A Bifurcated Coloring of the AIC Slink

In this post, the AIC slink produces an alternative solution of a puzzle originally solved by a rather extreme pattern coloring analysis. This solution demonstrates how the AIC Slink enhances the already powerful technique of Medusa coloring. The July 11 post introducing the AIC slink has been revised.  It now identifies the condition allowing coloring to be extended via the AIC slink, and names it the not-both condition.

Going back to the KrazyDad Insane review of July 2013,  I thought to have another look at my earlier reliance on the more advanced to extreme methods in that review. Have any innovations or experience since then made any difference?  I was shaken up a little by this data point. I may need to do more.

You have the givens grid, and possibly tried out the bypass route with it.  Anyway, here’s my basic trace.

The bypass makes it look a little different, but the result is the same.

This time, the 5-wing is detected earlier. The icons prevent the addition of 5 candidates in rows 3 and 7 as columns are marked.

Newbies, the font changed when Microsoft changed the definition of the font encoded into four years of slides. In the blog, you’re looking at pictures of those slides.

That earlier attempt amounted to a color trial which I now consider a “last resort”. There are only two possible 5 patterns, and the symmetric slink network of the 5’s allows a 4 candidate into the cluster. The bv slink in that cell is the terminal link for two XY chain slinks between the green 5 and each of the 3 and 7 candidates

Remarkably, the respective 4 candidates are false regardless of the not-both status of the two XY slinks. Take the 5447 slink. If 5 and 7 are both true, 4r9c2 is false. But if 5 or 7 is false (not-both), coloring extends to the slink and 4r9c2 becomes green.  This traps 4r8c3, asserting blue, and removing 4r9c2 anyway.

The same argument applies to the 5443 slink, removing  4r8c3. Thus blue candidates are confirmed.

Note that not-both is decisive in this case, whether it holds or not.

After a modest XY removal at right,

a coloring of the remaining candidates wraps with two orange 3-s in r9.

The red army mops up.

It was startling  to see this sudden collapse of an otherwise intransigent Sudoku, and to wonder how widely the coloring bifurcation of the AIC slink applies.

Next, a review of David Badger’s Sudoku 1001 Hard Puzzles, with preselected puzzles 1, 101, 201, . . . , 1001. The first checkpoint is 701, the only one that falls to the bypass. It’s not a pushover.