The Especially Nice Loop of KD Insane 465

This post reports several features of an update of the post that introduced nice loop coloring. The illustrating nice loop was in itself remarkable.

As shown already from books 1 through 5, KrazyDad’s hardest, the Insane collection, is hard enough to force new ways to use familiar tools. The blog explained the nice loop in early 2012, and showed its elimination power as the AIC forms of  the nice loop were encountered. But only when faced with nice loop fashioned with two ALS nodes did I realize the coloring established and given a direction by the loop could move off the loop in X-chains.

In the updated post of 8/27/13, KD Insane 465 finds a 7-wing on the last line of line marking. That applies the knowledge of X-wings while assembling candidates.

The X-wing enables a coloring cluster that can be completed by basic logic. How many times have I forgotten to do that?  After 465 gives the Insane password, a boomerang, we get an irregular XYZ with the YZ wing attached by a grouped X-chain. The post relates all this to AI.


Then we come to that rare gem, a nice loop made with two ALS nodes. But the beautiful thing has no victims! When you go there and look at it, you’ll see why. The ALS node groups take up all candidates that could see adjacent nodes of the nice loop, putting them in the nodes.



So how do you make use of this gem? By using it to introduce a new solving feature of the nice loop.  An AIC can spin off the loop in two useful ways illustrated here.

A slink chain can carry the coloring out into the grid. Here a slink chain colors 4r5c6 and the C 4-group.  Another connects the three 2-groups  and a single 2 into a slink loop, extending the blue/green nice loop cluster to two new groups. Coloring groups is rarely useful, but it is useful to know about it.


More frequently occurring is the type of ANL extension shown here with red alternating links. If blue is true, the extension 4-chain makes 4r4c2 true, so a trial of blue can include it.

After the pink olive strikes out, the KD Insane review’s first attempt at LPO, the pattern conflict side of pattern analysis is next. A tabulation overlays pink/olive 3-candidates and the red/orange cluster candidates. The result is indecisive, but the weakened KD Insane 465 is solved with  a coloring trial.

The next post looks back to the update of KD 475. These updates are more than cosmetic, and back up the original solution with Sysudoku interpretations of added Sudokuwiki moves. This Insane review is particularly innovative in coloring and pattern analysis.

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The Insane 455 Pink/Olive Pattern Trial

This post reports on the updated KrazyDad Insane still at its posted date of August 20, 2013, but now updated to continue the introduction of pattern slicing, or pink/olive pattern analysis, by showing how it leads to decisive trials when needed.

In Sudoku there are monsters, which require trials to clear the cloud of candidates before doing anything, and there are the toughest of the tough, where reasonable techniques work until they don’t. So far, KD Insane 455 is in that category, and the post of 8/20/13 can demonstrate how a trial is defined and conducted by pattern slicing.

After the customary Insane basic, an ALS_XZ in line marking and a boomerang ANL very unlikely to be found by a human solver, Stuart’s Sudokuwiki  finds an orphan where freeform enumeration would be beyond reason. Then begins a systematic pink olive pattern analysis over three panels

The first goal of the pattern slicing method is to divide all patterns into two disjoint sets, all patterns in each set starting with the same candidates in the freeform starting lines.  Panel cells are shaded in pink and olive colors to show where freeforms can cross starting cell lines while remaining in the pattern set it started in, pink or olive.

Using the KD Insane 455  3 freeform panel as an example, starting rows 9 and 8 divide the 10 freeforms into three pink and seven olive patterns. Cells of higher rows are shaded in columns above these cells to show where freeforms of the opposing set and color can cross the column. For easier interpretation, we duplicate the cell shading and put the two sets in separate panels.

The second goal of pattern slicing is to find additional cell shadings that will limit freeforms to a single pattern of one or both colors. If there is only one such pink/olive shading,  then the single color pattern is the true pattern, or the pink/olive pair of patterns is a coloring cluster. It there is more than one such pink/olive pattern, then each one is the logical basis for a trial.

In Insane 455, there are four possible pink olive maps of the two columns not containing a 3 in row 8 or 9. A pattern cluster is possible as the first one, shown here, restricts freeforms to one pink and one olive.

But then another of the  four possible maps produces its own pair of patterns. The analysis moves on to another panel in hopes of finding a coloring cluster of two patterns. Panels of values 4 and 6 are mapped, with very similar results. The 4-panel analysis produces an orphan, which nets an ANL and a small coloring cluster. The 6-panel is less restrictive, yielding three shadings and corresponding cluster pairs.

Once the freeforms are enumerated, mapping effects are easily determined. Any of the three panels will likely yield a decisive test, yielding the solution or pointing to the true pattern.

The post displays the solution path, merging the coloring cluster and the pattern cluster.  A Sue de Coq expands the merged  cluster into a wrap.

That illustrates how advanced methods are directed to a solution by trial concepts and set up.

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Books 3 and 4 In the KD Insane Review

Welcome to 2019 Systematic Sudoku. This post continues on the updated KrazyDad v4 review, with KD Insane 435 and 445. This is a brief report on what you’ll find in the updated posts of August 2013. The review update begins a general one over the most difficult, and therefore most significant, reviews, in over seven years of weekly blogging.

Insane 435 starts advanced with a hidden unique rectangle, and then becomes a stage show of ordinary XYZ’s with victims determined to “see” themselves to death. Here’s an example of how weird it got. An ordinary rectangular 136-wing inspires 6r5c1 seeing two toxic set members to find a way to look upon a third. A good example of filtering your looks.


Then 445 presents you with multiple exotic ways to get the same result, such as this gem, an XY wing, unless you want to claim a 3-set BARN. Or hidden UR, anyone? Can you make an APE out of it?

The show is over when this double ANL triggers a collapse, but KD 445 doesn’t let you leave without taking along a pink olive finish as well.




On the 6-panel, in the freeforms going  North from r7, olive must go to r6c1, making it, and r5c3, collectors. It’s the last chance for a 6 in c1

Now on r5, the alternatives to c7 must cross r3 at c8, a column already taken. Another collector.

Since r5c3 is a pink collector, the alternatives become orphans, confirming 6r4c4 as C6, which is enough for the collapse. However, you should be aware that you have just attended a trial. Pink has not weighed in, and if given a chance, comes up with two candidate patterns.

Interesting? Use the monthly roll on the right to dig back into 2013.

The number 5 in books 3 and 4 don’t prepare you for the one in book 5. Look it up on and try it, then check out Insane 455 in the updated post of 8/20/13 and tune in next week for my ideas of its value in Sysudoku.

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KrazyDad Insane 425 Introduces Pattern Slicing

This post reports on the introduction of pattern slicing, a.k.a. the pink olive, in KD Insane v4, b2, n5 of 7/30/13. The method is defined, and demonstrated on the 3-panel of Insane 425. This review is being updated first, as one of the most instructive.

After a terrific ANL boomerang series, the previous post leaves a challenge for pattern analysis to merge two limited coloring clusters with a common value 3.

To see if a merger is implied by pattern restrictions, the coloring is transferred to the 3’s freeform panel. Each of the three 3-patterns depends on a pair of colors, but all pairs are consistent with blue and/or orange as true colors, and no freeforms are rejected.




This simple case and successful application affords an opportunity to explain the pink/olive mapping process of two stages.  Here is the first stage, the coloring of columns and boxes as derived from the two starting rows r6 and r4.  Deriving the row coloring allows no alternate mappings.

The complete mapping rejects the two pink freeforms and allows the single olive one.

The combination of pink/olive coloring and posting the freeforms on separate panels clearly makes the case for pattern slicing.

Next post updates KrazyDad Insane review puzzles 435 and 445.

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The KD Insane 425 Boomerangs

This post reports on the introduction of spotting techniques for the boomerang ANL in the updated KrazyDad Insane v4 b2 n5. The cell based examples of this KD Insane review post of July 23, 2013 suggest the inclusion of both cell and unit based boomerang ANL in the sysudokie repertoire. The second Krazy Dad Insane gets Sydudoku naming credits for two spotting techniques, the boomerang ANL (almost nice loop) and pink olive  pattern slicing.

After finishing KD 415 with two irregular XYZ and a color wrap,  Sysudoku basic encounters a similar unbalanced candidate cloud in KD 425. The XYZ map brings a grouped 7-chain i173-wing with a very unlucky victim seeing two toxic set members via 3-chains. Unlucky and indecisive. That joy was dampened by my missing the only Sudokuwiki elimination prior to AIC building, a simple 1-chain ANL, similarly indecisive.

Then a string of three suggestive boomerangs highlight the spotting principle: A slink leaving the cell starting a chain worth following.  As you follow, look for a repeat of the starting cell values and a way to look back.

And if you are already following an AIC for another reason, and it leads you into such a cell on a slink, look back along your path for one of those other values. Is there a wink into the value here?

Both of these spotting signals go into the post, and the second way leads to the re-use of most of the path of the first boomerang in a second one.

And KD 425 keeps on giving. Here is a boomerang ANL with the 7-slink leaving a group, not a candidate, and leaving a box, not a cell. That has to be a unit boomerang. Or is it a cell boomerang with the 1-slink leaving the cell r8c7 and the returning wink defined in the box?  It opens the gate for much more AIC building.

We’ll leave for next week, and Christmas day, comments on the KD Insane 425 introduction to pattern slicing.

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KD Insane 415 Updated

This post tells the story in the solving of Krazy Dad Insane v4, b1, n5, as reported in updated Sysudoku posts of 7/13/13 and 7/20/13. It’s one way that coloring and pattern analysis work together.

Important features of Sysudoku Basic are illustrated on the first screen.  Always included is a complete basic trace in a very compact format. This service is not duplicated elsewhere.

The first grid shows a large number of bypass clues, with very few pencil marks. The 5-wing occurs on the second line marking. How was it spotted? In marking c2, the 5’s are placed at the Southwest corner, marking a line slink.  Form the corresponding habit: when you mark a line slink, look for a parallel one.

Now what happens? No immediate victim, but the fish icons remain and prevent the addition of the pencil marks added, then removed by many other solvers, human and computer.

Next is the line marked grid, where you can see the completed candidate field. If it doesn’t look like yours, then maybe you should look at what else happened to all those pencil marks. And what it means to have the marks placed in the cells as they are. Is this coded information to be used in advanced solving?

Also on the first grid, the first advanced method beyond the 5-wing is in evidence, a blue/green cluster.

The most significant figure of the post, however is this pair of panels. Patterns and coloring come together here. The 5-panel has the  very simple blue/green cluster.  Freeforms are not required to show that the cluster marks two 5 patterns.

Then the 7-panel jumps out at you as being very limited in patterns as well. A quick freeform analysis with r9 as a starting row divides the 7-patterns, three from r9c2 and one from r9c4. Now we mix in a little overlay, some LPO. The 5 and 7 patterns overlay without conflict, except in coloring. There is only one way for slinked 7’s to overlay colors consistently with the 5 coloring. All of the 7-candidates are compatible with all of the 5-candidates. Of course the coloring added to the 5-cluster is limited to the compatible coloring links of the 7-panel.

The benefit of expanding a cluster is to trap candidates and confirm one color. Here is the expanded cluster as the trap sequence begins.

The traps carry KD 415 past the first Sudokuwiki advanced move, but not to a solution.




Instead, three irregular XYZ-wings are found in the growing bv field to continue the blue/green expansion to a wrap of green, and a collapse.

Here is the first of these, a 376-wing where the weak link attaching the 36 wing is a grouped 3-chain. A systematic way to spot these without extensive searching is noted in the bv scan section of The Guide. An important element is the use of an XYZ map to limit consideration to the cell set that can form an XYZ-wing, without regard to cell location. Then for each possible set, you concentrate on building the necessary connecting forcing chains as winks.

The 367 hinge is placed on the map only because the bv 67 and 36 are on it. With the easy wink to wing 76, we are motivated to find a forcing chain to 36 on the grid.

On very difficult puzzles, it would be worthwhile to return to your XYZ map at the AIC building stage, when more types of wing attachments are available.

The second XYZ-wing is a regular XYZ wing, an occurrence more rare than an irregular one. The third XYZ makes up for it. One wing is attached by forcing chain, and the victim sees one toxic set member by forcing chain.

Finally, please be patient with the ads and with the Sysudoku practice of leaving something for readers to try, and backing them up next post. The latter is why the finish of KD 415 was held for the next post.


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Beware 195 Ends a Basic Review

In this final post of the review of Will Shortz’ Hard Sudoku v.1, Beware! Very Challenging 195 is solved in the bypass. The review table is included for comparisons.  A new mode of blog posts will include reports and links to updates on earlier reviews, beginning with the Insane collection from Krazy Dad.

On Beware 195, here is the grid as the fourth 3-fill ted in c6.





Beware 195 is in collapse as 3-fill c6[129] is marked, and we never get back to the previous 3-fill r8[589].

With the modest title, it might have been expected, but Hard Sudoku v.1 measured out to be the easiest of the three Will Shortz collections reviewed here. Three solved in the bypass, and the rest in line marking.

All while assembling candidates for advanced methods.

From one of the easiest to one of the most difficult outside of the monster class, the next posts are about an updated review, originally done in 2013, less than a year after the blog began. The  collection, Krazy Dad Insane stands out in its introduction to human solving refinements now being reported in a consolidated, more accessible form in the Sysudoku Guide.

The next post also marks a departure in the Sysudoku blog.  From 2013 it has been mostly a series of reviews on collections and the views of experts.  The 2012 year was taken up introducing advanced methods, and was written with very few sources of examples.

While such reviews will continue, readers will now be guided to update earlier reviews and navigation pages. The updated posts will remain in the original files by date. Current weekly posts will alert readers to the updates, and comment on them.

Also, where it corrects omissions and creates a more accurate account of Sysudoku methods, results from  Andrew Stuart’s solver, as accessed on, will be reported with acknowledgement.

The 2012 introductions to advanced methods still apply, but are now better accessed in the Guide, where the many refinements are explained in the same pages, and many more examples are cited.

So from now on, you can follow up on posted reports by looking up method explanations in the Guide by subject , and solving history to check your efforts in the original posts by date. Hopefully, most reviews can eventually be updated. Comment with suggestions are welcome.

The KD Insane review posts began with Insane 415 on July 16, 2013. No, there is no 405. The number 415 stands for volume 4, book 1, and number 5.  The review goes through the books in volume 4, picking on number 5 in each book. There is no book 0, but there is a book 10, and a review puzzle 4X5. Please talk me into doing another volume of Insane puzzles.

My advice is to start by going to, following links to Sudoku, Insane, v. 4 and trying book 1, number 5 yourself, just to get in the swing. The puzzles are free, but Krazy Jim wouldn’t mind a donation eventually.

Then go to the original post. If you haven’t tried it, use the monthly archive list to the right. On the page, you’ll see why each post begins with a brief summary. Click on The Insane Review Begins, and maybe bookmark that until you finish with the post. Read some, and you’re ready for the next post, which will comment on the updated solution.

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