This post displays the column and box ALS maps, and scans for AIC the columns. The box scans are started, but get interrupted by an ALS coloring expansion.

We start with the ALS column map on ultrahardcore 311 . It was drawn at the first ALS_XZ found by the Beeby solver after ALS building.

Matching columns as we matched rows, we add column ALS left to right, and scan left from each column for a match on any circled singles or bv, starting with column 2.

The long ALS with singles produce many long internal slinks between different values, but surprisingly, no significant connections occur between the leftover AIC segments.

In c3 ALS 2345/25678, the 6 value group is marked. It’s because it’s confined within West box. That means it can form a grouped wink with single or value group confined within the same box. The 6 group teams with the single 6 in the red c2 ALS we just added.

Now copying the matching ALS to the AIC grid, we can see  that that 2r5c2 sees the box confined 2 group of the c3 ALS and all 2’s in the c2 ALS.

The mapping and scanning process has led us to Beeby’s ALS_62 we saw two posts ago.

We might have marked the 9 group in SWc1 for possible X matches in c2 and c3, and removed it when we got to c4.

There were no further matches in the column scans. Moving on to box ALS, did you draw some?  Box susets are different. Cell positions are numbered in keypad order.

If you got past that, your box ALS map looks something like this.

Marking for the ALS_XZ partnering scan has a new element. Lines are added to signal when a value group has line alignment. 

A Center box ALS starts a cluster can you spread it?

When partnering box to box, we can follow the keypad order, west to east, and north to south. First though, we watch for ALS extension nodes from each box.

In Northwest, another unaligned ALS expanding the cluster.  The internal 26/258 slink turns 8r2c3 blue, and the cell turns 5 green. 5r2c1 gets trapped.

The removal makes ALS r2 13/358 an ALS in the NW box, but the coloring expansion shown here leads to the wrong conclusions. Alignment with r2 is the reason. In r2 ALS NW r2 13/258 is in conflict with ALS r2 1379/35789. We have to forego the color expansion and 8 trap.

Next time we’ll update ALS ALS maps and continue with ALS nodes and ALS_XZ scans.