This post begins my review of an instruction manual, Peter Gordon’s *Mensa® Guide to Solving Sudoku*, and the associated puzzle collection the book contains, by Frank Longo. Basic solving is covered here, with advanced techniques and the puzzle collection review to come in following posts. The Guide has been re-titled *Peter Gordon’s Puzzlewright Guide to Solving Sudoku*.

Gordon’s Guide is a gentle introduction to Sudoku, geared toward getting the reader started on basic level puzzles. It may be a good entry point for those who find the early posts of this blog too fast paced, or technical or abstract, but it does not prepare the reader for advanced or extreme puzzles.

As usual, my goal in these reviews is new insights into human solving. In this case, however, an added purpose is to counter the hype splashed on the soft covers of the Guide. This book will not give you an edge by disclosing “ingenious tricks that many experts don’t even know”. It is far from complete in covering advanced methods . And don’t expect to find “techniques that you won’t find in any other book”. Specifically, the “exclusive Gordonian Rectangles method” of the front cover is well known by a generally accepted name, *unique rectangles*, and is not at all attributable to Peter Gordon.

Gordan’s basic is reported below, but first, your X-treme homework. Here is the immediate “after” marking of 5r4c7 in X-treme 165. The naked triple289 in c3 confirms 5r6c3 and brings a naked pair 29 in c2.

From there, earlier marks N9 and the boxline SEr8bxln1 are pulled out to finish the collapse. A trace covering these events is:

Now turning to the Gordon Guide, Peter’s list of basic techniques begins with *one-choice*, defined as: “Find a cell in which there is only one possible number that can go in the cell, and put it in.” Sounds simple, but to evaluate where “one-choice” applies, we have to ask what that means.

According to Peter’s examples of “one-choice” , there are two types:

- Only one cell is left open in a unit for the number (a hidden single), or
- There is only one number not seen from the cell, and therefore only one candidate ( a naked single).

Searching for a “one-choice” as a first step usually means the naked single. For each cell, you look in all cells sharing a unit for eight other numbers. It’s the number scan, or completion strategy that this blog has repeatedly rejected as unnecessarily inefficient. Now as if to illustrate how difficult and inefficient “one-choice” is, Gordon comes up with a puzzle that can be solved by one-choice alone.

Want to try it? It’s right here. Get out your template and go to work. Remember, nothing but one- choice. No slinks or subsets, just clues. Gordon hasn’t even introduced “candidates” at this point.

You’ll need Gordon’s book for a checkpoint, and I would bet against you getting it right.

So Peter joins my “black magic” list of experts that require solvers to do the number scan, the completion method, but neglect to mention what that entails. He does explain and show how the one-choice solution is found, once a complete set of candidates is in place, then gives his readers a dozen more one-choice puzzles to number scan and solve. Following this introduction to the letter could destroy your interest in Sudoku.

By the way, Gordon doesn’t use the keypad system for candidate lists. He writes them in a string at top left. Give him credit for seeing that the keypad arrangement of candidates carries no information.

Gordon’s second basic technique he calls “scanning”. He defines it to be what my early posts called the double line exclusion, or *dublex. *, but also includes single line exclusions based on filled chutes, and cross hatching.

I was surprised that “scanning” , which requires no prior completion of candidates, is done second instead of first. Why? It may be second because “one-choice” is easier to explain. This is the first indication that Gordon’s order of presentation is not, as I was assuming, an order of battle. That observation is supported by the fact that nowhere does this book explicitly prescribe any order for its solving techniques. Just number scan for candidates and do all techniques at once. Good luck.

I believe Gordan’s “scanning”, if extended by filling locked sets and more aggressive depth first marking, can be a very good strategy for basic level puzzles. It may be a winning strategy for timed Sudoku solving contests, such as the Akron-Summit County Sudoku Tournament.

My introduction of this strategy, to be called the *dublex bypass*, is the subject of the next post. I’ll compare it with Gordan’s “scanning” in his introductory example, shown here.

Gordon’s third basic operation is “elimination”. It is defined only by example, but sysudokies will recognize it as the hidden single in a line, a frequent event in line marking. But wait, doesn’t that make “elimination” also a “one-choice”? By his definition above, yes. But In Gordan’s system “elimination” requires multiple scans working in concert for an elimination, and therefore candidate completion is required first.

Gordon’s Guide covers “regular”(naked) and hidden subsets by example, with a couple of hidden cases and a mention of the naked/hidden subset dichotomy. There’s no help in spotting them, and nothing about the role of naked subsets in filling cells of a unit in scanning.

Next there is an illustration of the box/line restriction, which is labeled “interaction”. He concludes it by defining “interaction” to include the remote pair elimination by box marks that is the primary reason for slink marking.

Gordon concludes basic solving in his Guide with a patched together version of slink marking. Strangely enough, he titles this chapter “Candidate-free solving”

The idea is to write a pencil mark on the border between the two cells sharing the link. That pencil mark then represents the two slink partner candidates, of course. In a section titled “Little numbers are not just for neighbors”, Peter suggests placing the number somewhere between the slink partners in separated cells and drawing a lines from the number to the two cells.

“Little numbers”? “Candidate free”? It’s painful to see Gordon dance around the Sysudoku cell position method of slink marking, and miss it so completely.

This concludes our review of Gordon’s Guide basic, whose major fault is the reliance on the cell by cell number scan, a dreadfully inefficient procedure for humans, however smart. Gordon also missed an opportunity to re-engineer “elimination” into the much more efficient Sysudoku line marking.

Advanced level instruction in the Guide will be examined when the basic clinic is completed. Next post, I show how candidate finding can be limited and deferred, and possibly avoided, when the level of difficulty is expected to be box marking, such as in a timed Sudoku contest.