The Pattern Slink


Here I introduce a new form of strong link, the pattern slink.  The letter assignment panel for pattern enumeration in LPO identifies such slinks.  Every unit induced slink between a number’s patterns identifies two mutually exclusive sets of patterns.  This pair of sets then are stongly linked wherever they occur across the letter assignment panel, producing new extensions of coloring clusters. Pattern slinks also create yet another form of shortcut wink.  Every candidate limited to one of the sets winks at every candidate of limited to patterns in the opposing set.

We will finsh off Unsolvable 40 with a pattern slink, but first I have an obligation to checkpoint sysudokies who  followed up on my suggestion to tally 1-patterns conflicting with all previously derived pattern sets.  The addition of 1 patterns of the previous post to the conflict table gives:

The tallies of 1-patterns against other numbers yields promising results:

Pattern 1k is removed for conflict with both 8-patterns.

Patterns 1cehi must go,  for conflict with every 5-pattern. 

No immediate eliminations, and therefore no cluster extensions, follow from these pattern eliminations, however.

Also, the tallies produce  1l => 5c, 1bd =>6a, 1bd =>7i.  These are pistols aimed at the heads of 1bdl.  If 5c proves false, 1l is also.  If 6a proves false, so is 1bd.

Although the 1-pattern tallies were a good illustration of follow up LPO results, they are actually not required for defeating Unsolvable 40.

As I was assembling freeform and letter panels for a final shot at Unsolvable 40, I was looking at the letter assignment panel for 7 in the previous post, and thinking about how letter panel coloring and grid coloring differs.  We can know the color a panel will have to be, but we cannot use coloring to extend a cluster.  Basically, this is because one of the cluster colors must be true, but of the many patterns, only one is true. Deep in this troubled state of mind, I suddenly realized that opposing patterns  form a pattern level  slink that can extend color clusters beyond Medusa coloring.

This version of the 7 lettering panel shows how pattern slinks extend Medusa coloring.  Pattern slinks in r3 and c3 determine that either 7i or one of the patterns 7abdf is true.  That fact creates a strong link between all 7i and 7abdf candidates, allowing the cluster to extend “around the corner”, linking candidates in different units.

Color traps and color wraps apply to the pattern extended clusters.  The patterns 7cegh were eliminated by the tallies of the last post, but are also victims of color traps when the above purple/pink cluster is transferred to the original letter panel.

Back on the grid left by the dismissal of four 7-patterns, we might be able to find further effects of the extra slinks on the 7 number.  This fails, but there is a new AIC hinge at r9c7, and and now we have additional the cluster logic:

!(blue&orange) &

!(pink&orange)&

!(blue&pink)&

!purple&green. 

The last term, marking pink and blue as toxic, dooms the 7-candidate in r6c1, and its color, orange. This is enough to plant Unsolvable 40 with the daisies.  The 1-patterns are not needed.  I’ll checkpoint you next post on the finish of Unsolvable 40 via LPO and the pattern slink, without trial and error in any form.  Have a go at it! The ending is not remarkable, but the route was momentous. For me, anyway.  Did you enjoy it?

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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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