Continuing the Box ALS Scans for UHC 311


This post continues with the box to box, row and column scans for ALS_XZ.

 The C and S ALS fit into one red/orange cluster with a trap. The clusters meet in cell r7c8, showing that blue or orange or both are true.

Box to box requires a plan to cover all pairings. Here’s one:

NW vs. N and NE, then NW vs. W and SW, Including W vs. SW, then

N vs C and S, including C vs S, then NE vs E and SE, including E vs. SE, then

W vs. C and E, including C vs E, then SW vs S and SE, including S vs SE.

It’s just single and lines matching singles and lines.

On my background grid with the new cluster installed, the C vs S scan picks up this ALS_46. The  restricted common curve was already there.

That’s not exactly what the Beeby solver found, and accounting for that teaches a new trick. The 8’s are so arranged, that removing cell r4c4 from the ALS drops exactly one value, or another ALS. In ALS W 45689/245678. we can remove 6r4c6 as well.

Moving on to box vs line, my biggest obstacle  is having to compare two maps at a time.  In ©PowerPoint, you can click View and pull up an extra window. Everything is harder on paper.

On boxes vs rows, we run into the same candidate being a single in two overlapping ALS. Here, with NW 246/2358 vs r1 25/256, a restricted common curve points out the problem, and the solution.

In the ALS_XZ , two 5 value groups would share a 5 value truly belonging to one of them because value 2 belongs to one of the ALS. Here that doesn’t happen. In the solution, candidate 2 belongs to both or neither of them. There is no ALS_25 here.

OK, let’s see if that answer gets us out of this ALS_XZ maze. It does. There are six possible ALS_XZ, but each is a pair of ALS with a common value group, just like the above. How about the 5 single  in red ALS? It can’t really see either of the two cell 5 groups in the two partner ALS.

That frequent occurrence dealt with, we’re into box vs line ALS_XZ. Nothing happens on r123 vs NW or c123 vs NW, or 123 vs. NE. Or c78 SE. Then ALS overgrown NE  159/2369 and r7 19/359 match on singles 3 we have ALS_39.

The removal leaves red and green candidates strongly linked. The clusters merge, and we choose to make red blue, keeping the expanded blue/green.

In the big cluster, we find a lite coloring trap. If blue, 2r4c2 is true and the c1 group is not, making r9c1 blue lite.

Next, an XY ANL or an ALs_52 captures three onlookers.

Next, hitting the Beeby simple ALS button repeatedly brings a series  of five ALS, expanding the ALS to a wrap. Map wise it’s a box to box, a bv to box, a column to column, a row to row, and a bv to box, and another row to row to a coloring wrap.

 Starting with the changes made to the ALS maps so far, you could follow map updates and get a feel for the effort involved.

Next time, we’ll see the play by play, and look into the place of Beeby’s ALS wings in Sysudoku with ALS maps.  

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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