## Dov Introduces Lite Coloring of ultrahardcore 311

This post finishes the lite coloring revisit of past trials with Dov Mittelman’s lite introduction. It leads to a solution of Stefan Heine’s UHC 311 without trial. This puzzle occupied 3 posts in the ultrahardcore review, starting with November 3. Dov’s solution begins at the first grid of A Coloring Trial Weakens UHC 311 of November 17, at the grid before the coloring trials.  I’ve added arrows for the lite trees, and the immediate traps and confirmation. I’m quoting Dov’s email of November 23. You can tell he’s been reading Sysudoku altogether too much.

“UHC 311 wishes to settle before going to trial.”

“Starting from the toxic orphan, in c2, 8(6,2) is light orange. 2(6,2) immediately vanishes in a puff of logic.”

Yes, 2r6c2 goes, because either red or orange is true.

“Also, we have a bridge between orange and green. Red and blue make a toxic pair. 5(9,3) storms off in a huff. “

“Light red can also grow, and 6(7,8) goes light red, bringing with it, in order, 1(4,8) and 1(5,5).”

The bridge at work in a lite trap. Note how the SE 6 group carries the red lite tree. Oops, my bad. I didn’t mark the c8 6 slink.

Now E1 => C1, for:

““The red-blue trap kills 4(5,5) and 1(8,5), establishing the 1-clues and expanding green-blue.”

Adding a lite blue tree from 5r8c1, blue light 4r8c9 and green 4 trap 4r8c7 to leave full blue 4r8c9, green 5r8c9 and blue 5c7c9.

As 5r8c6 is trapped, both 5’s in the South box become blue lite and blue is wrapped. Does that have consequence for red/orange? Yes, if orange is true, orange 8r6c2 sees green 8r6c5, its last candidate. So orange is wrapped. We have the clues of the color trial, without the trial.

Deleting the blue and orange candidates and trees, and promoting the green and red trees to full colors, we carefully pick out the second right page trial free solution among the 12 ultrahardcore review puzzles.

Deleting the blue and orange candidates and trees, and promoting the green and red trees to full colors, we carefully pick out the second right page trial free solution among the 12 ultrahardcore review puzzles.

Next time, we’re staying with this puzzle UHC 311 to revisit its AIC Building phase, and to show how AIC building can be organized for systematic, exhaustive exploration, without the human-like solvers.

And for the readers that have been looking at my early posts on Susets(10/25/11),  and ALS Toxic Sets(7/17,25/12), I’ll soon be updating and applying susets to generate the ALS map, and to duplicate by hand the review’s impressive solver ALS findings of 11/3/20 systematically and exhaustively.