Ultra 133 “Simple” Chains and Discontinuous Loops

After an productive naked triple in line marking, and two bv scan methods, left page ultrahardcore 133 starts AIC building with Beeby “simple” chains. Then we take in two “discontinuous loops, i.e. simple 1-ways. The decisive ALS AIC’s and colorful finish are held for the following post.

Here’s the basic trace,

and the grid after line marking, but before the removals. Beeby does the naked triple silently, but it’s worth a picture in my book.

On the grid is a hidden UR, and a BARN. In the unique rectangle, if 1r7c2 is true, 2r7c8 is, 1r8c8 is, and since 2r8c8 is not, 2r8c2 is, and a second rectangle solution is made by interchanging 1 and 2.

Sudokuwiki notes label the BARN a WXYZ, and Beeby duplicates the removal with a short AIC ANL.

The follow up

brings the first of many Beeby simple chains. The first two, a 9-chain and  its extension.


we get a  grid spanning 4-ANL, an AIC ANL removing 8r5c6, and extended AIC ANL removing 8r5c3.

Beeby’s simple chain series ends with this quick 1-way, after a long search fails to find a “Continuous” AIC. The 1-way removal happens to trigger a Wr6 boxline netting two more 6 candidates.

Why are  continuous searches long? Beeby’s continuous category includes any nice loop, without reference to a starting point, The search is expected to capture  any wink back to any candidate assumed false or slink back to any candidate assumed true,  when starting on a slink partner. If the search were limited to a wink back to the starting point, it would be much quicker, having a single target for loop back. But that’s not what users want. Users can accept the limited targets of the Boomerang and the 1-way. And the search can end when the last target is bypassed.

After one more simple chain, an AIC ANL, and it’s follow up

Beeby slips in another basic subset without comment, a West box naked triple.

With the cluster expansion trap of 9r7c6, which Beebie does (grey) by taking cluster slinks as winks, Beeby gains a slink into a simple  chain ANL.

Let’s wind up with this “discontinuous loop 2” (1-way) removing 1r1c2, which also functions as a boomer, coming back to wink into the starting cell. Since Beeby gave that label to the previous 1-way with extra removals by boxline, it must mean simple 1-way plus anything else. OK.

After the naked pair removals following this “type 2”,  ultrahardcore 133 continues with ALS AIC and a Beeby move you may be able to straighten me out on.

We’ll bring it in without a trial next week, Tuesday at 2.

About Sudent

I'm John Welch, a retired engineering professor, father of 3 wonderful daughters and granddad to 7 fabulous grandchildren. Sudoku analysis and illustration is a great hobby and a healthy mental challenge.
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