KD Insane 485 Introduces the ALS Boomerang

This post is about the update of the 9/24/13 post on KrazyDad Insane v4, b8, n5. An unrecognized type of ANL found by Andrew Stuart’s Sudokuwiki solver is accorded a spotting technique, and a name suggesting the technique. When the solver exhausts its human techniques repertoire, a Sysudoku pink olive cluster trial breaks through for a solution.

As if the puzzle were aware that KD 475 was solved by SASdC trial, 485 starts with a cautionary example on how to set up a Single Alternate Sue de Coq trial with the second alternate represented by a bv in the SdC intersection. The trial is deferred for a last resort, and is never needed.

Then after one X-chain ANL, Sudokuwiki offers a series of six AIC building ANL, the last three on the very same set of links.

This last structure is an extraordinary AIC ANL. One terminal of the slink chain is a value group in an ALS. The other is a candidate member of that group. In effect, the ANL proves that the 9-group is a toxic set, with three victim onlookers.

Two writers with two different purposes in mind are called upon to account for it.  Andrew Stuart, who built Sudokuwiki and wrote its code, classifies the ANL above as a digit forcing chain. The updated post on Insane 485 explains why this labeling is no help to the  human solver.

The description above covers what it is, but that isn’t enough. I didn’t find this thing. My job is to account also for how a human could find it, or recognize it when it occurs by accident. The distinguishing feature for spotting has to be the ALS value group with one candidate member slinking out of the ALS. If the AIC beginning this way gets to a candidate that sees another value group of the starting ALS, the value group is a toxic set. A  name reflective of all this is the ALS boomerang.

The solver continues with good examples of a Type 2b unique rectangle, a naked triple, two esoteric boomerangs and a rare form of ALS toxic set, but  eventually gives up.

A pink olive analysis of the 2-panel uncovers two disjoint pairs of freeforms for cluster trials.

Dashed pink and solid olive are paired, then solid pink and dashed olive, to give two complete pattern clusters.

Each cluster is added to a small blue green cluster for a separate trial. In the trial of the solid pink and dashed olive cluster, the latter is quickly wrapped. In this example of graphic confirmation, orange removes all 6 candidates from r4.

Next time I report an updated second chance solution by Stuart’s Sudokuwiki solver, when given the ALS boomerang’s clue by a very rare and very human pattern analysis.

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Insane 475 by Sudokuwiki and SASdC

In the updated review of the KrazyDad collection of puzzles, Andrew Stuart’s Sudokuwiki solver is a backup on advanced solving, except in irregular XYZ, coloring, pattern analysis, and trials. Prior to the update on Sysudoku review of Insane 475 in these areas, the post of 9/3/13 interprets the Sudokuwiki solving path, noting two areas of concern, given Andrew’s intent for Sudokuwiki to emulate humanly practical solving techniques. The second post, of 9/17/13, reveals a pattern slicing analysis  requiring too many trials, and reports the success of a more decisive Single Alternate Sue de Coq trial.

After two almost nice loops which Sysudoku identifies for spotting purposes as boomerangs, I’m inclined to name another new form of ANL, again an aid to spotting. One terminal of the ANL is an ALS with a single candidate value removed by an incoming wink. The victim sees the resulting naked pair. To call attention generally to this kind of AIC node, I call it a subset node. The strong link is between ALS value groups in the subset.

The corresponding Sudokuwiki message carries no spotting insight. That is the first concern, that the message reflects the solving code of the solver, but not the filtering necessary for practical human solving.

A second concern is that in the Sudokuwiki explanation of this example. It is treated as a loop around 2r8c1 such that wherever you start, the AIC in each direction forces 2r8c1 to be false. The two directions are obtained by choosing a digit on the loop and assuming it true, then false. In an AIC that sets the two directions of inference travel. Sudokuwiki messages use Stuart’s label, a “digit forcing chain”. That term has no added meaning, because you have to discover the almost nice loop before you identify a digit on it.

Next the Sudokuwiki path includes two cell forcing chains. Here is the second one. It is easy to explain in forcing chains, but impractical to find. Three forcing chains leave the candidates of r4c5 and terminate on 2r6c6. One of them must be true, so 2r6c6 must be false.

For your own experience with the impracticality of this, start at the top and send forcing chains out from every candidate of cells having three candidates. Similarly impractical is Stuart’s unit forcing chains sending forcing chains out from every candidate of the same value in a line. The solver also includes the special case for a four candidate unit forcing chain, the “quad forcing chain”, as a solving option.

The review post follows Sudokuwiki  all the way, seeing many interesting variations, including Sudokuwiki’s simplified coloring.

In the next post of 9/17/13, we return to the grid at the first cell forcing chain to see if we can finish off Insane 475 without them, and find no suitable pink olive restrictions on 3, 4 and 5 panels. This affords an opportunity to demonstrate another type of trial in the Sysudoku repertoire, the Single Alternate Sue de Coq.

The return point grid has two SASdC examples. One is Wc1, that would be a Sue de Coq if 1r6c2 were removed. It would have a bv to match each of the alternate terms in the logical description of its contents:


It so happens that a second SASdC is available in SWc2 to remove that impediment. Its three values are described by

5(1+4)(3+5) + 835.

Why is that? The bv 14r2c2 prohibits 1 and 4 in SWr2. If its 1 or 4, its also 3 or 5. The third possibility is for 1 and 4 to be missing. That would leave 835. Now if 1 or 4 is not missing, 5r9c2 has to go, because either 1 or 4 is required. And that (1+4) and the bv form a naked pair, removing the impediment 1r6c2.

So what? We put 8r7c2 and 3r8c2 and 5r8c2 on trial, winning either the solution or a very damaging set of removals, or winning the c2 removals and more removals in c1. What are they?

This is how the 835 trial turns out. Sysudoku trials are traced out in a breadth first way described on the Traces page, and diagramed with arrows to document the contradiction. See if you can follow the arrows showing how the 835 placement forces a contradiction, and what that contradiction is. Thankfully, in most cases, such diagrams are simpler, with most of the trace being bypassed by the arrows.

The enabled Sue de Coq enables an ANL confirming blue and the collapse follows.

Next is a report on the KD 485 post.

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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. It’s Sysudoku practice to collect X-wings while assembling candidates. The X-wing enables a coloring cluster to be completed by basic logic. How many times have I forgotten to check for that?

After 465 gives the Insane password, a boomerang, Sudokuwiki gives up.  I had an irregular XYZ  wing to continue, but watchful reader Dov Mittelman had my back, and called out a faulty inference chain attaching a wing.  Fortunately, there was another way to get that XYZ clue, an almost nice loop with a very unlikely ALS node supplying a slink chain terminal.




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 beauty? 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, and the weakened KD Insane 465 is solved with  a coloring trial. It’s too easy to be fitting

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 KrazyDad.com 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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