Extended Gordonian Overreach


In this blog, the Gordon Guide’s deceptive attempts to promote Gordonian logic are further exposed. The renaming of extended unique rectangles, and the introduction of a purported new method, the Gordonian Rectangle Wing, are debunked.

While attributing extended unique rectangles to Francis Heaney, Peter Gordon nevertheless attempts to extend his Gordonian brand by renaming them “Extended Gordonian Rectangles”. It’s possibly a mistake due to his belief that he invented unique rectangles, but an appalling one.

gordon ERU 1The Gordon Guide illustration of Gordian Extended Rectangles is obscured by his primitive brand of pencil marking. Are there other 1,2 or 3 candidates on the grid that could interfere?

gordon ERU 2Sysudoku slink marking shows the situation clearly, and Medusa coloring illustrates the conclusion that removing 4r2c9 will allow two solutions (the cluster) if any.

This example does bring up an issue with Medusa coloring. In this case, a normal coloring trap elimination becomes a confirmation of 4 as a clue instead. It’s because the cluster is a closed set, shutting off any interference by other 1, 2, or 3 candidates.

gordon ERU Ex 24The puzzle Example 24 in the Guide provides a realistic setting for an extended UR. The extended unique rectangle is highlighted here by coloring.

But the example is hampered by two problems. Gordon acknowledges one, that the dead unique polygon plus, already defined as a S box slink marking, is an unnecessary distraction.

The second, more serious problem is remote pair which triggers a collapse by removing 3r9c4. The remote pair is as prominent as the unique UR.

gordonian rectangle wingBefore the set of 12 puzzles that end each section – a good feature of the guide – Gordon makes another grab for the Gordonian brand. He introduces his Gordonian Rectangle Wing with this diagram, sans the red dotted square.

He claims it is “sort of a combination between the Gordonian Rectangle and an XY-wing, which you will learn about in Chapter 9.”

Really? Sounds like a real innovation, that other experts don’t know about, doesn’t it? Like on the cover of the Guide.

gordonian forcing chainsGordon traces through it in the following words:

“Cells 47, 48, 87 and 88 form a kind of Gordonian Rectangle. We know for certain that a 3 has to be in either cell 47 or cell 88.”

Why is that? Oh, yes. The UR demands 3r4c7 or 3r8c8 be true. Gordon then walks down the forcing chains (without showing them), leaving the impression that the whole formation is a new one, to be recognized by solvers. Actually, it’s just what you do with the guardian candidates in a UR.

Gordon’s next comment  is telling:

“Naturally the same kind of situation can arise with Gordonian Polygons. The possibilities are almost endless. For example, in the above diagram (with the red dotted square), if cell 58, c8, 77, or 97 (the square) had 3’s in its candidate list, the 3 could be removed, since having a 3 in any of those cells would create two solutions in cells 47, 48, 87, and 88.”

True, but deceptive to a highly refined degree.

To state it straightforwardly, the unique rectangle requires a slink between 3r4c7 and r8c8 making them a toxic pair. Any 3 in the dotted square sees both of them and can be removed. Conversely, any 3 in the square will remove the rectangle’s guarding 3’s, permitting a deadly rectangle and a double solution. The two forcing chains from this pair happen to force 5r1c3 to be true regardless of which of them is true. You could say that 5r1c3 sees them both, via forcing chains. That is the original application of forcing chains, with the starting candidates from any slink.

Instead of instruction on these fundamentals, Gordon paints this fantasy of a solving pattern known as the Gordonian Rectangle Wing.  He would have his readers haplessly looking for another one.

The limited vision of Gordonian logic is illustrated by the fact that his UR slink completes an extensive nice loop, with many more elimination and coloring opportunities.

I regret having to go on with this review, but there are two more chapters in the Mensa Guide, now PuzzleWright Guide, which – considering the purpose of this blog – I can’t leave to the unsuspecting. But don’t let my downer review of Gordon’s Guide get you down about the blog. The year 2015 is going to be another winner. Perhaps you could do with a preview, in order to buy up and bone up, and be in position to beat me to the punch on basic, advanced, and especially extreme human style Sudoku solving.

After briefly reviewing the Guide puzzle collection, I review of Antoine Alary’s More Extreme Sudoku collection. It is a basic workout , with advanced and extreme conclusions. I’ve preselected puzzles 2, 24, 44, . . . for the review.

Then I’m jumping aboard the Weekly Extreme Competition train with a sysudokie review of puzzles 426 through 435. A WEX fan presented me with a perfect preselection scheme by handing out copies of 426 at the Akron Sudoku Tournament. The solutions are archived on the competition website, so you can pick out the starting clues from an archive if you don’t normally do them. This review is helping me come to terms with what “extreme” should mean.

From there we go monster hunting. My 2015 addition to the Sysudoku trophy room will be Fata Morgana. Review the exocet as defined in the Golden Nugget posts.

I’ll probably conclude 2015 by continuing a sysudokie encounter with Denis Berthier’s The Hidden Logic of Sudoku. It will be a popularization project, translating Denis’ practically inaccessible solving ideas into Sysudoku speak, and dealing with human vs computer issues along the way. A big 4th blog year, but follow those links, the Find It page, and the scroll bar back to the earlier stuff, and see how I got here.

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About Sudent

My real name is John Welch. I'm a happily married, retired professor (computer engineering), timeshare traveling, marathon running father of 3 wonderful daughters and granddad to 7 fabulous grandchildren. The blog is about Sudoku solving. It covers how to start, basic solving to find candidates efficiently, and advanced solving methods in an efficient order of battle. It is about human solving methods, not computer solving.
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