Systematic Sudoku

This begins a review of Paul Stephens’ solving recommendations and puzzles.  The review is based on Paul’s currently offered books,  Mastering Sudoku Week by Week, subtitled “52 steps to becoming a Sudoku wizard” , and his The Sudoku Addict’s Handbook.  His website is www.sudoku.paulspages.co.uk .

I start with Paul’s basic solving methods.  To his credit Stephens offers humanly practical advice for basic solving , good enough for easy puzzles, and possibly superior for solving contests.  It just does not pick enough of the low hanging fruit for the tough ones.  He searches for clues, rather than following a systematic basic solving process that uncovers them, as sysudokies do.

For comparison, here is the grid of the championship puzzle of the Akron–Summit Library Sudoku Contest, at the end of the Paul Stephens version of basic solving.  The listing of all remaining candidates lies ahead.

Paul starts puzzles with the more obvious box marking sweeps and line marking fills. All sweep actions he calls “cross hatches”.  Our double line exclusions  he calls “group hatching”.  He fills lines of one or two free cells only. Paul does include naked and hidden singles and pairs in basic solving, actually using the term “hidden”.  He calls locked sets “multis”. When he can avoid the term no longer, Stephens uses “exposed” in place of that other word.

Stephens’ basic solving, however, is for clues only, not slinks.  He does very little pencil marking until it is time to list all candidates.  He only writes in clues, until there is a two cell fill with two missing numbers,  or when he constructs a “multi” from memory, to fill more cells.  Do you do that?

Foregoing pencil marking is recommended as a healthful exercise for the short term memory.  Slink marking is foreign to Stephens.  Paul never acknowledges there are such things as strong links and weak links. He never explains the remote pair power of a strong link to exclude candidates from other units. Instead, you are to keep the “claim” on cells by a remembered slink in your head and use it in a “virtual cross hatch”.  Perhaps you will recall the slink to pair it with another in a naked pair? Thanks, but I’ll stick with slink marking.

In basic solving,  Paul does not move through the numbers 1 – 9, or try to capture every consequence of a new clue, or apply any other systematic structure in basic solving. Therefore, he is never at any identifiable stage of basic solving until he runs out of sweeps and fills, arriving in a state he calls “gridlock”.  Then, as in the grid above,  it is time for candidate listing, a prolonged interlude of preparation before advanced solving.

Sysudoku readers face other oceanic hurdles in translating Stephens.  Cells are “squares”, units are “areas”, sweeps are “claims”.  Paul has no words for strong links, just the “two candidates in a unit” definition.  The last free cell in an “area” (a unit) is a “free gift”.

Indirectness  also clouds Stephens’ explanations of advanced techniques, as we will see later. Candidates “are related to” squares, rather than seeing other candidates.  The fundamental logical properties of strong and weak links, toxic sets, inference chains  are never explained,  perhaps because the necessary vocabulary is never developed in Stephens’ books.

For all that, Paul Stephens may be worth translating for some.  Stephens’ basic solving can be an alternative way of starting on puzzles expected to be easy.  His basic approach is particularly well suited to timed contests where scoring is based entirely on the number of correct cells, and without penalty for incorrect ones.  In fact, Paul gives expected expert solving times to compare with yours.

Getting down to specifics, let’s first consider how far Paul gets with your sysudokie homework puzzle Week 12.  Here is the checkpoint trace, showing that the puzzle does fall in box marking, but not without considerable resistance. Progress is slowed on this puzzle by the comparatively rigid tracing rules adopted in sysudoku to make checkpoint comparisons possible.

Now for the Stephens version.  You can try it first, using only clues and two-fill rows and boxes, , or just follow the trace below.  If you already have Mastering Week by Week, the trace follows Paul’s verbal description of page 59.

For Stephens fans who may be visiting the blog for the first time, our trace is read by adding clues to a fresh puzzle as you go.  The trace lists the clues placed by boxes named for compass points.  Your puzzle state tells you the clue number, and you, the reader provide the reason why this clue can be added.  The effects of a clue placement are listed below it on the next line. Post the listed effects first, then treat each effect, left to right as a cause, generating all of its effects below it, before coming back to the next cause on the list.  So you proceed all the way down on a slant, then hop up to the first unfinished list of effects for the next ski run.

Stephens basic carries the day for Week 12. Comparing the two traces, we see a shorter, and what seems to be a more straightforward route to the solution in the Stephens trace.  But if you actually follow the trace, and observe the logic of each step, you realize the economy is in writing, but not in thinking.

In timed contests, how typical is it for Stephens basic to go all the way?  Participants in the Akron contest can try it out on the earlier stage puzzles they brought home.  The grid appeared earlier.  Here is the Stephens’basic trace leading up to it.  Paul gridlocks with a lot of puzzle to cover.

To the clues Stephens’ basic solving finds in the Akron championship puzzle, I have added,  in sysudokie pencil marks, the fill strings constructed mentally in the line fills, and the candidate pairs that Stephens would find in basic solving.  This brings the puzzle to the next stage, Stephens’ “candidate listing”, the marking of each unassigned cell with its candidates.

Stephens titles the chapter on candidate listing “Through the Pain Barrier”, and for good reason.  He has not developed box slink candidates and collected the clues they generate in box marking. And not having the efficient and complementary process of line marking to find remaining candidates, Paul must go to number scanning.

Paul writes simple lists in ascending order for pencil marks, crossing out candidates as solving continues.  Two methods of building the lists are suggested.  One is the cell by cell number scan, the inefficient default of most writers.  His box  by box number scanning could save some time as the same list of missing candidates is compared to sweeping rows of each box cell, but Stephens doesn’t recommend jotting the list down.

Paul waits until candidate listing is done before considering “multis”, the locked sets of more than two numbers.  Most advanced writers consider them part of basic solving. In Sysudoku, naked subsets are encountered in box marking, and line marking picks up hidden subsets as candidate sets are completed in boxes and lines.

While writing this post, I’ve been trying out Stephens basic on the early week 1- and 2- star Dave Green puzzles I get in the Akron Beacon Journal.  Beyond that, it just doesn’t work for me.  I keep thinking,  why am I not writing down the slinks I’m uncovering for virtual and group cross hatches?  I get enough mental exercise working on tough and nasty puzzles.

It strikes me also, that another reason why Stephens pervasively jangles my sysudokie nerves is his search for a pattern to derive a particular clue, or solve an “area”.  What does this leave out?  The sysudoku modus operandi is to enumerate all patterns of each type, harvesting all the solving benefits, and returning only as candidate eliminations produce more patterns of this type.

Next time, we hop over to The Sudoku Addict’s Workbook to analyze Stephens repertoire of advanced techniques.  Addict’s Workbook has a nice summary of these, with interesting examples.  Yes I bought both books, and you should, too. I’ll review Stephen’s “extreme” puzzles from them soon.  Meanwhile, you can back me up by solving an extreme review puzzle, Week 48. Let’s converge on sysudoku box and  line marking for next week. Yes, I said sysudoku BM & LM.