A Lite Update on Castillo’s Only Extreme 347

This post updates a solution by coloring trial in the review post of 12/19/17. A bypass of 6 4-fills resolves 3 of them immediately,  but goes no further than the original 3-fill only bypass.  Then we follow Beeby through a parade of AIC and ALS eliminations, while wondering if lite coloring will show up. Then lightning strikes, and we have something new to look out for as we add light coloring arrows.

Here is the bypass just before the resolution on c4. Following the trace, note how the three 4-fills were resolved.

The basic trace includes a hidden single and hidden unique rectangle.

The hidden UR is signaled by the 35 naked pair and the perpendicular 5-slinks. Something must be going on. Then you see that if the slink partner 3r5c7 is true, 5 is forced into and 3 into the opposite corner for two solutions on the rectangle.

Then when you get to the harder fills, you notice the many line slinks on the bv values there. You throw the colors on, and there is a very subtle trap, and a boxline removal as well. 

I’ll leave it there for you to explain, and slip the full disclosure in a little later.

I have Beeby along, and it finds the grouped nice loop, but removes the two 4’s only. In a nice loop, one end of link, strong or weak, is true.  Beeby finds the other two later.

On the next grid, 3r1c3 is trapped in the NW box by the blue/green expansion. 2r2c2 is caught in the boyfriend trap. It shouldn’t be in a cell with a blue, when a green 2 can see it. Blue or green, it’s toast.  Like earlier, when green made a hidden triple rejecting 9r2c7.

The X, XY AIC ANL works harder to remove another 2.

Now the easiest AIC of all, an XY ANL, makes a naked pair. Notice the blue/green expansions. Any lite trees yet?

In the South, the Naked Pair combines with another hidden unique rectangle and the blue green expansion to remove 3 candidates. A northerly Beeby ALS_41  creates a grouped pincer ANL.

Beeby’s ALS_38 collects the 8-candidate it missed in the nice loop.

Finally, the cluster hatches a lite tree. After Beeby’s grouped ALS_93 on the right and the ALS-wing on the left, we see a blue green expansion coming.

Now there’s room to show some lite trees. A fourth one combines blue lite 9r4c1 and green lite 9r8c2 to create a damaging naked pair.

That’s going to confirm 9r8c2 and 5r8c5. Careful, that doesn’t mean green is true. In fact, after

6r9c5 remains firmly connected in the blue/green cluster.

The follow up marking includes a green lite tree from 9r1c8, which finishes Only Extreme 347.  

If another candidate in the starting cell r1c8 becomes green lite, the green is false. If green is true, there are two green candidates in the starting cell. Green can’t win for losing.

Next week, let’s trek back to another of my favorite collections, KrazyDad Insane, to take another look at Insane 425, (volume 4, book 2, number 5) in the post of July 23 2013. The issue is the two cluster coloring of the last grid of the post. In the next post of July 30 (one click reaches it) the two clusters are merged by pattern analysis. But you can ignore that. With the lite coloring reported so far, you can do the merge, and much more.

The KrazyDad Insane review was updated in December 2018. But it didn’t change the merge technique, so you can ignore that.  What you shouldn’t ignore is coloring, which experts and coders have for too long after Andrew Stuart. Especially now, with its latest enhancement, lite coloring.

About Sudent

I'm John Welch, a retired engineering professor, father of 3 wonderful daughters and granddad to 7 fabulous grandchildren. Sudoku analysis and illustration is a great hobby and a healthy mental challenge.
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