## 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?

My 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.

Turning 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.

After 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.

A 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.