A Coloring Merge Overwhelms Heine’s ultrahardcore 223


Continuing from last week’s post, Beeby’s  parade of ALS chains merges the clusters and a near BUG (Bi-Value Universal Grave) wrap finishes UHC 223.

Beeby does an ALS_12 with an aligned Z value group in r1 and a single Z value in the green ALS. In a DIY hidden unique rectangle, were 3r3c5 to be true, so would the adjacent corners be 8. Then 8r3c6 forces 7r8c6,   a value interchangeable rectangle, and an obvious double solution.

Continuing on a second 2-chain ANL we believe this may end, after all.

Beeby finds two ALS-wings, black and red, packaged in three ALS. This remarkable structure raises the prospect that other ALS aided ANL are invoked in the Beeby solver, beyond ALS wings.

Beeby follows this with two more ALS-wings. Here, one ANL terminal ALS value group is a single candidate, and the other terminal ALS value group is a box group. In the previous one, all terminal value groups were line groups.

In a surprising remap of the grid, a four member ALS-chain removes 3r3c3, with ANL terminals being a bv candidate and a box group. The removal triggers a Wc3 boxline.

Cluster expansions now show a merge:

red =>blue and orange => green.

The two clusters merge

Beeby doesn’t do color logic. On the merged grid Beeby finds this removal as a discontinuous loop, from 5r5c5. In coloring it’s a regular trap. 5r5c7 is false regardless of which color is true.  If blue, it sees a blue 5. If green it loses its cell to green 8.

The spotting rule is seeing one color and living with the other, out you go.  A   bit like marriage. As 6r5c7 turns blue, 6r5c9 is trapped.

With this extensive cluster, a color trial would resolve 223 immediately. Beeby brings back a variation of that four node ALS-wing, and a NWr1 boxline. Actually, you can leave out the orange ALS and make it an “Other” type of ALS-wing. The NWr1 boxline does the damage.

The follow up brings the cluster to the state below.

where NW3 erased 2r1c2, turning 2r9c2 green and removing 1, and turning 2r9c7 blue, springing the “home with blue and seeing green” trap on 7r9c8.

From there, 6r9c4, 6r7c9 and 6r3c7 are trapped, 7r9c3 turns blue, removing 1r9c4, for a blxline 1r7c9, establishing SE7 and wrapping green in r7c4.

The fully expanded cluster places everything. This time the human oriented  solvers of the review were stymied, until a simply conceived but arduous trial enabled one  solver to reach a coloring solution to ultrahardcore 223.

Next week it’s Stefan Heine’s UHC 267. It may have only one post on the trial schedule, because a trial solution comes next week. You can win it more space by sending in your description of a trial free solution. But in case you don’t have one, here is the grid for the following review puzzle, Stefan Heine’s ultrahardcore 267.

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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