## BV Scan Satisfaction in Saturday 2

This post continues the visit of Sudoku Satisfaction readers to Sysudoku with a tour of  advanced method principles applied in a Sysudoku solution of Satisfaction’s Saturday 2 puzzle. The roles of Rick Seemel’s Solution Rectangles I – IV in the Sysudoku Order of Battle are identified in this tour.

Welcome back, Satisfaction readers, for the final session of your Sysudoku tour. We hope your Sudoku satisfaction is strengthened and expanded by the tour, and that you will return to explore detailed explanations, examples, templates and reviews available at Sysudoku.com.

Before we resume with some advanced (after inscribing) attacks on Saturday 2, are there any questions?   .  .  .  Yes, what is a fish? And is the X-wing really a fish?

Sysudoku describes a fish as a competition among parallel lines for positions along the line for candidates of a single number. In a regular fish n lines make the case that they must have n or the positions, and other lines must give up those positions. Mathematically, it is another form of subset. Sudoku has many fascinating parallels of this sort.

We say “regular” because there are many irregular forms of fish. I suggest an overview trip to the aquarium in 2012 and following posts.  The X-wing is not well named. The X generally means one number, but that applies to all fish.  The X-wing is a regular fish, n =2, and it doesn’t fit in the wing family.

Oh, I might as well say it now, Satisfaction’s Solution Rectangle I is often an X-wing. Could we have that slide of Friday 2? Thanks.

Here is the Friday 2 3-wing, as we picture it. Columns c1 and c6 must have positions 3 and 8. I realized that as I marked r8, but if I had missed it there, I would not have going over columns in closure.  Columns 3 and 4 must give up 3 positions, leaving only one in c3. Game over.

The diamonds mark eliminations and the fishy icons point in the direction of eliminations. Wouldn’t you like to throw away your eraser pencils now?  I should mention that Satisfaction’s  Example 8-2 SR I might not be count as an 8-wing in the fishing tournament, because it is laced in box marking. I called it a hidden dublex. Since the permitted 8’s in SW and S boxes are blocked from r7, the SE box has to provide one.

On to Saturday 2! This puzzle shows off several of the advanced solving stations at our plant. By the way, “advanced” here doesn’t mean “hard”.  It means “with all candidates”, i.e. after line marking (inscribing).

We’ll just walk it through. Follow me. Please don’t touch the viewing window glass.

Puzzles first come through a unique rectangle screen, which removes candidates that would otherwise generate a glaringly obvious multiple solution. Satisfaction addresses some of the six regular UR types(see Tools on bar menu) , as an SR II.  Saturday 2 came through unaffected.

The next scan is for Sue de Coq, APE, BARN or ALS-XZ removals. Saturday 2 had a Sue de Coq infection requiring the removal of three candidates. “Sue de Coq” is actually the pseudonym of it’s discoverer. The solver writes a logical prescription for the contents of a chute (slot) with two alternate pairs of candidates forced by matching bv (bi-value) cells in the box and line of the chute. In this case,

Sc4 = 2(1+9)(3+4),

that is to say,  2 and (1 or 9) and (3 or 4). Now in c4, cell r1c4 must supply the remaining 3 or 4, so 4r6c4 must go. Likewise, 1 and 9 in S must go.

Other forms of Sue de Coq are detailed in Sysudoku, including one form developed right here, for trials.  What are trials?  A trial determines if a set of candidates, assembled for the purpose, are all true or all false. Its what we do when we don’t know what else to do.

Almost Locked Sets (ALS above) have a role in Sue de Coq.  Two of them can form an ALS-XZ with one or more toxic sets. APE is another way for bv to nibble candidates off of an aligned pair of cells. BARN is a form of bent (dove tailed) naked(plain) set of candidates in a union of a box and line. All of these are installed here at Sysudoku.

We watch now as Saturday 2 goes through the XYZ-wing machine.

An XYZ-wing is a hinge cell with candidates X, Y and Z, with two bv wing cells, XZ and YZ.  The X’s and Y’s are wink (weak link) partners. One of the Z’s is true, because if neither of the wing Z’s is, then they strip XY from the hinge, so the hinge Z is true. This makes the Z’s what we call a toxic set . “Seeing” all three gets you deported. The rectangular form of the XYZ-wing does fit the definition of Satisfaction’s SR IV, but seldom has victims.

Saturday 2 escapes unscathed, but not before showing us a valuable advanced tool, the forcing chain wink. We call this an irregular XYZ-wing, or iXYZ, because one of the wings is attached to the hinge by a chain of links. It is an alternating forcing chain (AIC), in this case an X-chain (single numbered links). In our grid diagrams, dashed curves denote winks and solid curves, slinks. Following the chain from wing to hinge, If 1r9c4 is true, 1r9c3 is false, so 1r7c1 is true, so 1r3c1 is false. The wing 1 sees the hinge 1. It’s a wink. Empty Rectangle(ER) is a special case of the forcing chain wink.

How about a look at Sysudoku’s XYZ control panel? Forcing chain winks in advanced methods is a distinguishing feature of the Sysudoku brand, but Saturday 2 is not impressed. I couldn’t find a 4-cano that “sees” all three 4’s of this iXYZ-wing’s toxic set (the squares). Want to try?

The XYZ map starts with the bv cells, then cells of three or four candidates are admitted to the XYZ map if wing components are available. As each hinge is admitted, the full grid is explored for AIC attaching wings to hinges, and when successful, outside Z numbers to toxic sets. Failing hinges are crossed off. At least my attention is focused on one task at a time.

Another tool of the same nature is the Sysudoku XY Rail for XY chains and loops. Starting with the same map of bv cells, draw all the curves you can through and between bv partners and between cells on winks. XY -chains lie along these curves. There is a slink between bv partners (think about it) and treat every link between partners as a wink. Slinks are winks as well (think about that, too). The result is an alternating chain, the simplest form of AIC.

Saturday 2 provides an excellent example. On any AIC, numbers  that match at the outer ends of slinks form a toxic set. One of them must be true. The reason is evident here. If 3r2c1 is false, then 2r2c1 is true, as is 9r2c6, 1r7c6, as is 4r9c4, as 3r1c4.  And reversing direction, if 3r1c4 is false, 3r2c1 is true. The diamonded 3’s see both.

After you draw it, this XY-chain looks complex. But it’s not. You don’t search for these things. You construct them one link at a time, along a guiding curve,then interpret the results. You only search for victims.

Three- cell XY-chains have an additional name, XY-wings. They work the same, of course. In Satisfaction, these are SR IV .

Before we leave the bv scan floor, I think we should take a short break. The cafeteria is right over there.  Meet you here in ten minutes (next week).