LPO Lettering on Insane 495


Advanced methods are exhausted on Insane 495 as I review the Insane collection on www.krazydad.com.  Basic solving results were reported on the previous post. This post demonstrates a new combination of LPO pattern slicing and pattern conflict analysis that gets me to a trial of two patterns and coloring.

LPO analysis was suggested by the small number of patterns in three numbers 1, 6, and 7. A pattern conflict could leave a single pattern with firm clues. I started with freeforms, of course, but represent them here in lettering panels because lettering did prove necessary.

IN 495 167 patternsThe 1a and 7b patterns conflict in r9c9, but more conflicts are required.  Here are the freeform panels for the numbers offering some prospects.  Remember I’m not a computer code, so I’m looking to deal with small sets of patterns.

IN 495 9 patternsMy pink olive freeform 9-panel revealed 4 pink and 8 olive, so I included only the pink patterns for possible elimination.

IN 495 4 patternsTurning to the 3-panel  and freeforming right to left, I get two appealing features: a single olive pattern, and six cells devoted to a single color. Both add to the power of a conflict.

IN 495 LPO conflictsAs on earlier posts,  I represent pattern conflicts in a set of tables. The conflicts with each pattern are listed as a separate row in the number’s conflict table.  Patterns conflicting with a pattern are designated by column letter and number on the row.  For example pattern 6c conflicts with patterns 3b and 3c.  Patterns 1b and 3b together imply 6b.

As to decisive results, the LPO analysis seems to provide little.  Pink pattern 4a can be rejected, because it conflicts with both of the available 7-patterns.  A similar result is not available for the 1d conflict with pink patterns 9abcd, because of the olive 9-patterns remaining.  We might remember that  (1a or 1c)and 6c => 3e.

IN 495 4b7b trialAlso, it is worth noting that if all but one pattern of a number m is in conflict with the same pattern of another number n, so that n fills all but one cell of a column of m’s table, then the confirmation of  that m-pattern rejects the conflicting n-pattern. This applies directly to the 7-patterns here, where 4b conflicts with 7a, so 4b => 7b.

We included number 4 in the conflict analysis, hoping to eliminate both 4a and 4b to make significant removals, and we now realize that a trial of 4b includes 7b. This trial turns out to be easy, as two of the 4b candidates force three cells of the Southeast box to share 1 and 5-candidates.  We get to remove those pink ab candidates from the 4-patterns, arriving at the grid below.

I have begun two coloring clusters on the post LPO grid.  Maybe you would like to see what you can do with Insane 495 now.

IN 495 coloring

One thing we know is that green and orange is not  possible, so blue or red is true,  making the seeing of blue and red capital offense.

I’ll continue to a finish next time, so it would be timely to look at basic solving on Insane v.4 b.10 n.5. I’m forced to go a little Roman and call it Insane 4X5.

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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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