Only Extreme 390 is Advanced

This post finishes the updates on Manuel Castillo’s Only Extreme Sudoku with a less advanced OnEx 390.  This one is a better example of the Sysudoku XY Railway than was the original post. No trials were required in the ten puzzles pre-selected for the review. A plan for summer Sysudoku is posted.

The original review solution was posted December 27, 2017. At that time, the 3-fill was not a regular feature of Sysudoku Basic.

In case you would like to compare the basic paths to the same line marked grid, here is the updated bypass trace.


On the XY railway plot below, these are overlaid in black and red.

Instead of the original’s accidental spotting of an AIC nice loop, Sudokuwiki adjoins another XY ANL(red) to its first XY ANL (black).




On the XY railway plot below, these are overlaid in black and red.


Sudokuwiki’s third XY ANL can be traced on the railway starting in orange at r7c9 and following black then red to orange at r3c1.







The fourth XY ANL re-uses the XY wing, extending from 8r9c5 in blue and following red to r3c1 to continue in blue.








gAnd finally, the fifth XY ANL triggers an 8-wing. It starts from the same r9c5 cell and moves along red and blue to emerge in green.

Although the XY ANL sequence was favored by the solver, it is entirely  within reach of the Sysudoku approach of creating the railway and spotting ANL along it.

The systematic search can have different results, depending on which XY-chains are seen first.

Next, Sudokuwiki responds to the growing coloring opportunity with  an unusually extensive cluster. In the trap,  2r6c6 is removed by both green and blue, one of which must be true.

From that,

E2m => C2=> N4=> green,

and OnEx 390 is done.


Here is the updated review table for Emanuel Castillo’s Only Extreme collection.

The plan for the Summer 2019 blog is two collection reviews of “Extreme” collections, along with reports on blog improvements too long neglected. The objective is to have the blog ready to support the Guide as a paperback and e-book publication. The pages on The Guide, Sysudoku Basic, and Begin With the Bypass have been re-edited, and Box Marking is next. The Titles page is updated.

The next review is LuckyPandaBooks 504 Sudoku Puzzles, by Markus Buehl. My pre-selection schedule is 48 to 480 in steps of 48. The book is labeled as “Extremely Hard” on the front cover and “Insanely Hard” on the back, but if you are following the Guide, anticipate an entertaining exercise with ordinarily advanced methods, with a possible collapse in basic.

Here is LPB 48.



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Sudokuwiki Solves Only Extreme 347 by AIC

In the original Only Extreme review, OnEx 347 was an example of a coloring trial on a limited cluster generated by pattern analysis. In this update, Andrew Stuart’s solver demonstrates a solving path to a final coloring without trials, via AIC building.

The basic trace is updated to include 3-fills. In line marking, rows dominate with fewer unmarked cells.







On the line marked grid, the tight square of 5’s has the slink corner  for a hidden unique rectangle, Type 1.   If 3r5c7 is true, 5r5c7 is not, and two corners are 5, the other two, 3.  Now 3 and 5 interchange for a second solution.

Nothing is found in the bv scan or the X-panels,


before Sudokuwiki ventures into coloring with this trap. Both green and blue remove 9r2c7.  The resulting NEr1 boxline removes 9r1c5, expanding the cluster.

Entering AIC building, an AIC nice loop combines an XY-chain, a reversed bv, and two X chains, one grouped.




A grouped cluster expansion is accompanied by a long and winding AIC boomerang.








The removal enables a Type 2b uniqueness rectangle. If 9r1c2, the ur candidate opposite the slink is true, the other ur candidate 5r8c2 is true and 5r8c5 is false. The slink makes 5r9c5 true.

The 5/9 placements in the rectangle can be interchanged for a second solution copying this one everywhere else.

In the trap, 2r2c2 is rejected by both blue and green. And in the East, an XY boomer starts from r4c7.

Sudowiki piles on with a third AIC boomer, and after


an XY chain placing S5,








and                              after

the bv field looks ripe for another cluster.



The red orange cluster is extensive, but short lived. In r1, if red is true, both blue and green are false. Then in c7, if we accept orange, we have to take blue as well.

Next is the conclusion of the updated review of Emanuel Castillo’s Only Extreme Sudoku.


In case you want to try the last review puzzle OnEx 390 on your own, work with this  copy, because recovering the givens from the original review would give you too much in advance.

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Only Extreme 304 Scavenger Hunt

This post finishes the updated review of Only Extreme 304, displaying the Sudoku moves listed last week for the scavenger hunt.

The ALS X-chain boomerang starts with the 9-chain emerging from r9c7 and terminating on the 9 candidate of ALS 249, which slinks to the 4 value group. The group sees 4 in the starting cell, via 4-chain.





Independent of that elimination is this grouped AIC ANL,










and this one, the third grouped AIC ANL of the series.










This time the elimination expands the cluster and enables an XY-chain.









A boomer that didn’t work before is activated by the new c8 slink.










Then an AIC ANL turns 7r7c3 green and traps 7r8c3.










The AIC building series finally ends with an ALS boomer placing 8r7c6.









The S8 clue brings a naked pair 29, enabling a swordfish, which removes 2r1c7 for a hidden pair 29.









The hidden pair removals trigger an XY chain that starts a major expansion of the cluster.









Or a merge if a second cluster had already been started. The r8c3 trap turns 8r8c2 green, trapping 8r9c2. The naked pair r9s13 confirms 4r9c5, confirming N4 and S2.







The wrap brings immediate collapse.










Next, the update of the Only Extreme review continues with OnEx 347.


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Only Extreme 304 is AIC Level

This post and the next update Castillo’s Only Extreme Sudoku review with a solution of OnEx 304 without trials. Most of the solution path is in AIC building, the most challenging level of Sysudoku Advanced.

The only move prior to AIC Building is this Type 2 unique rectangle, which enables the limited cluster and intersecting XY chain extended in the original post into a decisive coloring network by six trials.

The placement 6r9c1 brings the NWc1 boxline removing 3r2c2.



Sudokuwiki AIC building starts with a possible boomerang that finds an ALS node to get to an AIC almost nice loop(ANL).








The starting links are recycled into a grouped AIC ANL.










The first boomer has an obscure start, but comes back in an XY-chain.









Moving right to left in the South tier, boomer 2 is double grouped. The key is the first group, making the following slink out of r9c2.






Now that first boomerang throw can be  recycled, including the same ALS, for an AIC ANL.








The breaking point is the nice loop, which introduces Medusa coloring to supplement Sudokuwiki.









The cluster expands and north tier AIC boomer links with it.




The 7r2c8 removal provides the needed slink for a hidden unique rectangle, Type 2.  If 4r1c7 is true, so is 7r6c7 and 4r6c8.  The slink then makes 7r1c8 true, and the rectangle’s 4’s and 7’s interchange for a second solution, no matter what happens elsewhere.

It’s been a lot to wade through, but Only Extreme 304 requires a lot more. For next week, I’m sending you on a scavenger hunt.  You are to collect, in this order, an ALS X-chain boomer(4r9c6), a grouped AIC ANL(4r7c6), another grouped AIC ANL(8r7c2), an XYchain(2r2c8), an X-chain extended XY boomer(2r9c7), an AIC ANL(7r7c6), a coloring trap(7r8c3), and an ALS AIC boomer (1r7c6), a swordfish(2r1c8), a hidden pair, an XY chain(2r2c1), and after a large cluster expansion, a wrap.

Short of the final advanced coloring, you could just load the starting grid into Sudokuwiki and tap your way through it. If you do that, look up unfamiliar terms in the Guide and compare Sysudoku explanations with Sudokuwiki notes and drawings over this post. The drawings and spotting notes will be in the scavenger awards post next week.



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Classic Review Ends,OnEx 261 Escapes Trials

This post traces the bypass finish of Classic 240 and presents the review table for James Forest’s Classic Sudoku. Then it continues the update review of Manuel Castillo’s Only Extreme Sudoku with Only Extreme 261. Demonstrating a solution without trial, Sysdudoku assigns Only Extreme 261, along with other Castillo Only Extremes and KrazyDad Insanes, and Classic 144, a new level of difficulty introduced in this post, the AIC-net level.

With Sudoku experience – or the interest to work through the Basic Sudoku pages of the Guide – you can read the Basic traces of Sysudoku posts and observe its humanly efficient manner of solving basic level puzzles, while preparing the grid for advanced methods. It’s done by observing how your own solving steps are ordered and expressed in the trace.

Here is the folded trace for the last pre-selected puzzle of the Classic Sudoku review, Classic 240.

The review table for Classic Sudoku reveals a surprising range of difficulty level. Six of ten are Basic level. Four collapse in the bypass, while one is beyond advanced, requiring an AIC building project.

The book contains no notes about the collection, so we don’t know whether this diversity is intended or not. The cover description of “Very Hard” just doesn’t fit. Most collections are much more consistent on a level of difficulty.

Turning now to Only Extreme 261, here is the line marked grid, with a hidden unique rectangle, Type 2b that I missed in the post of 11/28/2017, Pattern Coloring Not-Both on Only Extreme 261.  The UR is signaled by the naked pair and a slink from one of its corners. If 8r7c3 is placed, the rectangle corner placements can be interchanged for a second solution.

Since trials was an issue in the Only Extreme review, it is relevant that NEr1 is a single alternate Sue de Coq, whose alternate term 8(27+72) solves 261 outright. The case was not closed with this trial, because there was hope for examples of not-both trial coloring extensions.

In the original post, a 7-chain ANL and an irregular 562-wing hinged at r4c8 are the only eliminations ahead of AIC building. In a failing session of AIC building, the not-both extension of an AIC slink was seen to be equivalent to a color trial of a pattern based cluster found earlier on the 7-panel. With help from a pattern analysis trap on the 8-panel, the trial turned out to be easy and decisive. But this success left open whether or not OnEx 261 could be solved without a trial.

Putting the question to Sudokuwiki in this update, the solver catches the 7-chain ANL, and moves directly to AIC building, demonstrating this AIC confirming ANL,

followed by a relatively easy boomerang  (left below),

and the duplication of the irregular XYZ effect by an AIC boomerang.










After the grouped ALS boomerang here, Sudokuwiki stalls, leaving only the limited blue/green cluster.








The 5-panel eliminations have left a single olive and three pink patterns.


Fortunately for trial avoidance, the three orphans include the blue 5r9c4, confirming green.






As the grid opens up, an irregular 152-wing brings more bv.









Sudokuwiki is revived by these results, and puts together an AIC  double grouped confirming ANL.

After the  follow up below, the red/orange cluster of the original post is  overwhelming.









 Red is wrapped in c8 and orange mops up.

Next is the update on Only Extreme 304 originally solved by six trials over two posts, starting 12/05/17.  With help from the Sudokuwiki solver, it is solved without trial.


Puzzles requiring extensive AIC building are deserving of a difficulty level to themselves. Reserving the “extreme” level for those requiring trials, Sysudoku will be calling the new level the AIC-net level.

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Classic 216 Bypassed and Only Extreme 132 Demoted

This post adds another bypass solving to the review of James Forest’s Classic Sudoku, Classic 216. Then a report on an update of the 10/24/17 post on Castillo’s Only Extreme 132, in which a hard, but indecisive not-both trial leads only to another trial based on pattern analysis. In the update, a more direct application of the pattern results, along with some remarkable coloring logic, reaches a solution without trial.

First, the bypass trace of Classic 216:

Get out a grid, copy in the givens from the previous post, and account for every move. The 3-fills are signaled by square brackets. Its challenging and worth it.

Now for Only Extreme 132, the critical pattern analysis occurs on the 7-panel, where freeforms from r1 enumerate three patterns. Orange and red colors are assigned, because coloring the single pink freeform red and the candidates common to the two olive freeforms orange, we have a second coloring cluster. An immediate benefit is that three orphans are eliminated.



Back on the grid, the new red/orange cluster undergoes a very unusual wrap. The intersection of clusters in r1c4 shows that red implies blue. But in the south tier, a red 7 and Sudoku slink marking would confirm 6r7c8, implying not blue. Red cannot be true, therefore orange must be.




The resulting expansion of the blue/green cluster  brings a productive XY chain, but the lesson here is how the remaining candidates of the two orange patterns form a third cluster, immediately wrapped for an immediate collapse. It’s all traced and displayed in the updated post.




Next up is the conclusion of the Classic Sudoku review, with Classic 240. Following that is an update of the post of 11/08/17 in which a Not-Both trial, with help from pattern analysis, reaches a solution of Castillo’s Only Extreme 261. In the update, the same pattern analysis rescues a Sudokuwiki impasse to solve 261 without trial.

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Classic 192 and Updated Only Extreme 3

First, a Basic trace of Classic 192. It can be solved in the bypass. In this post, James Forest’s Classic 192 is traced down in Basic. Then there’s a second Advanced level solution of Manuel Castillo’s Only Extreme 3, the first puzzle in the Only Extreme review. In the review, OnEx 3 was solved by not-both trials which promote an AIC slink chain – having slinks at each terminal – into a coloring link. The review was an occasion to demonstrate this tactic as a last resort, but with refinements introduced in Sysudoku AIC building, several of the Only Extreme “not-both” puzzles,  including OnEx 3 are solved without trial. An Advanced level solution of OnEx 3 appeared in the post of 10/3/17.  The second one of this post uses some interesting Sudokuwiki moves.

First, a Basic trace of Classic 192. It can be solved in the bypass.



For the Advanced level resolution of Only Extreme 3, start with the Basic grid and trace posted on August 29, 2017.

This time, right out of the hidden pair line marked grid, Andrew Stuart’s Sudokuwiki found a BARN, a.k.a. Bent Almost Restricted n-Set. After the BARN, the i186-wing, 4-chain, finned 5-wing and Wr4 Sue de Coq, still apply.

Then on the 6-panel a grouped nice loop takes out three 6-candidates.









An 8-chain triggers a naked pair.










In AIC building, two reverse bv support a confirming ANL.









The follow up marking includes a hidden dublex.



Coloring may be overdue. The blue/green cluster expands with two traps, with follow up marking.








This leads to three more traps, with follow up marking




Blue is confirmed, and the solution is immediate.








Next is Basic level Classic 216 and a report on the update of Only Extreme 132, originally posted 10/24/17. The pattern analysis that rescues an indecisive not-both trial now solves OnEx 132 without trials.

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