This post returns to AIC building after an encounter with a spontaneous ALS led to expanded coloring and a color trial. That will be normal under a plan of incremental ALS mapping.

The confirmation of red had the follow up of (N7, N2, S8) , and the blue/green gets an easy ALS to expand the cluster.

ALS building picks up with a grouped ANL.

What follows is a sequence of 1-way AIC, almost a Philip Beeby exclusive form of discontinuous loop.

For DIY performance, you start this one with an AIC from 6r1c7 because  it sees other 6 candidates. They are off when 6r1c7 is on. Your AIC from there assumes it is off, and if it winks at any of those 6’s, they are off regardless. The AIC is effective in only that direction.

A second 1-way starts from 1r5c7.

Then one cell gets robbed by 1-ways 3 and 4.

Next post introduces the next Sysudoku step after AIC building in human solving of extremely hard Sudoku. It’s the building of ALS maps for rows, columns and boxes. These completed maps become an updated solving resource, like X-panels. Building the maps is a solving process in itself, with every added ALS possibly being a new ALS node extending the AIC network or a new ALS_XZ partner, making a removal.  

Let’s review Almost Locked Sets and the ALS_XZ. An ALS is a set of n cells in a unit(house) containing candidates of n + 1 values. Candidates of the same value within an ALS we call value groups. ALS value groups of a single candidate we call single values, or singles. Group strong links exist between the n + 1 value groups of an ALS. If any value set is removed, the n remaining groups are locked, that is, each remaining group contains a true (solution) candidate of its value.

Group weak links can exist between value groups and outside candidates or groups. There are  strong links between the ALS value groups. If one group contains no solution candidate all other value groups do. The group wink into the ALS, the internal group slink to a group of another value, and the group wink out, these form the  ALS node on an AIC.

Here is the Beeby solver’s first ALS_XZ for UHC 311. We build ALS maps to find all ALS_XZ in the unlikely event that we need them all. The ALZ_XZ is based on the above mentioned locking property of Almost Locked Sets. A pair of X value groups see each other. Here one is a 6 group and the other is a single 6. The group wink (dashed line) is generally known as a restricted common. Only one of the two ALS will have X = 6 in the solution. The other ALS’s value sets, including it’s 2 group, will be locked.

A 2 candidate victim sees (group winks) both 2 groups, so it does see a true candidate. The victim doesn’t have to be in either ALS. , and it can be a group.

ALS_XZ is a consistent source of candidate removals, but spotting them is difficult. Finding them exhaustively seems overwhelmingly so, because ALS are so numerous, and because you have to see the X and Z connections between two ALS for each one. But like AIC building, there is a practical way for human solvers to do it, when you’re not lucky enough to spot the right one, the ALS maps.

First time through, we tried all ALS on a single map. Once was enough. The practical alternative is three maps, for rows, columns and boxes. Binary value cells, our bv, are ALS and can partner to form ALS_XZ. They’re already on all three maps, so we just include them as we scan the map for ALS_XZ partners.