This post reports on the value pattern trial of the last post, its results, and the relatively easy march to a two cluster coloring solution of Stefan Heines ultrahardcore 135.
The trial starts with the three 7 clues and naked pair E18. New clues are left in pencil marks, because they may be taken back. The cluster expansion can be taken back, as well. Still at the wheel, Beeby drives the trial on, with another hidden unique rectangle and a simple AIC ANL.
A tame looking AIC builder ANL
triggers a near collapse,
and a cluster explosion that wraps green with conflicts in c2, c8, c9, and the West box.
So 7r1c2 fails, leaving two 8’s in r5 and no 8’s in the West box.
We have to give it all back, and restart with the alternative 7r2c2 as a clue, dropping its slink partner, 7r2c8.
The cluster resumes at its pre-trail level. Tracing to the grid below,
NW7 produces three clues and the naked quad, which removes 27r7c9, allowing the hidden triple in r7. Clues are marked as real clues now.
It takes an AIC Almost Nice Loop next. Beeby’s note labels it a simple chain. But when there’s a weak link node, it takes an AIC building level of motivation to search it out. Here it can be a 1-way or boomerang from either bv terminal cell. The 1-way target is the any 8 seeing the starting candidate. For the boomer, it’s a slink into the starting 8, or a wink into its cell partner.
Without the computer, there’s just too much haystack and not enough needle.
The pay is good, though. Follow up
produces a host of removals from two naked pairs and a boxline, with accompanying cluster expansion.
This opens a double hidden unique rectangle, adding two more bv. Look at the effect of each removal, with the slink on the other side, and with the other victim in place. Either 4 causes a reversable rectangle by itself, so both are removed.
Add the second cluster,
then do the follow up without removing the wrapped candidates.
You then see how red is wrapped, and why orange implies blue.
Here’s the solution grid in color
Next time, its on to ultrahardcore 179.