Sadistic Sudoku Review

No, it isn’t a sadistic review. I’m reviewing Arnold Snyder’s Sadistic Sudoku collection of puzzles. Arnold’s solving advice, as presented in his “Sudoku Formula” books 2 and 3, will be analyzed in the following post. Two typical review puzzles are traced and illustrated.

Arnold and his publisher, Cardoza Publishing, describe his collection in Sadistic Sudoku, ©2012 as “200 extremely difficult, hair-tearing puzzles”. On the cover they are “brutally awesome . . . each one designed to sizzle your brain, frazzle your nerves”. Snyder also publishes three instructional books with puzzles, claiming to show ”never-before-published solutions … that unlock the most difficult expert-level puzzles quickly and easily”.

Naturally, such claims demand sysudokie attention. Snyder’s Sudoku Formula 3 came out in 2010, and Sadistic Sudoku, his capstone collection, in 2012. Where has it been?

Well, let’s find out what I’ve been missing. First of all, how does the Sysudokie Order of Battle protect your composure and your hair as you embark on Sadistic Sudoku? This will tell us if any of the never-before-published methods of Arnold’s are actually required. I started with number 5 and took every 20 to 185, for the following review table.

sadistic review tableNo threat to your composure or hair, but rough on Arnold’s pants, which are ablaze. One Sadistic is a victim of box marking, five more don’t get past basic. Survivors carry generous fields of bv, and are easily cut down by XY-chain almost nice loops and color wraps. Four x-wings, two unique rectangles, three naked triples, two hidden singles, and a naked single show up in line marking. The bypass stingy puzzles starting with six free cells per line may threaten a few follicles, but melt into naked triples before any hair comes out.

For illustration, let’s go through two, your homework puzzle 25, and the stingy 185.

Sad 25 basic trIn 25, the bypass closes 17 cells by clues or naked pairs, and the 9 pattern. Box marking and line marking are not difficult.

Sad 25 LM gridThe line marked grid shows the 1-wing and a typically generous bv field. As a matter of form I scanned for Sue de Coq and XYZ-wings, but was really pushing to draw the XY railroad and start coloring.



Sad 25 railroadHere’s my railroad. It easily produces some prodigious XY-chains and toxic pairs.


Below, I found the long black ANL looking for results on an even longer nice loop. The eliminations seemed indecisive, so I continued looking along the tracks.

Sad 25 two ANL


The red chain elimination leaves a clue and a boxline.

Updating the grid, I get SWnp15 and another ANL shown below. That’s two more bv.

In Sudoku Formula 3, Arnold recognizes the XY nice loop, calling it a cycle. I found no cycles on the railroad.

But apparently, Arnold missed the much more frequently occurring Almost Nice Loop, in XY-chain or other AIC form.

Or maybe he’s saving all that for the Arnold Snyder Sudoku Formula 4.

Sad 25 third ANLIn any case, why bother updating the railroad. With such a bv field, the crayons leap out of the box themselves.

Bad news. Arnold doesn’t do Medusa coloring either.

Sad 25 coloring

In our blue/green cluster, there is a double trap in the South Box, but it’s a game over home run when two greens compute into the same cell in the North box. The blue army of new clues is overwhelming.

I’ll report on how close Arnold comes to coloring, and where he goes instead, in the next post.



For now, we’ll see what happens to stingy Sadistic 185.

Sad 185 tr to nt 1After two cells are closed in the bypass, and no clues arrive in box marking, a hair tearing line marking is taking shape.

Sad 185 nt 1 grid

A naked triple jumps out, and it seems a little less grim. But now we have to deal with seven free cells per line. Ugly.

There are five five unmarked rows and five unmarked columns, all 7f.



But if you think this is bad, try it without line marking.

I go with rows, for no good reason.  I should have seen it when 2r7c9 was removed, but 2r7c2 is now a naked single.

Sad 185 SWns2


However, not much time is lost when it turns up in the marking of row 7.

Look at those fill strings. Its sadistic. Like a monster.



Sad 185 two nt bxl


Incredibly, the marking grinds to a halt after naked triples in W and r4, and a decisive boxline Cr5.





Sad 185 LMm1



During this marking, the unmarked row 9 let 185 off the hook again and again, leaving this line alone to finish.

But just as I formed the fill string, I noticed that S1 had confined S3 to r9c6.



This was enough to make Sadistic 185 give up.The trace to garbage time follows,

Sad 185 final tr

Sorry for the overly long post. Next, in more reasonable doses, is a review of Arnold Snyder’s instruction books, the Formula series. First I consider his basic solving method, as described and illustrated in Sudoku Formula 2. If you have that book, I’ll be working through puzzles 5 and 6, for comparison.

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Revisiting Wex 435

This post updates the Weekly Extreme Review with a revisit of Wex 435, a puzzle that proved resistant to the single alternate Sue de Coq and was deemed the toughest in the review series, inspiring an extreme ALS trial, the jump ball, in the review. But afterward, two setbacks at the hand of sysudokie friend Gordon Fick enables a kraken 1-wing and two advanced level finishes, one by Gordon and another by YT.

Wex 435 UR with SdcFrom the basic grid opening the post of June 2, Gordon noted a UR removal to go with the indecisive single alternate Sue de Coq. In Fick’s UR, the floor naked pair c3np19 force one of 9r2c2 or 9f8c3 to be true. Then if either 1r2c2 or 1r8c2 is true, a deadly rectangle, and at least two solutions, occurs.




Wex 435 W-wingNext in the bv scan, Gordon calls upon his Hodoku training, and finds a W-wing on the 1-panel. The W-wing is described on the Hokoku wings page as a pair of identical bv with one of the two numbers linked. Hodoku over specifies the link, saying that a strong link is required. Actually, the inference logic requires a weak link is made by forcing chain or ER. A unit wink would make it a naked pair. Hodoku’s two examples illustrate the W-wing with AIC winks. I now include a W-wing schematic and one of the Hodoku examples, translated for Sysudoku readers, in the XY-chain post.  The matching bv of a potential W-wing makes it a tempting target for building AIC winks.

Wex 435 ANL krakenAlong with the W-wing, Gordon came up with a 1-chain(green) removal that pairs with the W-wing to enable a kraken 1-wing on the 1-panel.

Kraken analysis is another worthwhile occupation for forcing   chains.  Here, double chains force through a grouped chain that gives the finned 1-wing victim its fatal vision of the fin.


Wex 435 nt boxlineThat is followed by a NW naked triple and a NEr2 boxline. At this point, Gordon and I part company.



Wex 435 color wrapI’m attracted to the meadow of bv for the coloring. The trial trace helps me find a quick wrap in which two blue candidates are found guilty of removing all 5’s from r5, proving green.

The collapse starts with 4r4c3.





Wex 435 Ficks wicked AICGordon, on the other hand, found Wex 435 to be a playground for AIC ANL, using XY-chains extended by slinks. His first blow was this wicked ANL with XY ends and a Medusa X-chain in the middle.

I added the relevant AIC hinge that would have helped me construct such a chain. My hinge marker encloses candidates bringing slinks into a multiple candidate cell. The slink pencil marking by corners makes hinges easy find, and they help you spot AIC strong links.

Wex 435  wicked trWex 435 second W-wingAfter the follow up, another W-wing:

As Wex 435 falls back on the ropes,


Wex 435  AIC hidden pair


Gordon wades in with another AIC ANL, this XY and X-chain mix bringing a naked pair to remove 7r7c9, and leaving a hidden pair 57 in the East box.

Wex 435  hidden pair trGordon’s knockout blow was a round house AIC ANL that covered the grid, and brought an immediate collapse.


Wex 435  AIC knockoutBefore the collapse, I got a snapshop of an irregular remote pair, in red. The victim sees one of the forbidden ending 5’s by forcing chain.

I hope these posts have alerted some dedicated WECers to new possibilities in the competition puzzles.




Please comment, particularly if my review of another Competition puzzle would be of special interest to you. I’ll try to enlist Gordon to attack from the other direction.

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The Olive Side of Fata Morgana

This post illustrates with Fata Morgana the practice of taking both sides of a trial, to be sure that a contradiction is found.

FM olive  trace 1The pink trial led to the solution. Fully expecting a contradiction, the olive trial begins with the four candidates included on all possible olive patterns. The marking ends without a conclusion.

FM olive ANL

The  bv scan with a bv map yields only an indecisive ANL.








FM olive finned 7-wingThe X-panel now gives a finned 7-wing, getting the marking moving again.. There are no kraken victims.





The expected contradiction appears as the marking places a second 2-candidate in the NW box.

FM olive  trace 2Given all that has been written about Fata Morgana, it is rather surprising that its complete analysis comes with such straightforward applications of sysudokie exocet, nice loop coloring, and pattern analysis trials.

Next, we revisit Wex 435, the puzzle concluding the recent Weekly Extreme review. An independent analysis by Gordon Fick shows that it doesn’t require pattern analysis, only a good eye for AIC. An acquaintance with kraken fish and coloring doesn’t hurt, either.










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Fata Morgana Wrapped in Pink Olive

In this post, the solution of the well known monster Fata Morgana is reached via pattern analysis, on a trial of pink patterns vs olive patterns, a frequently used Sysudoku extreme method.

In the previous post, the orange candidates of a nice loop cluster was confirmed for the exocet base solution 3 and 6. Readers were invited to do their own pink olive freeform analysis of the 1-candidates.

FM 1 pink oliveTwo pink and four olive patterns were found. One orphan candidate was left out of the six possible patterns. In the left panel, the light blue freeforms show failed attempts at complete patterns. The shaded cells designate three candidates in all pink patterns and three in all olive patterns. One of those sets must be true with the true 1-pattern being that color. The other set must be false.

FM 36 pink olive gridOn the grid, candidates included in patterns of only one color are shaded. In a trial, candidates in all patterns of a color are starting clues, and candidates visited only by patterns of the other color are removed. This makes it a trial of one color or the other, pink or olive.

This suggests we may be one or two trials away from a solution. We try pink patterns first.

FM pink remote pairIn the pink trial, the trial trace is extended by a remote pair, as shown here, which confirms NE8.

The trace runs to the solution of Fata Morgana. In the tradition of monster reporting, I’ll not show the solution , but following the trace after NE8 to the solution is easy.



Next post will close the books on the FM with the olive trial. That’s anti-climactic, I know, but I do it to show what would happen if we happen to choose the olive trial first, and as an example of good practice against multiple solutions.

FM final trace

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Fata Morgana Sysudokie Fried

In this post, the exocet trials are completed and a path to the monster’s cave is mapped and cleared of fog. A color wrap brings us to base camp, for the final ascent.

FM 16 nice loopThe nice loop generated by Cr5np16 is another figure 8, and its crossing cell is forced to have two loop cells of the same color. The blue candidates are wrapped.

And the blue removals in r3 leave the remaining 1’s and 3’s in the N box, forcing Nr3np16 and another deadly rectangle in 1 and 6. The trial fails, leaving np36 in Cr5. And it wasn’t that hard.

FM 36 nice loopSo now we’re ready to follow up on the third pair of ANL, a 3-chain and a 6-chain forming third fog clearing nice loop. This time there is no figure 8 and no cell crossing that wraps a color. We also note that the colors cooperate to avoid the row naked pairs that would constitute a deadly rectangle.




FM 36 clusterAs we trace out the red/orange cluster, it’s apparent that red forces two 9 clues, so it’s a more decisive choice for a coloring trial.  Monsters get no slack.







FM red trThe red trial reaches a contradiction placing two 7’s in r1. They are the N7 and NW7 effects on the bottom line.



FM 36 orangePromotion of the orange candidates produces only one additional clue, SW9, and the remaining the candidate grid resists advanced methods. But we’re almost there.

Next time we’re going for a pink olive analysis of the 1-patterns, where freeforms from the left side are significantly restricted. With a little boning up on that, you could get there first.

My pink 1-freeforms will start at r7c1. Go for it.

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Trial 13 of Fata Morgana

This post checkpoints the third “figure 8” nice loop generated by the FM exocet, and follows up on the first, the exocet trial Cnp13

FM 36 ANLAs to the homework, Yesss! It happens again. The FM exocet defines the endpoints of two X-chain ANL that link together at the ends to form a luxuriously long nice loop

Were you tempted to go ahead with the Cnp13 case?

You really could have. I wouldn’t mind.



FM 13 nice loopUnless you just joined us, it goes pretty well. First, we color the two directions of the nice loop. We have a major result right away, so obvious I missed it at first. Got it?


Yes, two orange candidates in the crossing of the loop is a color wrap. Red candidates are true, in the 13 trial, that is.


FM 13 deadlyGoing red, the departure of orange candidates leaves a naked triple c7nt457 that confirms SE6. Together they create a deadly rectangle of 1 and 3 candidates.

No, thanks. If there is a solution here, that makes it at least two. I think that our chance of discovering an undiscovered multiple in the famous Fata Morgana is too teeny weeny to bother with. I don’t play the lottery either.

So do you want to wring out the Cnp16 nice loop on your own? Be my guest, but you only have one week.

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The Fata Morgana Exocet

Here we do the Sysudoku basic solving of the celebrity monster Fata Morgana, and develop a trial plan based on its exocet. The Sysudoku interpretation of the exocet as a trial generator is reviewed and two of the three exocet trials are defined in detail. A third is left for sysudokies wishing to get close and personal with this monster.

Diligent readers might recall the relentless Sysudoku campaign of the Golden Nugget exocet. The exocet has been widely described as an elimination method, but against the GN it was a trial generator guaranteed to corral the solution. The GN had the monster trademark, an intimidating fog of candidates emerging from basic solving, blinding advanced solving methods. In GN’s case, the exocet generated a series of four closely related trials, with interchangeable forcing chains. Each trial cleared away enough fog to allow solving to a contradiction, and in one case, a solution.

Basic solving of the FM reveals another exocet. The bypass, box marking and line marking leave you in dense fog of candidates:

FM basic trYeah, that’s it, pilgrim!

FM basic gridWhen you see this field of candidates, you know you have a monster.

Having seen the exocet mentioned in discussions of Fata Morgana, I first looked for the 4 candidate base cells and two candidate target cells similar to the GN exocet, but the ones I saw were spoiled by clues. Then I realized that the r5c46 base and the r6c8and r4c2 targets qualify as a 3-candidate exocet.

If you don’t mind a little math, this FN exocet is even better than the GN’s. In the GN exocet, there were four candidate numbers in the two base cells. That comes to 6 combinations of two numbers, or possibly 12 grids to be tested.  In the FN exocet the three candidates can form only three combinations and only six possible solutions. The critical issue is the effect that each combination has on the candidate fog.

For the GN I prepped for the 6 exocet trials by working hard on pattern analysis, and had some restricted pattern sets to help out, but it was still a lot for Sysudoku readers to wade through. But the effort convinced me, at least, that a logical solution to such a monster is humanly possible, and worthy of the attempt.

Let’s start the FM with a base solution of 1 and 3. We can hope, as in the Golden Nugget, that we can meet the exocet condition without having to designate which cell has which. Remembering the GN trials, we look for 1-chains and 3-chains between the target cells. X-chains are not as easy as XY-chains, but they glow infra-red in the monster fog.

FM 13 ANLThe X-panels reveal a long-1-chain ANL c1. This prompts a look for the similar 3-chain ANL, which is just a bit harder, requiring some grouping.

But that’s OK. Chain construction, as opposed to searching, is what sysudokies do.

Remarkably, the ends of the ANL stitch together to form an AIC nice loop, eliminating 246r4c2 and 6r6c8. The target solutions are guaranteed to be 1 and 3 by the ANL forcing chains, meeting the exocet condition for base solution 13, without specifying cell locations for 1 and 3 candidates.

There are more immediate consequences of the nice loop for you to discover, and I will catch up to you in the next post, but let’s continue here with the other exocet combinations.

FM 16 ANLIn the Cr5np16 trial, the same 1-ANL is joined by a 6-chain ANL and the two form a nice loop removing 234r4c2 and 3r6c8. Can you believe it?

Again we leave the nice loop follow up for later, and move on to the 36 combination.

Have you been paying attention? If so, you will have no difficulty in finding a nice loop for the Cnp36 trial, to be displayed next time.

Covering the three possible exocet solution pairs will guarantee the elimination of candidates 2, 4 and 6 from the exocet target cells. That is the stated objective of the exocet elimination method. But it will also guarantee that one of the three trials can end only in a solution of Fata Morgana. That is the objective of an exocet trial generator.

Experts, please compare the logical transparency and human accessibility of this mode of solution with the others published. That is the objective of Sysudoku.

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