Basic by Our Fingernails

Here we continue a salute to Dave Green in the current Sysudoku Basic clinic by illustratively checkpointing a highly challenging Sunday 5-star published in the Akron Beacon Journal on June 29, 2014. Box marking goes nowhere in this gem, leaving it to alert line marking to keep the puzzle within basic boundaries.

Green 629 BMAssuming you took up the challenge, how did you feel when you finished box marking  with no clues and 6 slinks?  I felt puzzled. What was this mini monster doing here? Dave does the 6-stars in the LA Times. Did this one escape to Akron?

It put me on the alert to be especially careful in line marking. We start in ”4f:” and with six blank lines. Take the paper up and transfer the givens to the ©PowerPoint grid. Its going to be a long Sunday afternoon.

But then, a naked single on the first line and a productive naked pair on the second put me in a more positive mood. The good vibes continue as I trace out:

Green 629 4f tr

Green 629 4f gridAmong the resources explicitly held in reserve as I go to the next line, are two naked pairs, two X-wings and a naked triple.

I leave the X-wing icons in place on the grid as an aid to further line marking.



Continuing the trace as it runs off the page, I copy the last effects list to the left, adding the X-wings as possible causes.

Green 629 final trWadiyaknow? I never had to face the line marking of those blank lines.

green 1019If you haven’t done so already, please try out your dublex bypass, box marking, and line marking skills on this typical Dave Green 5-star from the paper just this past Sunday, October 19, 2014. There is moderate progress on the first two stages, but it requires a very careful line marking. Look for some Green whimsy, and a rarely seen trigger for the collapse. It’s my final Dave Green checkpoint in the current Sysudoku basic clinic.


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Green Pastures

Continuing the basic clinic, this post recognizes Dave Green for his Sunday 5-star syndicated series, and checkpoints an illustrative example of Sysudoku marking on one of them. The checkpoint compares the traces, with and without the dublex bypass.

Finally I turn to my daily puzzle supplier, Dave Green. His syndicated King Features puzzles from 1-star (Monday) to 5-star(Sunday) fit right in with our current basic clinic.

For me, Dave does what Nikoli claims to do. You often see a whimsical pattern in his given clues. A cross-hatch pattern may be repeated several times across the puzzle. And as to feelings, sometimes I get the eerie feeling that Dave is chuckling as he throws me a curve that I’m going to miss the first time through .

green 62214 db gridDave varies the collapse point a great deal, but his level of difficulty is unusually consistent. Except that his 3 and 4 stars sometime rival the 5 stars, at least for me. Starting with the dublex bypass up to 3 stars, I usually wind up with pencil marks for anything above 2 stars with Dave.

Our homework on Dave’s 6/22/14 5-star was surprising on two counts. First, on how far the dublex bypass took me, and secondly, the number of operations compared to straight out slink marking.  The bypass leaves a lot to do, but you get there faster, and there is a lot less slink marking before the collapse begins.

Here is the complete trace. The DB part in number order, but without number sections. We just add in box marking and line marking as before.

green 62214 db tr

There are no decisive highlights in the slink marking trace but you probably struggle if you miss anything. This trace certainly represents the best of grind-it-out Sysudoku basic.

Green 622 1-7 tr

Comparing the traces, the without DB box marking goes further through the numbers. There’s not much difference in the number of operations, but the dublex marking is faster when you are not tracing. Anyway, what you really need to assess is not the writing time, but the searching time – how long it takes to identify the next move.

It does appear so far that the bypass does not impose extra work, and could be used on all puzzles. I’ll continue evaluating.

Green 6-29-14For contrast with the early generosity of 6/22/14, the next Sunday paper brought what might be the absolutely stingiest 5-star Dave has ever produced. It’s still basic, but you have to scrounge and be extra sharp, picking up every crumb to avoid starvation – and advanced solving. See what you can do with Dave’s Sunday 5-star of 6/29/14. I’ll make the same with and without DB comparison in the checkpoint.

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The Dublex Bypass

This post describes an adaptation of Sysudoku box marking which is suitable for timed solving contests. I call it the dublex bypass. You apply Sysudoku box marking to clues and unit filling naked pairs only, bypassing other pencil marks. Here it is illustrated and compared with the Gordon Guide “scanning”, and with full box marking, on the example that introduced “scanning” in the Guide.

I’ve gladly admitted, after each of the Akron-Summit County Library Sudoku tournaments, to be nowhere close to being a contender. Of course my tender age of 76 may have something to do with that, but another telling factor is that only clues count, not pencil marks. In the Akron tournament in fact, all pencil marks that are put in must be erased. Going through my Sysudoku traces of the championship puzzles, you can see what a great excuse that is.

You know that this blog is directed at human solving of the toughest Sudoku, but even the championship puzzle of many timed contests are basic level. They never make it to the advanced techniques that require pencil marks. If we expect a basic level puzzle, why not just bypass candidate pencil marks? Or at least, put them off until they are easier to do, and there are fewer of them. In a timed contest we won’t be tracing or reading a trace, but I’m including traces so you can “read” in a 2-D trace how fast the dublex bypass would be.

mensa ex3 1 - 5Gordon’s “scanning” and Paul Stevens’ similar “cross-hatching” incorporate the dublex, or double line exclusion. Let’s examine Example 3 of the Gordon’s Guide.   Peter scans numbers in order, 1 – 9. In the Guide he does a few scans out of order to begin his discussion, but we’ll go by his regular order, for a better comparison.

Here is the grid after scanning 1 – 5 :

The trace is in the 2-D format. For this introduction only I’m adding cause coding:

h – horizontal dublex, v – vertical, oc – one-choice. Cause and effect is shown by indenting, and ordering is 2-D style, i.e. depth first.

mensa ex3 15 trNote that NE5 triggers NE4, but SW8 does not generate SE8. That is because 4 was an earlier scan, but 8 is a later one. The dublex scan will be depth first regardless, following each cause as far as it goes.

Also note that the r7 fill is not made when SW5 reduces free cells to two. That is a speedup feature of the dublex bypass.

Gordon says “Whenever I put in a number using horizontal scanning, I like to immediately look vertically to see if that gave me enough information to make a conclusion based on vertical scanning.” Actually his marking is stronger than that. His SEhv2 requires a simultaneous cross hatch. Neither the horizontal or vertical scan would do it alone. What Gordon actually does is box marking for clues only, less slink marking, and two-cell fills.

mensa ex3 69Continuing through the numbers, Gordon reaches this grid with the trace below.

mensa ex3 69 tr



The Cnr1 is a surprise for Guide readers. I’m coding it as “nr”, for “new rule”. The clue could have been traced as Cv1, but Gordon uses it to call attention to his number closeout procedure.

He mentioned before that he notes when 9 clues of a number has been found, so that he will not have to consider the number again. But he also notes when the eighth clue shows up, because then the location of the final number is known. Its row and column are the only ones missing the number.

Let’s think about that.

Do we agree that it isn’t really necessary to track numbers of clues to do this? The two clues in the horizontal and vertical to cross hatch the last clue have to be there when the count reaches 8.

With scans left pending, Peter starts through the numbers again. His count tells him that two 2’s are missing and he accounts for them, but the counts and this accounting take time. At the 3’s, he finds Nh3, and uses the new rule for Cnr3, but we can see he simply missed Nv3 when he entered Soc3. He should look both ways after a one choice, as he does after a scan effect. And the Nh3 generates Cv3 without the new rule.

Next found is the Wv4. We look at the trace to see which came first, the W9 or the SW4. It’s the SW4, so Peter did not note that the W9 closes the Wc2 chute, and look for a vertical scan that might result. The correction brings in a pile of clues. In Gordon’s accounting we learn that he doesn’t regard the last number in a line as a one-choice.

The second traverse of the numbers goes to 7 before the puzzle is finished, but we have learned enough. The dublex scan will carry every effect clue as far as possible, using the same form of 2-D trace. Two free cells in a unit will be filled with clues or a naked pair, as soon as created. There is no second traverse of numbers.

Here is the grid after the dublex bypass on 1 – 3:

mensa bypass 3To the trace below, NE3 closes a second chute in the NE box, and NE5 takes away the alternative for NE4, leaving a “one-choice” for NE9. NW5 brings the first two cell fill, and NE9, the first naked pair fill.

Pencil marking the naked pair fills is optional, but I think it pays. Foregoing other pencil marks does concentrate the marking effort on clues.

It may delay the collapse, but in a timed contest, who cares?

mensa byp 3 tr

mensa bypass 4The 4: trace shows how you can go wrong with the dublex bypass. When you are not tracing, it may require some training to be able to recall listed effects for further marking.

mensa byp 4 grid



The grid at Cnp46, along with the tail of the trace, shows how the pencil marks can speed up recognition of the last few clues of the collapse.


Adding to the success of the dublex bypass, I can report that a full slink marking of this puzzle does no better, and undoubtedly takes more time.

mensa byp BM

The Guide example was certain to show off dublex bypass well. You might want to evluate it against the Akron Tournament championship puzzles reported here in November 2012 and 2013. I will suggest and do more such evaluation ahead.

green 6-22-14Continuing the basic clinic, I’d like you to solve a 5-star by my daily breakfast composer Dave Green, that appeared in my paper, the Akron Beacon Journal last June 22.

Compare traces with me. I think you’ll find full slink marking necessary, but start with the dublex bypass, and see how far you can go. Then do box marking. Enjoy.


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Gordon’s Guide Basics

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.

extreme 165 afterGordan’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:

extreme 165 final tr

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:

  1. Only one cell is left open in a unit for the number (a hidden single), or
  2. 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.

mensa one-choiceWant 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.

mensa scanningMy 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.

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X-treme Hidden and Naked Treasures

This post features hidden and naked subsets in two Sudoku X-treme review puzzles. All occur in line markings. The first continues from the previous post.

xtreme 210 LM 1The X-treme 210 line marking features two naked triples. The first one breaks up a discouraging train of clueless lines.








xtreme 210 LM 2 tr

The second follows soon thereafter in the closing the first column. Below is a trace of the collapse which follows.

xtreme 210 collapse tr





The X-treme review puzzles also demonstrate their fair share of hidden subsets.

In X-treme165, the very first line marking, shown below, is a very obvious hidden single. There is only one location permitted for a 6. Of course the always complementary naked triple is no less obvious.

xtreme 165 hidden 6Box/line restrictions are also about available cell locations along the line. After four more lines, the marking of r9 confines 5’s to the SW box, denying them to SWr7 and confirming SE5.

xtreme 165 boxline 1This box/line could easily have been noticed earlier, but it is the line marking procedure that assures that it is seldom missed.

xtreme 165 nq or hpTwo lines later in line marking X-treme 165, we encounter another subset situation. In r8, do we have a naked quad or a hidden single? The answer is, it’s both. Whichever you find easier to recognize.

extreme 165 ntThe new clues 7r8c5 and 7r8c4 trigger the box/line eliminating 1r9c8, and shortly thereafter we have a surge of eliminations as 5r4c7’s naked triple generates two naked pairs. Here is the “before”. Want to mark it from there? Next post will show the “after” that sends X-treme 165 into collapse.

If you have it, dust off your copy of Peter Gordon’s Mensa Guide to Solving Sudoku. Very recently, the Mensa association was dropped, with the re-issue under a Sterling Publishing imprint PuzzleWright. We’ll be doing a detailed critique of Gordon’s instruction and examples, in two parts. The basic solving part continues this basic clinic. The advanced solving part – and a review of the puzzle collection by Frank Longo – both follow later, after the basic clinic is completed.

I’m hurrying the basic part of the Gordon review into the basic clinic to get to a related strategy for timed solving contests of basic level puzzles. The next  Akron, Ohio Sudoku tournament is coming up.

Wish me luck Saturday. I’m running the Akron marathon.

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The Empathy of Nikoli Composers?

Here we briefly consider Nikoli claims of a “human touch” quality in their puzzles, and continue demonstrating Sysudoku basic technique with X-treme Sudoku review puzzles. These are presented by Nikoli as their toughest.

Is there a communication between Sudoku composer and solver that is nurtured by Nikoli composers , but is missing from computer generated puzzles? In X-treme Sudoku, Nickoli chief editor Kanamoto claims there is, in a very indirect way. He states that good composers “are always considering (the) solver’s feelings” and asks if a computer can “take into account the way a solver thinks”. In my opinion, the composer should be considering the logical unraveling of the puzzle and the beauty and elegance of that, rather than any emotional state of the human solver. And, if Nikoli masters truly understand how human solvers think, as Kanamoto’s question cleverly implies, they should compose a truly lucid and inspiring handbook on human solving, from basic through the most advanced.

Anyway, I felt no special connection to the master composer as I solved the 10 puzzles of this review. Maybe it’s my engineering approach to basic solving as a systematic process to get the human solver to the advanced stage as efficiently and accurately as possible. That’s the roses fragrance I smell in the solving of basic level puzzles.

To Nikoli’s credit, these puzzles do challenge the solver’s basic skills in diverse, interesting ways. They are worth your time. My only objection to Nickoli’s window dressing is that the puzzles are basic level, period.

So let’s take care of business. These reviews are a clinic in Sysudoku basic, in that you, the reader, can follow checkpoint traces on your own copy of the puzzle. You see the exact grid as each marking is made, and can pick up every “give away” the puzzle yields. There is even a likelihood of discovering one that I missed.

First, a trace of the collapse of X-treme 180 on box marking 8:

xtreme 180 8 tr

The trace of a collapse looks complex because of the large number of logical effects. But bear in mind there are a lot of cells to fill, and there is very little searching involved in the effort reflected in the trace. At each step it’s within view of the cell you are on. It goes fast when you are simply filling in the grid.

Usually, we just terminate the trace with “. . .” when it becomes very apparent that the collapse will continue to the end. The solution itself is of no consequence. The trace tends to run out of room on the page. It’s just the way it is.

Next up is the box marking checkpoint for X-treme 210. A quiet box marking suddenly explodes with a near collapse that runs out of horizontal space. Notice I had to jump back left into empty space to continue.

xtreme 210 box

The grid with bv marked for line marking:

xtreme 210 LM readyNext time, in addition to closing out X-treme 210, we’ll wind up the review with some highlight hidden subsets from X-treme 165.

New readers, especially, I hope you are following these checkpoint traces, on your own copy. If you have some experience with Sudoku, you can probably “catch on” to 2-D traces without directions. If not, look on the menu line.


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Nikoli’s X-treme Sudoku

Here we begin a series of reviews that are a clinic on Sysdudoku basic solving skills. Each collection of the survey will be introduced, with several puzzles checkpointed by 2-D traces. This post introduces the Nikoli Publishing top toughy, the “Very Difficult” section of X-treme Sudoku, published in the United States by Workman Publishing.

On the X-treme Sudoku cover, Nikoli bills the collection as “the toughest, roughest puzzles from the Japanese creators of the game”. If you read that as the toughest from Japanese creators, the claim is probably true, simply because there are no other Japanese creators of Sudoku puzzles. Nikoli fiercely defends its Japanese copyright on the game itself. The “Very Difficult” half of the X-treme collection does appear to be the toughest collection Nikoli has published.

But don’t read it to mean Nikoli created the game. Read “creators of the game” as “makers of puzzles”. Peter Gordon in his 2006 Mensa Guide to Solving Sudoku, details how Nikoli named the game, and where it was born in the United States in 1979. I’ll be reviewing Gordon’s guiding instruction in this book, as supported by Frank Longo puzzles, starting in December. Of course, the clinic is based on the beginner’s page and early, basic solving posts of this blog

xtreme 180 1Your homework puzzle, the X-treme 180, starts box marking very aggressively, showing how the immediate follow up of completed chutes and squares pays off.

The “1:” trace is below.

In this series, I am leaving each effect clue in candidate size font until it has a turn as a cause. The final number of unused effects is a measure of the difficulty of the puzzle. The more, the easier.

xtreme 180 1 trIf you missed some of the low hanging fruit, you can follow the trace to improve your marking technique. New readers can find directions for reading a 2-D trace on the trace page(link above). Also, this is a good time for a reminder that my email for requesting ©PowerPoint box marking grid template is on the tools page(another link above), along with detailed help. It’s a good way to save your solving states for later review or sharing. And it’s so easy.

If you had to upgrade your fruit picker after that checkpoint, try out your new version on box marking 2: through 7: before looking at the checkpoint below.

X-treme 180 is one of 10 X-tremes preselected for the review. I started with 165 and selected every 15th puzzle, reaching 300. The survey results are tabulated a bit differently than previously reviewed collections(Find It above), because in this basic series, advanced methods are not needed.

xtreme review tableX-treme 180 is one of four that collapsed (—-) in box marking. The slash notation for box marking survivors denotes marking clues/marks or locked sets. Parentheses enclose (clues,marks) over a range of scan numbers or for locked sets, such as naked(n) or hidden(h) singles(s), pairs(p) or triples(t).

xtreme 210One of the reviewed X-tremes, 210, almost made it to advanced Sysudoku solving, collapsing in the close after two naked triples.  I’ll checkpoint the box marking next time

If you’ve put off learning the 2-D trace conventions, now is the time. Many readers are checkpointing their Sysudoku blog homework. For maximum basic skills, you might want to buy a copy of X-treme Sudoku, and ask for my 2-D traces of all ten puzzles as a Word file from If you don’t have it already, you can ask for the ©PowerPoint grid template at the same time.

xtreme 180 7OK, here is the grid after box marking 2 -7: of X-treme 180.

Miss anything? Find its immediate cause in the trace below.

Next time, we’ll wrap up X-treme 180.





xtreme 180 7tr


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