Moito’s Road to Sudoku Mastery

My first Sysudoku review of 2018 is one of a host of new collection books with the same grid format, some with an unexplained rating system, some with listed authors A.D. Ardson and Rebecca Bean. Moito and Bean’s  Extremely Hard Sudoku Volume 10 seem to share common difficulty rating system. The puzzle ratings are two decimal places, from a presumed zero, up to 1.00.

Sudoku: Road to Mastery is a collection of 400 puzzles without listed author, described on the cover as “Hard to Devilishly Hard”. It is divided into a “Hard Sudoku” section of 200 puzzles, ranging in difficulty from 0.60 to 0.74, and a “Very Hard Sudoku” section, ranging from 0.75 to 1.00.  Each section is divided into four sets, I through IV,  of 50 puzzles. Rather than my dart board selection of a start and a fixed size step to cover the collection, I tested the rating system as well by preselecting the 10 most difficult puzzles, according to the difficulty rating,  from the “Very Hard” section. The result is the following review table:

The Moito difficulty rating is very inconsistent with the review results. The most highly rated puzzle fell in the bypass, and three more of the highest rated collapsed in box marking. The third above, III – 47, is the only contender for an extreme rating. I finished with a coloring trial, but perhaps I missed something you can find.  

The 0.91 rated IV-6 has multiple solutions of a peculiar nature. Missing a boxline removal after a spectacularly irregular XYZ-wing, I reached a double solution on unique rectangle too late to reject it.  The Moito solution was different, so I retraced, and found the omission. This time it was a  different double solution on an extended unique rectangle formation of six bv, and this time, including the Moito solution. Related to earlier 2017  revelations, anything can happen with multiple solutions. They follow no inference rules. Details to come.

I happened upon two more glaring errors on the Road to Mastery.  Puzzles III-5 and III-6 are destroyed by a sloppy paste-in of puzzles III-7 and III-8. Raising a more serious issue of trust, your homework III-47 above is identical to I-28.

Now to checkpoint your III-47. First a bypass typical of the Moito collection, reading:

C29, W4, W5, SE5.           Yes, that’s it.

ANL with grouped ER victim in Moito III-47Box and line marking are routine, and the bv scan brings only this XY ANL with a grouped ER victim, or if you prefer, a grouped AIC ANL.






Next, fishing is bad on the X-panel, but an extraordinary set of 9-slinks can be assembled into an X9-chain ANL to trigger a SW/c2  boxline 9m removal to create a naked triple.





No fixes on the X-panel, but coloring around the 9-slinks produces three coloring clusters that do not bridge.







Conflicts in c3, c7 and r3c9 give bridging combinations:

not(green&red) => blue or orange,  not(red&tan) => orange or purple, and

not(blue&purple) => green or tan.  Bridge toxic sets don’t materialize.

With the X-panel showing little prospect for pattern restrictions, I’m ready for a color trial. From the bridge combinations, blue => tan. I go for a blue trial.

The trial trace reveals how blue inferences coordinate to force two 2’s into SE. Green => orange, but the marking stalls, but an XY chain from my updated railway wraps purple, with an immediate collapse to green, orange and tan.


Next post, I checkpoint your version of the I-4 bypass, and show several highlights reported in the review table above.

Also, four of the five Guide pages are up. They explain and demonstrate Sysudoku Basic via worthy examples.




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Only Extreme 390 – a Fitting Finale

In this post, the last preselected Sudoku of the review, Only Extreme 390, is solved by only advanced methods, but by an extremely thin margin.  The first crack in the armor is an irregular XYZ-wing. At first I missed an XY-chain ANL on a very extensive XY railway, that expands into a decisive nice loop. The railway is included so you can trace around it to verify the ANL and see if I missed any others.  I had solved 390 with a coloring trial, which would rate it as Sysudoku Extreme. After the ANL, however,  the expanded cluster merges with a second cluster for a follow-up wrapA review table and general conclusions on Only Extreme Sudoku end the post. 

As for Only Extreme 390, here is a basic trace that carries you to the first grid:




In the  irregular 893-wing, the 83 wing winks at the hinge via a forcing chain. The almost nice XY loop (black) removes one 8, but then an 8-slink  in c1 winks in to the chain terminals to form an AIC nice loop, duplicating that removal and adding three more.



To practice the Sysudoku search for ANL along the XY railway superimposed on the bv map, here is the 390 example.  Find all of the starting terminals, and on each unvisited terminal follow the chain. On each incoming  digit, test each repeated outgoing digit along the railway but not in the same unit, for an almost nice loop victim. It’s faster than it sounds. Some segments are one-way. That’s why it’s called a railway.

Powerful as it is, the railway exploits only one feature of the bv field. A more powerful , but still only advanced feature is the Medusa coloring network that the bv field supports. After giving single value X-chains and cross unit fishing restrictions their due diligence, as we did here, the Sysudoku Order of Battle returns to coloring. The blue/green cluster traps three candidates.

A second cluster brings a merge:

Not(blue & orange) and not green & red makes red function as blue and orange function as green.






Nothing changes when we merge the two clusters, but the traps of the bridge are exposed.

The marking confirms green, and 390 is done.




Overall, Manuel Castillo’s Only Extreme Sudoku shares with Krazy Dad Insane the honor of being the hardest reviewed here, outside of acknowledged monsters. As to the “Extreme” label , the Sysudoku “extreme” rating is reserved for necessary trials.  Among the 10 selected, Only Extreme had 5 extremes, and 5 only advanced. That’s equal to KD’s Insane’s. That collection t forced me into the effective freeform approach to pattern analysis. Only Extreme Sudoku forced me into series of trials extending a coloring  over AIC slinks.

The Weekly  Extreme Competition series I selected for review had 7 of 10 extremes, but there, in consideration of the by week deadline of the competition, I took the first trial opportunity presented. Advanced alternatives were probably available. Outside of that, my position is to defer, and often discard, trials. Thanks, Gordon.


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A Coloring Trial for Only Extreme 347

Here a Manuel Castillo Sudoku sends me directly to last resort city.  Although the bv field eludes productive XY-chains or AIC, coloring is decisive enough to solve 347 in a single trial.

Your first view of the grid comes with a blue green cluster, and six AIC hinges I marked when I came up with nothing from the bv scan and X-panel.

If you’d like to work it from the beginning and didn’t  get Castillo’s Only Extreme Sudoku yet, just load the clues and go for it. The grid is in the line marked state.


You can check your basic against my Sysudoku basic trace.

My inner engineer asked me why I continued to put the naked pair “np” and other subset symbols in the trace. He’s right. It’s clear and consistent with the clue marks to just list the numbers in any subset, after the box name.

When I had nothing better than a coloring trial, I did look at several X-panels with slink corner formations that might add candidates to the trial sets. The 8-panel illustrates the idea.  In the cluster on the corner, here’s only one pattern that includes 8r1c2 and 8r4c7. There are four green patterns, reaching every other 8-candidate.  I pick blue.

Only Extreme 347 is useful as an illustration of the trial trace and corresponding graphic demonstration. In the trial trace, instead of finding all effects of each cause, we list only the first level effects, of each item on the list, returning on the next line to pick up another level of effects.

Here is the trial trace for the blue trial, arriving at a contradiction when two 2’s are forced into r4.

In a graphic overlay, we trace down from cause to cause on a direct path to the contradiction, ignoring effects that have no bearing on it. 

Going back to the trial setup grid, we use clue cause-to-effect arrows and supporting weak links to display the shortest, most direct path to the contradiction.

Here blue candidates see two candidates in r9c1, starting a chain of inferences that place 2r4c4, and 2r4c8.




Now knowing that green candidates are all true, we can use normal depth first marking to reach an immediate solution.



Next, the final post of 2017 takes up the final Sudoku of the Only Extreme review, 390. Another review will follow, but in 2018,a series of pages will be added to consolidate and illustrate Systematic Sudoku developments in these seven years of the Sysudoku blog. 

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Dragging in Only Extreme 304

This post continues with three more trials, two to reach a solution, and one to guard against multiple solutions, in Castillo’s Only Extreme 304. This is getting reeeaallly extreme.

Last week, we managed to extend and XY-chain across the grid and over a the bv field of a coloring cluster, and by three not-both trials, extended coloring over this chain. The cluster expansion trapped a 7-candidate, but little progress had been made against the brambles above and below the cluster.

The last not-both trial was close to a blue trial on the completed coloring of the XY chain, so between blue and green, I choose blue for a coloring trial. As before, an 3-chain covers one 8 in c6, and 4r2c7 is confirmed to help confirm 8r7c7 to eliminate the other 8 in c6. Blue goes down.

When green bogs down,  another trial possibility emerges.There is a Single Alternate Sue de Coq:

SEr7 = 3(1+8)(4+9) + 934.

One chute cell is (1+8) or that alternative is missing from the chute.   In the latter case, the solution is exactly 934.

It’s not too surprising that (SE9, SE4)  marks immediately into the solution.  



The difficulties to this point argue for a final trial to guard against a multiple solution.  

We should see if the alternative chute description

SEr7 = 3(1+ 8)(4+9)

leads to other solutions.  The  good news is that the resulting clue 7r7c6 forces 1’s in r7c2 and r8c4, allowing no 1 in r9. Knowing this is impossible without a trial trace.

Next week, it’s on to Only Extreme 347.

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Definitely Extreme 304

This post encounters what seems to be a monster in Castillo’s Only Extreme 304. A stingy basic leaves a near monster cloud of candidates resistant to the ordinary advanced repertoire. Following a theme of this review, a small coloring cluster is extended across the grid by not-both trials. It takes two more trials in the next post to defeat 304.  Or perhaps you can find a less extreme path.

The ordinary looking basic trace

leaves this formidable grid to navigate:

There is a Type 1 UR and a resulting box/line to start, but then I find nothing else.








In the swath of bv cells across the middle, I latch onto a tight little XY-chain intersecting a very modest coloring.

The potential for  coloring the XY-chain is enhanced by an AIC with numbers common to both the cluster and the xy chain.

If blue 8r4c2 and 8r3c3 are not both true, then 8r3c3 is green, and working back 7r3c3 is blue, 7r2c2 is green, and 2r2c2 is blue.

Testing terminal 8’s on the subchain from r4c2 is a start. The 8’s are not both true, along with blue,  because this forces both 3 and 8 in r1c7.






The cluster expansion removes four candidates. Clearly, a further expansion to 3r3c1 does further damage.

Again the not-both trial, testing blue + 3r3c1, is required for the extension.






If both terminals of the X-chain are true, c6 gets no  3’s.  Not acceptable.








The expansion turns 8r3c1 blue, generating three traps that expand the XY-chain further.








The final not-both trial to extend coloring over the XY-chain determines that 3r3c7 and 4r6c7 are not both true. If they are, 1,3, and 7 are removed from r2c5, and 1 and 3 are removed from r9c4, leaving two 4’s in c5.

Unless you have found a less extreme path, let’s see how you would continue with the fully colored XY-chain.  My finish of Only Extreme 304 comes next week.






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Pattern Coloring Not-Both on Only Extreme 261

On this post of the Manuel Castillo Only Extreme review, Only Extreme 261 justifies its “extreme” label. After limited advanced moves, a pattern based coloring suggests an extension via a not-both trial on a long AIC strong link. The not-both trial rejects the coloring by reaching the solution. A counter trial assures that this unexpected result does not signal a multiple solution.

First, the basic trace. Simple to follow, but leaving a distracting host of candidates, and not many clues, on the grid.



My first advanced nibble is a 7-chain and extended chain (red) for two almost nice removals in c8.









One of them enables an irregular 562 wing. The weak link attaching the 26 wing is a 6-chain, lining 2’s up for the victim.


It was a bad day for fishing on the X-panel, but 7-freeforms from the West side were only three.  By assigning colors by starting point, and coloring only where all patterns of a color cross, a blue/green cluster is created. Only the blue or the green candidates in common, can be true.




Applying this coloring to the grid, where several AIC  chains had been fruitless,  the conflict between the blue and solid green patterns at r4c7 has a counterpart. The coloring of candidate 7r4c7 is also the issue in the Not-Both condition for extending the cluster over two more candidates of the AIC slink .

It’s getting creepy, how  AIC  slink coloring  keeps coming up. The color of the East 7’s is not decisive either way, but seriously affects the solution path.

Before the trial, however, there’s a cheap removal to take.  In a red/orange coloring  of 8-freeforms from West to East, the ending candidate on the same row will have different colors. We don’t have to enumerate the freeforms for the trap.



In the trial, if both 7r9c4 and 7r4c7 are true, green is confirmed. The red/orange cluster explodes. There is no color wrap, but red forces two 5’s in column 5. Orange gives an immediate solution of Only Extreme 261.





This unexpected success leaves us needing to see if the AIC slink coloring, making 7r4c7 blue, brings more solutions. From the freeforms 7-panel above, the blue 7-pattern is confirmed in that case, and both green patterns are false. A trial trace makes it easy to demonstrate that no more solutions exist.  Blue implies red (E6) and forces two 2’s in c6. Time to move on to Only Extreme 304.



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Only Extreme 218 by SASdC Trial

This post demonstrates the Single Alternate Sue de Coq with Castillo’s Only Extreme 218. The opportunity for this kind of trial is spotted early in the bv scan, but is best deferred until it is needed as a last resort. Only Extreme puzzles certainly qualify as possible candidates for the SASdC.

Sue de Coq is based on a logical description of a chute as three factors, one a clue and two binary factors, the alternates. In classic Sue de Coq there are two ALS in the box and line remainders of the chute, each ALS matching the two numbers of an alternate factor. The true candidate must be in the factor or in the matching ALS, and can be removed from any other remainder location.

In the single alternate form, only one of the alternate factors is matched by an ALS.  This match allows only one of the matching number to be in the chute.   If one is indeed present in the chute, one position is left for the two unmatched numbers, and removals of the matched numbers can be made in the remainders. A trial determines if both matched numbers are missing.

We pick up the solving of 218 right after basic, in the scan for APE and Sue de Coq. You could be on the lookout for ALS-XZ and BARN as well.

In SEc9, the possible contents are 9(5+7)(1+6) + 9(16+61), the first term being the classic Sue de Coq with the alternate (5+7) present, and the second, its contents with alternate values 5 and 7 missing. The SASdC trial follows up what happens if the alternate values are missing. If this trial reaches a contradiction, then the regular Sue de Coq is in force, removing 5r1c9 in this case.

What happens is a bit unusual. Instead of a contradiction or a collapse to the solution, the trial makes some updates, and stalls. We must continue from there


We look up to realize the “missing alternate” being tested has placed the 8’s and added bv and slinks to open up coloring. We dutifully add another tan/yellow cluster to take up the slack, and look for overlaps for bridging and merging of clusters.



It’s easy to conclude that if

not(orange and violet) and not(red and violet) then not violet.

Yellow quickly confirms both orange and blue, and the solution pours out.

The trial of missing matched numbers in the SASdC is often decisive.  I think you would agree, that logic based trials are far better than arbitrary guesses, or abandoning the puzzle.  Done too early, trials risk concealment of advanced logic and put a cap on learning.

As a last resort, a trial temporarily concedes that the puzzle is extreme.

Next we take another leap of faith, to Only Extreme 261. Four to go.

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