Closing Out ultrahardcore 133

Resuming on ultrahardcore 133 after two 1-ways, and a r1 naked pair 16 removing 16r1c3, and the resulting NW naked pair 48 removing 4r3c3.  Solver Beeby finds this ALS node AIC.

Starting from 6r2c9, it was a possible exit from the cluster for an ANL on 6. Instead, the 4-chain reaches a single in the C238 ALS 2689 with internal slink to single 6 for the ANL.

Beeby diagrams this as an ALS_46 as well, possibly because ALS chains were recently added to the AIC request options.

Next, a grouped 1-way through the cluster from 6r6c5 (black), is also extended in the cluster(red) to the 6 value set in r127c4 ALS 1469 seen by ANL victim 6r6c4. This is an  example of expanded possibilities of AIC building via ALS chains.

The follow up is modest, but we’ll take it.

After this simple chain,

Beeby describes a discontinuous loop 2 with a wink that doesn’t work:

(1)r7c4 = (1)r1c4 – (1)r1c1 = (1)r3c13 – (1)r89c3 = (1)r9c1 – (1)r9c5  => -1 r9c5.

Here’s what that looks like. A grouped 1-chain wants to go to a second group to reach the opposite terminal of an ANL and remove 1r9c5. But what about the red weak link? It’s saying that if group 1r3c13 is true then group 1r89c3 is false. Is that a fact?

Not exactly, if the group 1r13c3 is true, then 1r3c1 or 1r3c3 or both are true. If it’s  1r3c3, group 1r89c3 is false, and the red wink works. If it’s 1r3c1, then 1r9c1  is false and that makes group r89c3 true. Oops.

Fortunately, the removal is duplicated later before it is needed.

Beeby does bring an instructive example of ALS node AIC building. Starting on 6r3c3, you’re looking for a wink back into r3c3 but get lead away to 1r7c8. Are you going to see the possibility of an r8 ALS with single 1 and  a 6 group skipping 6r8c3? That would lead you to the effort to construct r8c2789 ALS 12346.

Now having the ALS, would the 4 value set skipping 4r8c3, and the 4-chain  from 4r9c3 back into the 6r3c3 lead you to this one?

If so, it leads to a simple chain, and a follow up trap.

Leading to an expanding cluster wrapping blue in c6. The solution is green.

Next week, we start on ultrahardcore 133+44 = 177.