Cycling Blindfolded with the Guide

This post calls out Gordon Guide misguidance related to coloring, slink chains and the XY chain. AIC fundamentals are omitted in favor of ineffectual strategy and renaming of well known AIC formations.

gordon 32 LMFirst, lets checkpoint the basic solving of the Gordon Guide Example 32, through which we meet its “nonrepetitive bilocations”.

My bypass produced only N4, and box marking was similarly anemic. That left a demanding line marking. That must have been challenging for the Gordon guided.

A 7-wing was left in place, which eventually generated a naked pair 25 in r9, and NW2.

gordon 32 AICThis sets the stage for Gordon’s illustration of an AIC form he calls the nonrepetitive bilocation cycle. He calls it non repetitive, because two different numbers are members of the loop in all cells. We show the wink in each cell that makes this clearly an alternate inference chain. Its single AIC hinge is marked in the usual sysudokie way. The rest of the cycle is actually an AIC with winks connecting slinks of Gordon’s bilocation graph. Do you like my angry fish?

Gordon explains this elimination by going around the loop, which his way of making solving structures seem like procedures. He neglects to explain that the angry fish as a nice loop, making every adjacent pair of candidates a toxic set. The 57r7c1 pair is removed because the 5 and 7 see the toxic 4 and 9.

Gordon’s implied claim is that he found the angry fish with his bilocation graph. As always, he just points it out, implying that it’s quite obvious. If he showed what is actually involved, readers would have reason to complain about his Guide, rather than becoming discouraged about missing the obvious.

gordon 32 bilocation graphHere is the bilocation graph, which Gordon attributes to the web site of a Professor David Epstein. Take a moment . Do you see what it is? Now trace around it until you come upon the angry fish. Or don’t, if you value your sanity.

Those following this blog know that there is a much better way to represent this nest of slinks. Of course, Medusa coloring.


Unlike Gordon’s grid coloring, Medusa clusters are factual structures, not graphically supported guesses.  Coloring clusters are slink nets, organized into opposing armies, one side true, the other side false. And without the chicken scratches.

gordon 32 coloringIn this case, the candidates enlist in a blue/green cluster and most of those without connections to do that get into the red/orange cluster.

The green forces are proved false when two green 6’s are forced into r5. Then cell r1c5 shows that blue => not orange.

Blue and red candidates leave little else to decide.


The AIC is a fundamental concept of advanced solving, occurring constantly in many forms. The Gordon Guide conveys nothing about this important concept. Instead, in example after example, Gordon walks through the alternating strong and weak links, saying how this one is true, making that one false, making this one true, etc. That’s why those relying on the Guide may understand the turbo fish of the last post, but have no clue regarding X-chains in general, including the simple 9-chain ANL on the same grid. They also have no clue on where to start looking for another turbo fish.

In this blog, AIC were explained first as X-chains, their simplest form, followed by XY-chains, the automatically alternating and most frequently occurring form, with toxic set and nice loop eliminations working the same as X-chains. Then more rarely occurring general forms of AIC with inverted bv, mixed links and ALS nodes could be understood and constructed when needed.

gordon 32 railroadIn the Order of Battle, however, XY-chains come first, being more frequently occurring. They are made easy to find, even to exhaustively enumerate, by the use of a railroad diagram.

Here is a very  extensive railroad diagram from Guide Ex. 32. There are more connections to be made, but this enough to give us plenty of toxic sets to chew on.

gordon 32 ANL partyIn fact, we would have found a solution to Example 32 much easier with an XY-chain, and never had to look for a nonrepetitive bilocation cycle. Every repeat of numbers along the rail marks a toxic set.

A few of the decisive eliminations along these rails make the point.



gordon repetitive ANLGordon’s repetitive bilocation cycle, Example 33, has a single cell with one candidate in both slinks. The almost nice loop confirms that the candidate at the converging slinks is true.

It’s an AIC ANL, reversing the slinks and winks of an XY chain. It doesn’t actually require that the node cells be bv.


Either Peter doesn’t understand or conceals the AIC fundamentals of this example. I suspect the latter, as a means of pretending to publish methods that “experts don’t know”. I’m led to this opinion by the “Gordonian” claims which to this date Gordon seems to have escaped any censure from the Sudoku expert community.

gordon ex 34Gordon’s single example of the XY chain ends the chapter. It is not the frequently appearing ANL so prominent in Example 32 above, but the more rarely encountered nice loop. The XY ANL is a sad omission.

The last instruction chapter in the Gordon Guide is, appropriately enough, an apologetic defense of guessing. In an ridiculous final section, “To Guess Or Not To Guess” , Peter claims that Guide readers “now know everything”, and will be forced to guess only by “ridiculously hard puzzles written by someone who thinks guessing should be allowed”. This is an ironic “defense by offense” twist of logic that would make the most blatantly illusive politician proud. My respect for Frank Longo certainly dipped when I realized he had allowed his work to be promoted in the same paragraph.

mensa 775Speaking of Frank Longo, whom we awarded a superlative review for his Absolutely Nasty IV collection, our next task is to review his collection of 704 puzzles composed for Peter Gordon’s Guide. The 800 puzzles claimed on the cover include the sets of 12 puzzles following up each chapter of the Guide, which are, in effect, reviewed already.

I took every 75th puzzle, starting with 100. Only two of my preselected review puzzles reached the advanced level. To get in the mood, see what you can do with the only one I’m going to analyze in detail, number 775.

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Wings and Chains With the Gordon Guide

This post reviews the Chapter 9 of Peter Gordon’s Sudoku Guide, entitled Forcing Chains and Grid Coloring. The guidance is very limited, and what there is, promotes guessing as opposed to solving by logic.

XY wingThis verdict is confirmed in the first topic of the chapter, the XY wing. Going back to the Sysudoku schematic of the wing, picturing the wing and a victim candidate, I described it as a bv chain connected by weak links, in which a toxic set is generated. If either of the wing’s Z candidates is false, then the other wing’s Z has to be true. Since one of them is true, the Z candidate that “sees” them both is false.

Peter leaves the structure of the wing unspecified, but places it on the grid where the soft links are evident. When you try both X and Y values of the hinge, either value makes the outside Z false.

These descriptions may seem equivalent, but they are not. The sysudokie version expands easily into longer XY chains with matching end candidates, and into forms with weak links other than shared units. The Gordon guide version makes it to be a form of trial and error, which is fictitious, because if you recognize the structure, the result is always the same.

The Guide explains very few solving structures, but does explain the XYZ-wing. To do so, Peter introduces his concept of the “seeing”. A cell sees its buddies, which are its fellow occupants of its row, column and box. On that side of the pond, cells, not candidates, see each other.

The XYZ-wing is defined this way: “Any cell that is buddies to all three of the XYZ, XZ, and YZ cells cannot contain a Z.” Accurate enough, but what is he talking about? A toxic set of three Z candidates. It’s the outside Z that is the victim, not the cell containing it.

But why is a toxic set generated? Peter falls back on his forcing chain version: Whether the hinge cell is X, Y, or Z, the victim Z will be forced to false. We’d explain it that regardless of the hinge value one of the wing’s Z candidates has to be true.

Guide readers are to try X, Y , and Z and see what happens. Sysudokies are looking for possible “seeing” chains that tie together irregular wings or allow potential victims to see the toxic sets.

As to longer chains, here is the Gordon Guide’s advice:

“Sometimes you can find situations more complex than XY-wing or XYZ-wing where there are two possibilities, either of which leads to the same result. Here’s an example:”

An example of what? XY chains, and all other AIC are left out. Some guide.

So where do “Forcing Chains” of the chapter title come in? Peter seems to think that the act of trying multiple candidates of a cell to see what happens is a forcing chain. That would certainly be something experts don’t know about.

In the next section, Grid Coloring, Peter adds some helpful technology to picking a value to see what happens. Early on, I called this a truth net, and warned beginners of its nihilistic consequences. Grid coloring has nothing to do with Medusa coloring , the representation of slink nets intensely exploited by sysudokies. That “coloring” is addressed haphazardly in the next Guide chapter. Besides, Peter only applies Grid coloring to one value at a time, i.e. to X chains. Grid coloring is a little like the trials we use on very hard puzzles, except that it’s a single arbitrary value on trial, not a logically constructed set of values.

Can I mention, in connection with the bv scan, two more glaring omissions in this Guide? One is the Sue de Coq, a very effective elimination method. Even the verification of its structure solves puzzles.   The second glaring omission is any real help for finding all possible wings, or  chains of any type.

The title the final section in this chapter is Turbot Fish. You might be thinking that Peter will be talking about X-chains and loops. But no, it’s about his truth net, the grid coloring technique. Peter just wants to show us how grid coloring discovers a turbot fish. Ironically, the Guide is not published in color.

gordon find turboSo here is the turbot fish, Example 30, ready for you to find it. Peter even defines it for you:

“It requires five cells that are arranged so that two pairs of cells are in the same rows, two pairs are in the same columns, and two cells are in the same box. If three or four of the pairs are the only places where a particular number can go, you have a turbo fish. If there are only two such pairs, then it still works, as long as those two pairs don’t share a cell. “

OK, got it? Start grid coloring. What’s that? Oh, Peter didn’t mention it, but we are looking for an X-loop. That’s how five cells can have pairs of the same number in two rows, two columns and a box.

A pair of the only two places a number can go is a slink. Now sketch this out. Got a piece of paper? If three of the loop links are slinks, you have either an eliminating almost nice loop(ANL), with the two winks together, or a confirming ANL, with the two winks apart. If only two are slinks, then the slinks must have a wink between them, and the two intersecting winks eliminate the intersection candidate. The four slink case is an eliminating ANL, with the two slinks apart from the wink used as winks.

So we have solved Gordon’s riddle and know what to look for. But now can you tell me why you would do that by picking a candidate to be true and following it around the grid to see what happens? That’s finding a turbot fish by grid coloring.

gordon turboThanks a bunch, Peter, but I think we’ll just do an X-panel. The 6-panel reveals two Turbot fish that have three slinks and share two of them.

If you sketch in the slinks and fill in the winks, they jump out at you. Sysudokies don’t search for Turbo Fish or any other special type of X-chain. They construct X-chains and watch them form loops, and toxic pairs. The X-panel helps you focus on that. From the 9-panel, a simple 9-chain ANL removes 9r4c5.

The Gordon Guide doesn’t cover X-chains, but has room for a laborious search for the very specialized, rarely encountered turbo fish. A perfect way to discourage new solvers. Don’t give it to a friend, without telling her about these review posts.

gordon ex 32We’ll finish up our Guide review next time by reporting how Gordon overspecializes and fails to explain, alternate inference chains. AIC’s are a matter of some importance in advanced solving. Maybe you’d like to do the basic solving on his Example 32, which illustrates what he has named the Nonrepetitive Bilocation Cycle. We’ll checkpoint that, and tell you what it really is, next time.

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An Update on the Dublex Bypass

This first post of 2015 updates sysudokies on the dublex bypass, a preliminary stage of box marking introduced in late 2014. Experience now warrants that the bypass, as it will now be named, be accorded a permanent starting position in the Order of Battle. Earlier assessments of its worth, as opposed to going immediately into full slink marking, are revised. An outstanding example from this week’s Sunday 5-star by Dave Green shows off the bypass at its best.

I had decided give myself a break, and put Dave’s Sunday Sudoku on the template for a relaxing hour, before doing the last minute editing of this very post on the Gordon Guide review. I soon discovered I had stumbled on a much better start for the bang up 2015 blog year I have for you.

green bypassIn case you don’t get the paper with Dave’s Sunday 5-stars, and would like to take your own shot at it before reading further, here it is:

To review the brief history of the bypass, it started just last October as an adaptation of Peter Gordon’s basic solving process, to be used in timed Sudoku solving contests. Peter was using the double line exclusion (dublex) and cross hatching to find clues, then doing a full number scan for candidates. Sysudoku basic finds candidates much more efficiently, but I thought it even better, under a time control, to bypass writing in marks in the search for clues. In contests you thus avoid wasting time filling in candidates that never get used. Our Akron Tournament is all about doing basic solving fast.

The bypass makes one exception to “no pencil marks”. We mark naked pairs as Sysudoku slink marks. I suppose if I actually find other subsets in the process, I would mark them too. The point is, to put aside closed cells and concentrate on still open ones.

At the October bypass introduction, I already had the Fiendish review posts on Wayne Gould’s “no pencil marks” (NPM) in the can. I was rather hard on him for pretending that hard puzzles could be logically solved, not guessed through, without them. The bypass did very well on the Fiendish review puzzles, but I thought the puzzles were probably tailored to make NPM look good. Now I know better. Sorry, Wayne. Now the sysudokie way is to start without most pencil marks, and add them as required.

In the meantime, I’ve concluded that starting box marking with a separate slide for the bypass takes no more box marking time. If anything, I get more total clues, which must mean that I see more. And the kicker is, that I look forward to that opening bypass stage. At this stage, 2-stars, 5-stars and monsters are treated the same. I now plan to make revisions in my early posts, to steer beginners into the bypass as they get sufficient experience with regular box marking, and can follow a chain of unwritten slink marks.

So if you took advantage of my beginning offer, and have now bypassed your way into Dave Green’s Sunday 5-star, you either need a checkpoint, or you don’t. The following trace continues past all the uncertainties. If you didn’t try it, and you are absolutely new, then review the first Sysudoku posts of 2011 to get up to speed on regular box marking first, then looking at the trace page as necessary, follow the trace on this one. It will open your eyes.

green bypass trYes, a 5-star solved by the bypass, but that doesn’t mean it isn’t a 5-star. Your trace can be very different, yet lead to the solution easily. My traces have to follow the sysudokie 2-D tracing rules, so that readers who follow those rules get a matching checkpoint.

Next we return to the Gordon Guide review for a few more posts. I’ll be glad when it’s over, and I think you will be too.

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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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Plus and One-Sided Unique Polygons

In this post, the Gordon Guide’s Gordonian Polygons Plus and One-Sided Gordonian Polygons are shown to be variations of the unique polygon, defined here as a loop of cells, containing the same two numbers, which become a loop of conjugate pairs when extra candidates are removed. The name Unique Polygon, or UP, is proposed for all of these variations, since Peter Gordon’s Guide does not adequately defined it, or explain how it works.

gordon UP plusGordon’s example of the “Plus” variation does not require a remote pair to close the ring. Removal of both 4 and 6 from the “crown” cell r1c5 will result in two solutions at least, therefore 1 and 7 can be removed. The resulting 46 naked pair in c5 starts the collapse.

Gordon starts the one-sided polygon example with “You had to know it was coming.” Indeed, this is a variation already covered in the definition of my previous post.

gordon UP one sidedAgain, in the Guide’s “one-sided” example, a six member conjugate pair loop emerges if both 5’s are removed. This would guarantee at least two solutions, therefore the 5-group is true, removing 5r9c2 and triggering the collapse. You could also describe the uniqueness condition as imposing a box/line restriction.

This variation suggests we leave the “crown cell” out of the Unique Polygon definition, to include this variation. The UP is the “gem in the rubble” I mentioned earlier. Clearly, the extra candidates do not even have to be in the same side of the UP, for eliminations.

Also, let’s note that when “extra” guardian candidates are not confined to one crown cell, we may not find guardian candidates whose confirmation is required to avoid the removal of all UP extra candidates.

Next post, we show how the formation generally known as extended unique rectangles, but claimed by the Guide as “Gordonian”, is systematically revealed by Medusa coloring. The Gordon Guide provides the example, but as we will see, the Guide does not cover coloring, and actually invites confusion by using the term “coloring” for a trial-and-error method.

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A Gordonian Fantasy

Here we spring a booby trap laid by the “definition by example” policy of the Peter Gordon Guide. It is the Gordonian Polygon, as demonstrated by his Guide to Solving Sudoku. The correct interpretation and application of the strategy are revealed. Also, a counter example shows again why this “Guide” cannot be trusted.

The first sentence of the Guide section on Gordonian Polygons reads: “What works for rectangles also works for figures of more than four sides.” That is true, regarding particular arrangements of identical candidate pairs described in Beyond the Rectangle. But these uniqueness figures are not mentioned, much less identified, in the Gordon Guide, and the reader is left to interpret Gordon’s sentence to mean any polygon (of identical pairs) of more than four sides. Gordon’s first example suggests he means exactly that, with one of the cell vertices of the polygon containing extra candidates along with the bv candidates, and no apparent connection between all vertices. From the “extra candidates” cell, he says, the bv candidates can be removed, because one of the extra candidates must remain to prevent a double solution.

gordonian polygonGordon’s first example, Example 23-1, is a loop of 57 bv and extra cell 357r3c2. Peter’s rationale for removing bv numbers 5 and 7 from r3c2 is that, if 3r3c2 is removed, the polygon loop of six 57 bv can never be resolved.

By this argument, if you can draw in a six- sided polygon, you’re Gordonian, and the removal can be made.

But this just isn’t the case.

gordonian fantasiesFortunately, one of the Guide’s Gordonian examples demonstrates that this simple rationale is a fantasy.   Going back to Example 20-1, the grid for the one sided Gordonian rectangle, a dead remote pair forms four sides, allowing us to complete a Gordonian Polygon in three different ways. Problem is, they place the 1-clue in the three different wrong places.


Do we need a magic rule? Is it because we can add only one side to form the polygon? The Guide doesn’t say.

gordonian unpolyThe Guide does mention another reason why the particular Example 21 case works, but it has nothing to do with polygons. Going back to the diagram, the 3r3c2 removal allows the set of bv to remove all outside 5 and 7 candidates that could resolve whether each cell contained 5 or 7. The puzzle would have at least two solutions. No polygon is necessary.


Gordon’s polygon argument is that, going around the polygon, there would be no way to decide which alternating cells are 5, and which are 7. Again, two solutions.

But what kind of loop is Gordon’s polygon? Why should the bv in r5c3 and r3c5 be considered adjacent cells in a loop? Unfortunately, the Guide has not developed the Sudoku fundamentals to explain it, but the loop is of conjugate pairs. Lines and boxes define most of the pairs, but r5c3 and r3c5 form a conjugate pair as a remote pair, bookending a series three conjugate pairs.

Bottom line, Gordon has stumbled over something that works, but he is unaware of what he is dealing with. There is certainly no reason to name it a Gordonian anything.

BTW, Example 21 is easily solved without assuming a single solution and using any uniqueness argument.

gordonian coloring 1Two clusters are well supported, and the bridging logic is

not(blue and red) =>

green or orange,

removing 5r5c2, which proves green, and  catches two orange 5’s in c2, proving red. No resistance is left.

To guard against a more complex multiple solution, I tested orange, but it quickly asserted that both blue and green are false.

The Guide follows with the Gordonian Polygon Plus, the One-sided Gordonian Polygon, and Gordonian Extended Rectangles. I have to see if there is actually anything new under these titles, and I invite you to come along on the next post. Have a groovy Christmas.

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Gordonian UR-ology

This post continues a review of advanced instruction in Peter Gordon’s Guide to Solving Sudoku, by explaining why unique rectangle methods need not be renamed “Gordonian rectangles”, and why you can’t count on Gordon’s Guide to make you an expert Sudoku solver.

Before we get to the Guide’s Chapter 8 on Gordonian Logic, which Gordonian jellyfish of the previous post did you find first?

gordon jelliesMy post Casting for Regular Fish details the blank line tally, a marking method using blank lines on the panel to mark fish lines by dashes or vertical bars and victim lines by plus marks. Like most authors, Gordon provides no visual tools for actually finding fish.

If you had difficulty finding one of these jellies(and who didn’t), try going high tech with my suset fish detector. On the rows, the row/position susets are 2/12389, 3/137, 4/2346, 5/79, 6/26, 7/67, 8/1234789, 9/29. Taken in increasing order by number of position digits, the list makes 5679 rows/2679 column positions obvious. To the point, the “expert” Guide has nothing like this. If you haven’t tried it, do it on the column jelly above.

There is a choice of jellies, because a complement fish of (9 – #clues – n)  lines is defined along with an n-line fish, having the same victims. This makes most searches for jellies and all searches for squirmbags unnecessary, the complement fish being simpler.   Experts know this, but it’s not in the Guide. When you go fishing, leave Gordon’s Guide at home. It’s not waterproof and it doesn’t make a good boat seat either.

gordon ur 1Turning to UR’s, here is the first unique rectangle example in the Gordon Guide:

In this simplest of all UR, 8r3c5 must be present in the solution, to prevent a multiple solution.

Only Peter has chosen to call it a Gordonian Rectangle. That didn’t catch on.

Along with this example Peter Gordon relates how he independently discovered the unique rectangle. My UR post of January 8, 2013 recounts the descriptions of unique rectangle variations by other experts. These include the Guide’s “Gordonian”(single guard) and “Gordonian plus”(multiple guard) variations, and more. Gordon reports that he dubbed this strategy “Gordonian rectangles”, and that his partner Frank Longo came up with “Gordonian plus rectangles”. As always, the Guide only demonstrates in several specific examples what to do when that UR situation is found. It defines no general procedures or logical ground work for UR. As far as I know, Gordon has never offered evidence that he is the innovator deserving to name the UR strategy for himself. No such evidence appears in the Gordon Guide. In my opinion, “Gordonian Rectangle” is nothing more than misleading and shameless self promotion.

gordonian plusAfter another example of the very same UR type, Peter presents this “Gordonian Plus” unique rectangle at left. Gordon’s argument is as follows:

“Once we eliminate 1 and 3 from cell 58’s candidates, we have a pair. Both cell 57 and 58 have 6 and 8 as their only candidates, so one must be 6 and the other must be 8, That means that cell 55 can’t have a 6 or 8 in it, so it must be a 4.”

This explanation, though accurate, shows why Gordon’s Guide is not going to help anyone become a Sudoku solving expert. It starts with the wrong problem. The right problem with multiple extra candidates is to prevent all of them from being eliminated. We have to find a different culprit in each case. In this case, we must find means to prevent the simultaneous removal of 6 and 8 from r5c8. Having decided that, we see that removal of 4r5c5 creates a naked pair that does just that, so 4r5c5 must be true.

Now look at Gordon’s argument again. He has the reader wondering why both 1 and 3 must go, and then goes through the argument candidate by candidate, avoiding any Sudoku algebra that shortens the logical trail. He walks it out, avoiding the term “naked pair” or any equivalent term, along the way. If the reader synthesizes any generally working procedure from this, it is in spite of this introduction and long winded account of events specific to this very case. There is no insight into why the solver is doing what he is doing.

gordonian one sidedA similar “from scratch” explanation obscures Gordon’s example of a “one-sided Gordonian rectangle”, also well known among unique rectangles. The UR requires a 1-slink removing 1r8c3. The slink also creates a box/link restriction eliminating 1r1c2, which Gordon neglects to point out.

Next post, we’ll debunk another Gordonian “innovation”, the Gordonian Polygon. There is some innovation, but it isn’t Gordonian.

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