## Advanced Stephens

The review  reports how much of the Sysudoku Order of Battle Paul Stephens covers , and evaluates the explanations of advanced techniques in his two currently available books, Mastering Sudoku Week by Week, and Sudoku Addict’s Workbook.  This post is about his “advanced” techniques.

In Weeks, the school year has three semesters.  The first is about starting basic solving the introduction of candidates.  The second begins with candidate lists completed, and continues with locked sets,  box/line intersections, remote pairs and unique rectangles as “advanced”  techniques.  The wings, fish, “colouring” , and limited inference chains are third semester, “extreme” material.   Stephens’ ”colouring” is not what you might think it is.

In contrast, sysudoku regards locked sets as a basic tool, explicitly using them to filter candidates prior to advanced solving.  Sysudoku advanced solving includes the above and considerably more.  As to extreme,  I’m thinking the sysudoku extreme repertoire begins with Limited Pattern Overlay.   Sue de Coq, APE, and AIC and ALS methods, beyond Stephens’ extreme limits,  are quite reasonably considered to be  simply “advanced”.

As mentioned in the previous post, Stephens’ explanations  of techniques are obscured by a shift in paradigm across the Atlantic.  Sysudokies  think of candidates seeing each other, and links and chains as consisting of candidates.   Paul thinks of candidates as relating to (seeing) squares, and squares relating to (seeing) each other.  Paul defines “relating to” as belonging to the same area(unit).  Sysudokies include ER and forcing chain vision in “seeing”.  It’s hard to visualize squares relating to each other via ER and AIC.

The paradym clash continues into the advanced semester.  Paul considers a remote pair chain to be a series of squares related to each other, each containing only the same two numbers.  Alternating squares on the chain are labeled “A” and “B”.

Here is Paul’s example with sysudoku marking.  “A” cells are tinted blue and and “B”cells, green.  The same two numbers are 6 and 8.  A candidate of those two numbers can be eliminated from any square related to (seeing) both an “A” and a “B” square.  Believe it or not, that is Stephens’ full explanation.

Compared to this blog’s remote pair post, this treatment is a magic formula from a sudo-guru on the mountain.  There is no way to explain how it works without alternate inference chains, which Paul describes next semester in the extreme solving course.  Describes, but again, does not explain.

I think that, even to accurately describe the patterns to be recognized in an advanced technique, you need to clearly explain how it works on a candidate by candidate level.  Universal  logic concepts like strong and weak links and inference chains are fundamental to the explanation.   Paul fails to make the necessary investment in these concepts, and it shows.  I don’t believe that anyone should invest their time on hard Sudoku puzzles looking for patterns defined by guru, do you?

Stephens’ second “advanced” technique is the unique rectangle, which he chooses to calls the non unique rectangle, or NUR.  Paul makes a useful distinction between internal and external remedies for the deadly rectangle.  Internal remedies remove rectangle candidates from a rectangle corner, while external ones remove  candidates outside  the rectangle.

Paul recognizes two types of internal NUR.  His Type A (Weeks) or Type 1(Addicts) is the same as Andrew Stuart’s Type 1, having a single extra candidate in one of the corner cells.  Instead of confirming the extra candidate to remove the possibility of a deadly rectangle, Paul interprets the remedy as removing the two rectangle numbered corner candidates from the square of the extra candidate.  It’s the same thing, but I think it is an extra mental step to get to the point from there.

Stephens’ Type B or Type 2 NUR  can have one or more extra candidates in both corners within a box, but with one of the rectangle numbers having no other candidates within the box.  In this case, number 9.  Since 9 must occupy one of the boxed corners, and an extra number 2 or 8 must occupy the other, 5, the other rectangle number, is removed from both corners.  This turns out to be a form of the unique pair in the Sudocue Guide, or Stuart’s type 4, presented in our UR post.

The only external NUR type presented in Weeks and Addicts removes the external candidate that sees the single extra candidate in the rectangle.  This is Stuart’s Type 2 and Sudocue’s unique side.  More NUR types are promised at Paul’s pages.

Do you get the idea that there are no standard names for unique rectangle formations? Yes, but the important part is recognize the rectangle, and then find the unique means of disturbing one of the bv corners.  In the blog since the Sheldon review, we have presented several external UR examples in which an external candidate is found guilty of forcing multiple extra candidates out of a UR roof, and pays the price.

Next time, we review Paul Stephen’s “extreme” repertoire, and you can back me up on what I found in Week 48.  Box marking didn’t rate a trace, but here is the grid for line marking.  Two columns are 3f, but they succumb immediately.

My line marking trace reads:

3f: r9=>Sns9=>(SW9, N9m), c3, c7.

4f:r8=>np26, r3, c6, c9.

5f: r1, r2, r4, r6=>np28.   6f: r7=>np14.  7f: r5. Close: c1, c2, c4=>(Nbxl2, np89), c5, c8.

Here’s what Paul says we should find after listing candidates: “Gridlock can be broken with a Swordfish, two non-unique rectangles, two XY wings and a forcing chain – or a six-square conjugate pair chain that solves three squares instantly and leaves the rest solvable by simple methods.”

Oh, I forgot to mention that Paul calls slinks “conjugate pairs”, and his “conjugate pair chain” is a simple coloring cluster,i.e. no bv slinks.  In Stephens speak, a forcing chain is what we would call an X-chain almost nice, eliminating loop, i.e. an X-chain with toxic end candidates, plus a victim. That is a radically  narrow definition of the term.

Perhaps you will find all the above in Week 48. I’m still looking for some of them.

For the next post, let’s go for the bv scan on Week 48.

## 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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### 2 Responses to Advanced Stephens

1. Big says:

I just found my copy of Mastering Sudoku week by week. I will be following along.

• Sudent says:

Great! I’m hoping for some pushback from Stephens fans. It would be a sign of life from the Sudoku community.