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.