## Basic Sudoku With Arnold

This post compares Arnold Snyder’s basic solving methods, the techniques leading to a full set of candidates, with Sysudoku basic.  Snyder’s basic methods are described in Sudoku Formula 1 and Formula 2. A second post will evaluate the Snyder advanced methods covered in Sudoku Formula 3.

I haven’t had the pleasure, but I think it would be a delight to talk with “master gamesmith“ Arnold Snyder. I had the impression that he is a poker and gaming professional recruited into Sudoku by his gaming publisher, Cardoza Publishing of Las Vegas, NV. Now, having examining his approach to Sudoku solving, I wonder if Arnold has sufficiently mastered the science of probability to be a successful gaming professional. On the other hand, I see a streetwise intelligence in Arnold’s Sudoku work that could make up for such a weakness.

To his credit, Arnold is the first author I have reviewed who explicitly recognizes the value of strong links in basic solving by developing a marking technique for them. His “key numbers” are pencil marks at the bottom of a cells to mark candidates as box slink partners.

Here is the key numbered grid of his instructive Formula 2 #5 puzzle.

Unfortunately, Arnold’s key numbers marking does not identify the row, column or box of the slink, or multiple partnerships. I wonder if Arnold ever thought about line slinks, and using the corners of the cell to represent them, as in Sysudoku basic.

At this point, Arnold says it is time to find all candidates, and describes his version of line marking. But first, you might want to compare this with a Sysudoku box marked grid:

Well, “key number” marking includes aligned slinks only, and also leaves out triples. Recalled in the bypass or written down in box marking, these omitted slinks can make the recognition of naked pairs and filled chutes automatic. Such is the case with the naked pair Wnp49

Arnold gives his readers extra credit for recognizing these “forced twins”, once they have completed the assigned line marking. They also earn an A+ for recognizing the hidden single 3r5c7.

The value of the unaligned slinks is demonstrated by the fact that we had to stop the 9: marking at the first level in order to make any comparison. The truth is a precipitous collapse of Formula 2 #5, as evidenced by the trace.

Aside from leaving a good part of slink power unused, Snyder never, even in Sudoku Formula 3, explains the concepts of the strong and weak link. This leaves him very limited in his ability to exploit candidates in advanced methods. But that’s for the next post.

In basic solving, Arnold is superior to most Sudoku writers in another way. He does not leave readers entirely at the mercy of number scanning for enumerating candidates.   In Formula 2, he describes a line by line process similar to line marking, but without sysudokie refinements. There is no ordering of rows and columns by increasing free cells. No reusable fill string is suggested. There is no marking of bv to aid in the free cell count. And to bring up another serious omission, there is no marking of line slinks.  That’s why there is no corner marking. All candidates are placed in a list across the top of the cell, including key numbers.

These omissions make Arnold’s line marking much less effective, and much more of a boring interlude, longer and less often interrupted by x-wings, naked pairs, and marking runs.

Arnold duly defines naked and hidden subsets beyond the “forced twins”, but offers no guidelines or algorithms to find them in the sea of candidate lists. In his last instruction puzzle of Formula 2, #6, his challenge is to find the naked quad and the naked quint in line marking, but the puzzle is felled by a naked pair induced by an X-wing earlier in the sysudokie line marking. The boxline exclusion is another elimination often seen in line marking, but ignored in Snyder basic .

I didn’t purchase Sudoku Formula 1, designated for EASY puzzles, to go along with Formula 2 for HARD ones, and Formula 3 for KILLER ones, but the way 3 repeats 2, I think I have the gist of how Arnold starts off beginners. Arnold lumps double line exclusion and cross-hatching together, explaining them informally by shading cells excluded by the outside clues in examples. He refers to the process as scanning and shading, as if shading is a solving technique, rather than a simple vision aid. Arnold dresses up the idea of outside key numbers excluding cells in neighboring boxes from containing that number as inferred shading.

Arnold includes one special configuration of clues in box marking, the wall, or filled chute. He calls it a trio. He doesn’t call attention to the 2×2 square or four corners or pocket. Maybe they’re in Formula 1.

Bottom line, Arnold Snyder is not the best advisor for Sudoku basic solving. If you gifted a beginner with a Sudoku Formula missive, don’t feel bad. Make it up to them right away by putting them on to sysudoku.com/beginners.

I thought about contacting the Sudoku Formula n cover endorsers, the Sudoku Puzzle Society and the Puzzle & Sudoku Enthusiasts Club about better information for starting Sudoku solving. But I found no evidence these authoritative bodies actually exist. I’d like to hear from their members.