Insane 455 Does a Twisting Pink Olive Dive


This post presents a second demonstration of LPO pattern slicing,  which divides patterns of a number into two disjoint sets, often extending Medusa coloring in the process..  This new coloring LPO method puts Insane 455 down with two convincing blows,  after  the puzzle  has shrugged off the advanced sysudokie repertoire.   

IN 455 naked pairInsane 455 conceded only two clues in box marking, and emerged snarling.  Line marking started with  5 free cells. The first break was the naked pair shown here . 

No more concessions were forthcoming in basic solving:

 

IN 495 basic traces

IN 455 LMWith nothing to else to the point of coloring, I’m showing, as a basic checkpoint grid, my attempt to start two clusters, and with AIC hinges.  It’s looking grim as I turn to my extreme weapon, LPO, to inflict some damage somewhere.

Starting with the 4, 6 and 9 coloring at the lower left of the grid, the 4-pattern freeform enumeration is  below.

 

IN 455 4 lpoFreeforms are drawn left to right, taking advantage of the slinks in c1 and c2  to divide patterns into blue and green sets.  Its pink olive analysis, but with Medusa colors.

Fortunately there are only two blue patterns, and these share five 4-candidates exclusively, that is to say,  with no green patterns.  The blue/green cluster can be extended by coloring these candidates blue.  In the C box, blue patterns are limited to r5.  The blue candidate in r3c5 further limits the blue C candidates to two.

IN 455 4 patsNo green pattern includes  r6c1 because a green freeform crossing this cell cannot visit the East box.  The green patterns visiting Er6 must also include r4c1. Four candidates in the C box are orphaned.  Very effective.

It’s a good idea to track what else is happening on the bv map and the x-panels as pattern analysis results come in.  Here, the 4-candidate coloring enables a 348-wing that failed before.  

IN 455 ANL boxlineThe removal in r6c1 adds a bv to the map, and enables  an XY-chain ANL, leading to an SWc3 boxline removing two more candidates.  This very productive pattern slicing was not enough to get anything started, so we continue with the 6 patterns, based on the expanded blue green coloring.

 

 

 

IN 455 6 bluegreen LPOStarting freeforms in r8, where we have a colored slink, we discover five blue and two green patterns.  Two of these can be dismissed for conflicting with the blue 4-candidate in r3c5, but there are no additional candidate eligible for coloring.

There are, however, other slinks available in the 6-panel, and therefore,  additional ways to slice patterns, and expand coloring.

 To illustrate with a simpler case,  compare the two different sets of freeforms below, defining the same Insane 455 5-patterns.

In the left panel, freeforms are drawn left to right, as in the 6-panel above. There is one pink and two olive patterns, with three candidates eligible for color. 

In the right panel, with the freeforms drawn top to bottom, the same patterns are present, but they are represented differently by the freeforms.  They are also colored differently, with four candidates eligible for colors. Patterns are divided  into two sets, in both panels, but not the same two sets.

This suggests that we might get a different result by redrawing free forms  of the 6-patterns in a new direction.  I use my pink olive colors for this pink olive analysis.

IN 455 6 po 1Would you like a pink olive in your next martini? Here is the next best thing.  In this division of 6-patterns there is only one olive pattern.  It contains the blue candidate, and a 6-candidate in the same cell as the blue 4 candidate of r3c5.  What does that tell us?

It tells us that the olive pattern is false.  Since it is the only olive pattern, every candidate on it is off limits for pink patterns, including the blue candidate.  We have already accepted  the blue candidate, but since it creates a blue conflict, we reject the olive pattern that includes  it. All of the olive candidates are therefore orphaned, and all of them, other than the blue candidate, can be removed.  Another remarkable LPO slicing result.

IN 455 naked tripleWe can hardly expect a puzzle, even an Insane one,  to survive this. The cluster expansion from the 4-pattern analysis generates this naked triple.

Then it easily expands to force two green 1-candidates into r5, wiping out all green candidates.  Blue quickly proves orange and its time to move on.

Come back next week, after trying out Insane  v.4 b.6 n.5. and keep your Powerpoint crayons sharp, especially your pink and olive ones..

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About Sudent

My real name is John Welch. I'm a happily married, retired professor (computer engineering), timeshare traveling, marathon running father of 3 wonderful daughters and granddad to 7 fabulous grandchildren. The blog is about Sudoku solving. It covers how to start, basic solving to find candidates efficiently, and advanced solving methods in an efficient order of battle. It is about human solving methods, not computer solving.
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