## UHC 89 Breaks Out from a Monster Basic

This post coordinates the two DIY solvers used in the ultrahardcore review, choosing and interpreting solver methods and ignoring some removals to match the Sysudoku DIY order of battle. A series of early moves breaks the ice for AIC building that continues in the following post.

In Sysudoku Basic, what  do you get when the bypass zeroes out? Maybe, a good reason to move on to the next ultrahardcore? Not this time.

With the box marked grid alone, you get an example of box marking notation. It’s a set of slink lists, one for each value, with cause and effect expressed by string indenting.  S => SWt. N => S. You figure out what S, SWt, and N mean by examining grid results.

As you fill out your grid, what would you do next. Check the trace, did sudent do that? It beats reading explanations.

Now work your way through line marking. It’s about getting this grid constructed, one line at a time. What do those digit strings on the side and bottom represent? What is the order of processing lines in the trace? Why that order? It matters what corner or side a candidate is placed on. What does the cell position tell about strong links?  What is different about Close lines? Need the Guide? This line marked grid has a few encouraging signs, once you get it constructed. And every move is recorded in order in that grey box trace above.  How can that be?

Starting the bv scan, Andrew Stuart’s Sudokuwiki makes a find. It’s a BARN, a bent region quad with a single value in both box and line. One candidate of each quad  value is true, removing any outside candidate seeing them all.

Working with two very different solvers, a single solving pat requires  keeping  them synchronized on removals.

Neither solver does Bent Almost Restricted n-set (BARN), but Sudokuwiki interprets BARN as a form of WXYZ, and Beeby often duplicates them as ALS_XZ. It does this matching removal by ALS_53.

The first Beeby AIC is this 1-way from 3r6c4. In the 1-way, 3r5c5, which is false if 3r6c4 is true (the wink), is found to be false (the AIC wink) if 3r6c4 is false. In AIC building, this is also a boomerang starting from 8r5c5 and returning to the starting cell.

Beeby follows with a second 1-way or  boomer.

As a 1-way, it starts from 5r3c2, a bv partner that  sees 8 5 candidates cells and starts an AIC  looking to wink into any of them. It finds r3c2. You could branch off the AIC with slink or wink, as needed, to see if there are others. Or starting a possible boomer from 3r3c2, you have a more focused search with one cell as a target.

Next, a Beeby complex 1-way. 8r91c is a plausible start for a simple 1-way, given the starting chain just seen, but in the search for complex 1-way, when we get to 6r2c2, and don’t have a wink-to-slink combination to go further, we look back along the 1-way AIC for a wink out to a slink denying candidate. That would be a one of two candidates of the same value in the same box or line.

That process is so much more complex, that to reflect practical DIY solving, I ignore the removal until it is shown to be essential. It may get itself removed first.

I do the same with the next, and last practical DIY move, a grouped common ALS_98.

Luckily Sudokuwiki is aligned enough to step in with a couple of its digit forcing chains.

I don’t go along with the solver’s spotting rationale for digit forcing chains, or dfc, but they  can be interpreted as Sysudoku AIC building repertoire. On your left, and the puzzle’s right, is a grouped boomer from 7r6c8.

Then another dfc,  a twin grouped boomer from 3r6c7.

Looking at the full grid, the 2 removal from the triple makes a hidden pair E27 removing 4r7c7 and the boxline Er7 carries away four  more 4-candidates.

This leads Sudokuwiki to a coloring trap  on 4r7c3, and an APE that may be hiding something.

It rightfully discards 26r9c8, whose combinations with all r2c8 candidates see two value sets in one of the ALS. So why couldn’t any candidates of r2c8 be discarded?

Because they all form a combination with 4r1c8.

These two removals prove to be essential, but APE by cell combinations or by ALS_XZ  both require exhaustive search of cell combinations and their ALS sets. The problem for DIY solving is the number of possible APE cell pairs, and ALS aligned around each of them.

Another resource delayed for  exhaustive ALS analysis is ALS wings. Here is one available at this point, involving a box, line and a bv. The removal can be ignored, because it is duplicated before it is needed.

Next week continues on ultrahardcore 89 with a series of eliminations by a single box ALS working with bv. These  AIC with simple ALS nodes are favored above APE or ALS_XZ for DIY solving, because there is no searching. ALS are constructed as a means of continuing an AIC.