This post completes a survey of ALS-wings in the review of Stefan Heine’s ultrahardcore collection. The study was to determine how ALS-wings can be constructed as ALS maps are built. This post covers five more examples in UHC 443 found by Phillip Beeby’s solver. The survey shows that all of the ultrahardcore ALS-wings are constructed in the systematic ALS mapping process.

Ultrahardcore 443 and 487 were added to the review when the 400 puzzles I based my selection on turned out to be 500. It turned out well.

In 443, this severely overlapping ALS-wing defies graphical display. My rendering of Beeby’s notation is

(5=1)blue – (1=8)red – (8=5)green => -5 r6c1

A possible remedy for the congestion is a modified grid giving the congested row an extra line. Ahhh! That reads better.

The next column vs box ALS-wing had to be redrawn to fit in one column on the map. It differs from the 311 column vs row case above in that the bv is linked to the column ALS is already on the map and  and is roughly confined to one column. A possible remedy is to have the wink to the small green square to signal a bv attachment. Then the scanner can refer to the current grid to determine the matching value and its location for the ALS-wing.

This case is also covered by the preliminary scan for wink out bv and the match list. The preliminary scan puts bv 27 on the c1 red match list, and black ALS finds it there.

A second 443 example in which the row ALS entry on the ALS row has a small green square winking at 5r2c4 awaiting the scan from the red ALS being entered on the ALS box map.

Alternatively bv 59 is put on the blue ALS match list on its preliminary bv scan, the red ALS row scan includes matching bv partners on the ALS being scanned, in this case 9 on the r2 blue match list.

Continuing on 443, a bv ALS-wing, and another ANL with a value group at one terminal and one of its members on the other. The victim 7r6c1 sees both.

Why is it not a confirming ANL making 7r6c8 a clue? Because the value group 7 is a terminal, acting as a candidate. It is not an internal slink.

The wing happens with the blue ALS on the row map and as we draw the red one on the box map. On the way down the map, we already examined row ALS matching the bv partners of red single 9. Now we have to recognize this one as a value group  aligned match with red single 7. Then we can see the AIC around to it.

Here’s an easily read ANL. At construction time, blue and green ALS are on the row map when the red ALS  is added. Blue matches the red 8 first and goes on the c8 red match list. Then green’s 5 group matches the red 5, we note the match of blue and green value groups, and see the victim before we even copy the blue and red ALS to the grid.

One more. An ANL with bv 8 on one terminal and value group 8, including bv 8, on the other. The red ALS pulls up the blue one by either the match on exit 5 or the match on bv 8. Both matches are required

UHC 487, the last puzzle of the expanded ultrahardcore review, provided Beeby no ALS results prior to trial. This ends the review survey..

Have I made the case that ALS-wings, like ALS_XZ can be constructed with ALS maps? The will and patience to construct suset tables and ALS maps is a large order.

Next week we consider what  Beeby’s complex 1-way is and what a DIY version of it looks like.