A Pink Pattern Trial on Insane 495

LPO is delayed one post in the Sudokuwiki aided update of the KD Insane review, because two more effective methods are highlighted in KD Insane 495 of 10/08/13. A second ALS boomerang turns up, and after a similar pattern analysis isolates two orphans on the 5-panel, a trial of the 3 pink patterns on the 8-panel decides which candidate of the boomerang’s ALS 8-group is true, and continues to the solution.

Here is the freeform that demonstrates how a dumbfounding announcement by Sudokuwiki can be humanly verified. It was that 5r9c9 is an orphan, i.e. it belongs to no 5-pattern. That hits anyone defeated by twisted jungles of freeforms where it hurts, especially when looking at such an X-panel. But then, when you see that the South box claims the only remaining r8 5, and SW must have the r7 5, you’re more prepared to look at how far this goes. And it’s not far.

The announcement orphaned 5r7c  as well, so before looking at the 2013 post, you can freeform your way to that conclusion. We both can remember to check  three line banks or towers to see what gets through.

Now in a puzzle saturated with 8’s Sudowiki demonstrates that a cloud of candidates can have weaknesses. Two ANL strung together eliminate two from a column of eight. One uses  an ALS 8-group as a slink chain terminal.

Then we get the second ALS boomerang ANL in this series.  An ALS 8-group and a candidate member are terminals of the slink chain, confirming the group contains a true candidate.


Then when Sudokuwiki retires to a neutral corner to catch a breath, I pile on with a pink olive move very similar to the 5 orphan eliminations above.

Here are the 8-candidates that are left.  The two members of the ALS 8-group are involved in a pink olive slicing that is smothered in candidates. However there are only three patterns that follow the pink slice established in the first three lines. In a trial of these three patterns, 13 orphan 8-candidates are removed, and new clues and bv are created by the removals. That means the likelihood of a solution or a contradiction is very high. Either one is a large advance. A contradiction would remove at least the three pink candidates and create at least six clues. Both of these prior facts are evident in the grid as the trial begins.

In the trace to the solution, you can see where the continuing collapse is dependent on one clue. And as you step through the trial, you can see the near ambiguities that make Insane puzzles so hard.

Next report is on the update of KrazyDad Insane volume 4, book 10, number 5.  Sorry about bypassing the LPO examples in 495, but 4×5 fills in for a process demonstration. There are other places where it is more needed, and more decisive.

Posted in Extreme Solving, KrazyDad, Puzzle Reviews | Tagged , , , | Leave a comment

Sudokuwiki Gets a Second Chance

In a second updated review post on KrazyDad v.4, b.8, n.5 , Andrew Stuart’s Sudokuwiki solver gets the clue that the ALS boomerang left unresolved, and finishes the solution, with more instructive moves. You get a shot at that unusual clue.

Here is the 9-panel when KD 485’s ALS boomer discovers that 9r2c2 and 9r2c9 are a toxic set. It looks unpromising, until you take the toxic set into account.  Do that for yourself, then enjoy  the parade of Sudokuwiki moves in the updated post. There’s a BARN, an unaligned APE, and classic 263-wing.




A particularly impressive move is this ALS aided confirming ANL promoting  9r5c4. For you or me, it could have started as a possible boomerang, leaving 9r5c4 in search of a wink back into 1 to eliminate that 1. But since the cell is a bv, it also puts two slinks around 9. Actually it’s the same result, whether you list it as a confirming or eliminating ANL. With another candidate in the starting cell, it would be only eliminating.

When the solver invokes coloring for a single trap on 3r4c3, we expand the cluster as far as it will go, in pursuit of a possible wrap.  The 363-wing and Wr6 boxline elimination are reported on the same grid.  The wrap is not long in coming.

The next update report is on KD Insane 495, already up.

Posted in Advanced Solving, KrazyDad, Puzzle Reviews | Tagged , , , , | Leave a comment

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.

Posted in Uncategorized | Tagged , , , , | Leave a comment

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.

Posted in Advanced Solving, Extreme Solving, KrazyDad, Puzzle Reviews | Tagged , , , , , , | Leave a comment

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.

Posted in Advanced Solving, Extreme Solving, KrazyDad, Puzzle Reviews | Tagged , , , | 2 Comments

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.

Posted in Advanced Solving, KrazyDad, Puzzle Reviews | Tagged , , , , | Leave a comment

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.

Posted in Advanced Solving, KrazyDad, Puzzle Reviews | Tagged , , , , , , , | Leave a comment