing. The SdC, when verified, will remove 6r3c3, and 7r7c3.





The verification is dowex 426 sdc v gridne with a trial trace, which reaches a contradiction, if there is one, in the lowest number of inference levels. The basic traces above are regular depth first traces. The trial trace is breath first.

Compact traces are very helpful in analysis, and could greatly improve communication among experts.


wex 426 sdc vtrAre you on to my link conventions? It’s all there in the diagram: weak, strong, confirming links and grouping.  If you look into what’s going on, that is.

Follow up on the SdC removals was anemic, just  NW7 => SW7 => S7m.

WECers note, SdC’s are more plentiful than you might have thought. If you use the sysudokie definition, that is, including only one forced alternative and ALS removals.

wex 426 354-wingThe 7r7c3 removal adds a bv (bi-value cell) to the bv map, and permits a regular 354-wing that would go victimless in the shared unit weak link vision of most Sudoku writers and many solvers, human and computer. But after fitting the 4-candidates with the grouped forcing chain sysudokie vision, two of them see all three members of the wing’s toxic set. Tell ‘em where you got it.


wex 426 clustersContinuing with the Sysudoku Order of Battle, I looked for XY-chains with the bv maps, then went on to the X-panel for X-chains and fish. In this case I was pulled along toward coloring by the luscious field of bv.

I went to blue and green on the isolated 6789 cluster in the East boxes. A more integrated red/orange cluster traps a 6-candidate.

The number 8 is the only value connection between the two clusters. Along row r8, there is bridging opportunity. The wink between blue and red 8’s asserts

not (blue and red) = green or orange.

But a true green 6r8c9 would color a second 5r8c5 orange!  That is to say:  green =>red.

OK, so that also is to say that:   not red = orange => not green = blue.

And more to the point, either (green and red) or (orange and blue) is true. It’s a merge into two opposing armies!

WECers, does your platform do coloring this well? My ©PowerPoint screen templates are available via email. You don’t have to construct them yourself. See the toolware page. No charge. Not kidding.

wex 426 blue orangeI picked orange and blue for a trial, and that forced two 6’s in r6, so its green and red.

I’m particularly anxious for my WEC friends to know what I mean by a trial.  It’s a test of a sizeable set of values, constructed logically to be all true or not all true. It is meant to go all the way to the solution, or to a profitable contradiction, proving an opposing set of candidates to be true. And it is meant to be a sysudokie alternative to the arbitrary election of a cell value for trial-and-error.

Sue de Coq verification, illustrated earlier in this post, is a trial, but in an early stage of solving, with generally less at stake. It puts a smaller, but far from arbitrary, combination of values on trial. I concede my early use of the advanced, “missing alternative testing version of Sue de Coq is a grey area in the T&E debate. Comment to this post and voice your opinion.

wex 426 solutionIf you are one of those whose path to the WEC solution is littered with arbitrary guesses, you are missing challenges that would suit your abilities better.

Here is the 426 solution in merged green and red. I don’t consider the trial of an extended cluster to be particularly extreme.

Maybe you’d like to look over what you did on 427 before my next post at 2 p.m. EDST next Tuesday.

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Finishing More Extreme 200

This post continues, slicing the 9 patterns of More Extreme 200, and conducting trials of the divided sets. A brief, but decisive cluster merge ends the struggle.

Antoine was right. #200 is outstanding. Following a pink/olive analysis on the 9 patterns, I suggested you try another one on the remaining 9 patterns, with 9r2c6 shaded pink. Here is my division, with two pink patterns with one clue, and three olive patterns and one clue. A pink trial throws out five, and the olive trial, three.

more 200 pink olive 2more 200 2nd pink trialIt’s generally best to try the more decisive side, because you want the trial to come to a conclusion, positive or negative. In the pink trial, the remote pair =>9r1c8, E3 => SEnt278 =>r9np36 =>SE8, removing all 8 from c8.





more 200 guardianAs we install the olive pattern set, the remote pairs seen in the pink trials come back to haunt # 200. The removal of 9r1c8 allows 3r6c8 to produce five 5 conjugate pairs in a loop, and therefore odd sided slink loops in 7 and 8, making a solution impossible. This also confirms 3r7c8 as a necessary guardian.



more 200 collapse trThe final collapse unravels a curtain of naked pairs which explain why #200 was so extraordinarily tough.

Let’s close the review with a round of applause for Antoine Alary. Wear your helmet, my man.

Next I’m going tackle the extremely tough, but popular, Weekly Extreme Competition series, at www.sudoku.uk . My review puzzles start with #426 and end with #435. All of the puzzles are available, packaged with their solutions, in an archive table on the competition site. The competition is to complete each puzzle within a week, and key in the solution to the site before the midnight deadline. Winners over the whole year get their names on the honors list.

I hope Weekly Extreme competitors will follow my posts, and comment on them. If you know any, let them know about it. Of course, we will always be seeking humanly efficient, entirely logic based route to the solution, which is not the only way to succeed in the competition. But these compeititors are serious Sudoku solvers, and could easily become sysudokies as well.


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Taking on More Extreme 200

This post and the next checkpoint a sysudokie solution of Antoine Alary’s extra tough More Extreme 200. Sysudokie readers are given an opportunity to get a little extreme, as well.

Happy St. Patrick’s Day. Let’s do the 200. But first, your kraken analysis homework on More Extreme 144:

more 144 6 krakenYes, the other 6 in the fin box is removed, but the four kraken hostages escape.

The basic solving of More Extreme 200:

more 200 basic tr

more 200 basic gridIt’s a semi –monster all right.

more 200 finned 78-wingThe next result is from the X-panel, and is quite unusual. A simultaneous, finned 7-wing and 8-wing, but no krakens.

That’s all I see for X-panels, coloring or AIC, but the 9-candidates are relatively sparse, with slinks in both directions.

Going to pattern analysis, I have two pink and five olive, with many 9-candidates in one set or the other. A trial of the pink set of patterns could take a big step.

more 200 9 pink olive

more 200 pink trial trIn fact, in the trial of pink patterns, the two 9-candidates in both are confirmed, and the seven exclusive to olive patterns are removed.

As luck would have it, the trial fails with three bv 36 cells in r9. The true 9 pattern is among the olive five

more 200 olive gridThe olive trial brings in only one clue, 9r5c5, but removes two. C9 generates a boxline in S. It’s 3 removals in S allows a Sue de Coq.








More 200 SdCThe contents of Sc5 are 3(2+6)(7+8) if 7 and 8 are not both missing and the naked triple236 if they are missing. But the latter generates three bv 36 cells in r9. So the Sue de Coq is verified to contain 3(2+6)(7+8), removing 78r2c5.

Now, how would you like to do the next pink/olive pattern analysis? The remaining 9 patterns can be divided again.


To be sure of agreeing with the checkpoint, make 9r2c6 pink and shade the 9 cells accordingly. Two clues are added in the olive trial, but only one in the pink trial, so we do the olive trial first, hoping for a more decisive result. As usual, you have a week. Lay off the Paddy’s day cache.

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Just One More “More Extreme”

This post concludes the Alary More Extreme review puzzles with More 144, Basic marking features a timely naked quad, and advanced solving is another parade of highlights.

more 144 basic trThe basic trace classifies More Extreme 144 as a tough one. I would hate to be faced with the task of starting it with the number scanned candidates. I wouldn’t even want to do it with the grid encrusted with computer generated number scanned candidates. Are you listening, Antoine?


more 124 nq gridIf you don’t go through it, I’d like you to see at least the naked quad along the way. Note the long fill strings, loads of candidates, and the few sparse,and therefore promising numbers.



more 144 fin swordThe bv scan is a bust, but the X-panel offers some promise. The 6-panel delivers a finned swordfish, with one victim in the fin box. All of the kraken victims go free.

Your challenge for the next post is to identify the kraken victims and to show how each of them escapes. A potential victim that sees the fin by any means is eaten by the fish. Forcing chain vision is necessary.

more 144 9-patternsGoing on through the  X-panels, a 9-swordfish deletes all candidates impeding a coloring cluster of two 9-patterns.

If you don’t see the swordfish, look for its victims now missing from the previous grid.

These patterns extend the coloring into the 6-panel. What happens then is LPO magic.



more 144 6 LPOOne of the two 9 patterns is true. Together, they limit the blue or the green patterns of other numbers. The limits go both ways. The partial 6-patterns allow two blue 6-patterns, and zero 6-green patterns, with freeforms from the left. It’s a pink/olive wrap, in blue and green! Green candidates, and others orphaned by the blue patterns, are eliminated. That’s nine 6-candidates gone!



more 144 blue ntThe surviving grid sports a naked triple forcing 8r6c1, a fatal wound. If you care to follow it, the autopsy report is below.

It’s time to close the review. Again, I do enthusiastically endorse Antoine Alary’s Extreme Sudoku and More Extreme sequel for advanced level sysudokies.



It would be nice if we could can the wild claims and honor  good advanced level Sudoku books for what they are.

more 144 autopsy

OK, a promise is a promise. Next time you can compare notes with me on a sysudokie solution of More Extreme 200. You have yours all ready, don’t you? If not, get the book and get busy!

And don’t forget to do your More Extreme 144 kraken homework. Virginia is in high school now, so I had to do the kraken analysis myself. Fortunately the ©Word X-panel template makes it sooo easy. Just copy the numbers in, delete the ones seen by a true victim and it’s confirmed cohorts, and see if the fin survives.

Yeah, I know.  Virginia says that laptops and Office aren’t cool anymore.




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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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