## A Bv Scan of Week 48

Here we checkpoint the sysudoku bv scan on the blog homework puzzle, Week 48 in Paul
Stephens’ Mastering Sudoku Week By Week.  The scan includes Sue de Coq and APE, two
techniques ignored by Stephens’ books, and two techniques, XYZ-wings and
XY-chains, which he considers “extreme”.

After the line marking we traced last post,  there is UR23 in r79c25. It is a Stephens type 1, yielding a 6-clue in the South box.

Remarkably, this clue generates one of Andrew Stuart’s avoidable rectangles  on numbers 2 and 6 in cells r78c48. Avoiding it requires the  8-clue confirmed in SE. Maybe that accounts for Paul’s two NURs, but I find no mention of anything like the Avoidable in the Stephens’ books.

On another front, Stephens’The Sudoku Addicts Workbook endorses the BUG+1 technique of resolving the “almost” Bi-value Universal Grave.  Stephens agrees with Stuart on the resolution by confirming the candidate occurring three times in its row, column and box.

Continuing with Weeks 48,  the two NUR’s  yield:

S6=>(S2=>(S3=>(SW3, SW2), SE6), SE8=>SE2) .

By keeping the line marks updated through this, we come upon this 8-wing:

When we scan the chutes for Sue de Coq and APE, two live SdC turn up. In SdC NWr2 = 2(3+4)(6+8), the ALS 689 of r2c59 forces a 6-candidate from the row remainder, once we confirm the alternatives cannot be missing. Alternative (3+4) is easy, and implies the removal all by itself. The alternative (6+8) is difficult.  We use forcing chains from r2c9 to show that an SdC NWr2 of 342 forces two 8-clues in c4.

In SdC Wr4 = 9(1+8)(4+6), the row remainder ALS 346 locks in both alternatives. The bv 46 in the box remainder pairs with the (4+6) alternative, removing the 4-candidate.

This is as tough as Sue de Coq gets, but each step points the way to the next.  It’s not extreme.  Stephens skips the well known Sue de Coq and APE. Then when gridlock arrives, he turns to Nishio. More on that later.

Cranking up the bv map with two more bv from the SdCs, I am reminded of Stephens’ reluctance to pencil mark, because I’m sure the same reluctance carries over to aids like the bv map and the x-panels.  To each his own, but IMO, many solvers would enjoy expressing themselves sysudokulistically in PowerPoint graphics.  Maybe I should add a “how to” page on that, to show how easy it is.

As an example, take a look at this. An ER aided 468-wing and a 13-link XY-chain bringing two toxic set removals.

In the 468-wing, the victim sees the hinge and the 68 bv easily, but requires an ER periscope, shown as a forcing chain, to see the 46 wing.  This goes way beyond Stephens’ definition of “related to”.  Paul fails to include ER and the forcing chain as a way of being related to, i.e. seeing, i.e. forming a weak link.  This failing is due, in part, to the position that  squares see each other.  Also, Paul’s readers are hindered by his inept definition of forcing chains, which is considered in my next post.

The maroon curve in the grid above may be  one of the XY-wings Paul previewed. It removes the same candidate as the 468-wing. The blue section of the long XY chain removes a 9-candidate to imply N9 and N6. The  green extension removes another to imply NE9 and NE2. The second removals are redundant, but illustrate how multiple toxic sets occur along XY chains.

Stephens readers should take in the sysudoku bv maps  for Week 48 at this point, shown below. The XYZ map is for easy recognition of XYZ-wings, WXYZ-wings, and Death Blossom light formations. The hinges for these formations are placed among bv that potentially support them, for a detailed check. The Week 48 map shows two tests for XYZ-wings, one successful.  As solving continues, the updated map reveals newly generated wings and blossoms.

The XY track is the path along which all XY chains travel. Notice how the tracks limit the direction of travel .  After drawing these curves, XY road kill are collected systematically along the tracks.

Following up on the removals above, Week 48 collapses.  It is mortally wounded where the trace leaves off.

Next we parse Paul’s prognostication for Week 48, which was repeated at the end of my 3/16 post.  We will find out what he means by a “forcing chain”, a “conjugate pair chain”, and “colouring”.  We will also see a zombie version of the recently deceased Week 48.  Interested?