The 2014 Akron Sudoku Tournament


Here is a report on my experience in the Akron-Summit County Library Sudoku Tournament of 2014 last Saturday. In particular, it’s a brief review on how well my recently introduced dublex bypass worked on the tournament puzzles. Each puzzle came from a different Will Shortz book, with his kind permission. This post also contains a very detailed walkthrough on solving the championship puzzle. By following it, and as necessary, looking up strange words on the Sudoku Speak page, tracing questions on the tracing page, and related posts on the Find It page, new readers get immediate entry into Systematic Sudoku, an Akron product, in one post.

Happy Turkey Day! I’m thankful for every interested reader.

Personally, I had a great time at the third annual Akron Sudoku Tournament. I earnestly tried to pick a lucky contestant number, and apply my latest secret weapon, the dublex bypass, to get on the championship stage. But I flubbed it royally. Nevertheless, more careful analysis at home reveals that DB worked very well. Let me explain that for those not following the recent posts of the basic solving clinic.

Dublex stands for double line exclusion, whereby if a number is known to be in two lines running through three boxes, then it goes in the third line in the last box. What is bypassed, temporarily, is the marking of box slinks. The DB, or dublex bypass, is box marking of clues only, plus naked subsets that reserve cells of a unit, but cannot be exactly placed within the subset. The naked pair is the only type of subset that is frequently occurring. One advantage of doing the bypass first and strong links later, is that there may not be any later.

In the tournament, there were three 20-minute rounds, then a championship round on the auditorium stage. Three puzzles in round 1, two in round 2 and one in round 3. Scoring was on the number of errors and blanks, with a bonus for finishing early.

akron 14 tableFor the tournament participants, who took home a fresh copy of all the puzzles, here is the tournament review table.

Under “Clues” is the number of given clues. The DB column shows the number of cells assigned to clues and pairs. The box marking column gives new clues/slinks marked. Line marking reports the number of lines marked with 3 free cells, 4 free cells, etc. The dashes mark collapse points.

The number of puzzles and the level of difficulty reflect the practical limits of an afternoon human solving tournament. Within these limits, the dublex bypass did very well. Of the five puzzles solved in box marking, only one required further slink marking. In my limited experience with DB, slink marking often reveals overlooked DB clues.

So, Akron participants, how did you do on the championship puzzle? Let’s walk through a sysudokie solution. To follow up on this, tournament participants can get free detailed traces of the other six puzzles by requesting “2014 Akron Traces” on sysudoku@gmail.com. The traces show exactly what is involved in collapsing these puzzles quickly. But first you need to learn about box marking traces.

Get out a fresh copy of the onstage puzzle, and let’s go. We start by scanning 1 to 9, looking for clues and for slink marks and triples that produce clues. This goes much more quickly when we write in only the new clues, and naked pairs. What’s the first one? ‘1’s dublex and two crosshatches give three box slinks, but no clues.

‘2’s first crosshatch has four free cells. The second generates a slink, which makes a dublex, which makes another box slink. Nothing to write down.

Look at NE3. Its NW crosshatch makes a NW slink, making only a N slink. but its dublex with SE3 implies E3. Writing in the 3 clue alerts us to the filling of the E chute, forcing a 1 in Ec7, giving us NE1. We look at the new clue’s crosshatch with SW3, then going down the grid, we look at dublex and crosshatches from C3, and SW3.

The ‘4’s don’t cooperate. The ‘5’s make a SE slink, but the dublex is clueless. We could look for a second dublex to partner with the ‘6’ dublex to get a naked pair in the N box, but it’s not there.

akron 14 DB trI think you must be ready to explain for yourself the next trace effect NE7, so I’ll leave you with the entire DB trace, and a quick update on reading 2-D traces.  First of all, the trace is a list of causes and their effects. A single effect, or a list of immediate effects in parentheses, is indented under its cause.

As you read, the effects on a list are posted on the grid together, then each effect becomes a cause, going from left to right. In the depth first 2-D trace we have here, all effects of a cause become causes before the next effect on the list becomes a cause. So the posted order of the DB trace above is

E3, NE1, NE7, N7, SE8, Snp38, S1, SW1, NE6, N6, SE2, SEnp57, SEnp69, SW2.

It’s up to you to determine why each cause has its effects. Never leave an effect without understanding why it happens. Besides learning particular tricks, being able to watch flow of action is the value of the trace. Solving can go in many directions, but a strict order is followed in writing Sysudoku traces so that solvers working independently can compare results. But trace readers do not have to know the ordering rules.

In the DB trace the current state of your updated copy should show why the naked pairs appear. The solver is to notice when a clue leaves only two free cells in a box or line. The effect is a pair of clues or a naked pair.

akron 14 DB gridSo now what does your puzzle copy look like? Did you put your naked pair candidates in a simple list, or in their keypad positions.

Well, you could go sysudokie and put them at the top of their cells and in corresponding corners, to mark them as strong link (slink) partners.

 

 

The significance? The slink reserves the two cells for the two partners. Why hide it? Especially since we are now going to add more slinks to the grid, in box marking.

The task of box marking is to add those box slinks to the grid that we saw, but did not record, in the dublex bypass. Without looking at the grid below, read the trace in the same way, updating each effect, to get the swing of box marking. We did without number list labels in the DB trace, but life was less complicated there.

akron 14 BM trN9 means a 9 in the North box. You decide where. Cm mean slink marks (two candidates ) in the C box. We start with an aligned triple of 1’s across a chute in the E box. We know its 1’a because the effect is on the 1’s list.

akron 14 BM gridWhen you add S4, you should have this grid, except for the green squares dragged over the borders of bi-value cells. I call them bv, singular and plural, because of the central role they play in advanced (beyond basic) techniques.

Currently the only bv we know we have are the naked pair cells. There are others among the candidates we still need to identify to solve this puzzle. The most efficient way to get all candidates is to fill lines, starting with those with the least free cells, in continuing in increasing order of free cells. I call it line marking.

The most efficient way to get all the candidates for advanced solving, namely the box marking followed by line marking described in this post, was published first in Akron Ohio, and so far, nowhere else.   It’s true. Not in London, New York, LA, Australia or New Zealand, but in this very blog, back in October 2011, and in the posts since. If you run across any evidence to the contrary, send it to my email sysudoku@gmail.com and I will acknowledge any prior discovery and your correction, anonymously or not, by your choice. Also, you can comment on the relevant early posts, and have the comment appear with them, with my reply.

I haven’t exactly hidden this under a barrel, and no experts have disputed it in the three years since.

Having read the principle of line marking in one sentence above, you could now re-invent it for yourself. But do that now, because next, I’m going to walk you through the few lines that finish the 2012 Akron Tournament Championship puzzle.

Where is the line with fewest free cells? Actually, its easier to count cells locked by clues, naked pairs or other subsets. Row r9 has none, while rows r7 and r8 have three. There are ties, at 3 free cells. My resolution of ties is rows top to bottom first, the columns left to right. We only want the first one, because when we mark that line, the order may change. Actually, I look no further than r1, because 3 is the least number possible after DB. Right?

So we start with r1. Watch closely. My first task is to make up a list of numbers that may be new candidates in the three free cells. I see 5, 6, and 8 in r1 already, so I won’t need more. But 6 and 8 cannot add new candidates in r1. You figure it that out. So my list is: 5. On my PowerPoint template, which was not available on the tournament stage, I place my fill list on the side of the line, or below the column and then copy it into each free cell. Then I eliminate candidates from the copy that can see the same number in its box or column. Marking a column, it’s the box or row.

Moving on, r2 has four closed cells, and five free. But r3 has only six closed, and three free. Make up the fill list and mark it. Now review the number of times each fill list number appears on the line. If a cell contains only on number, it is a naked single and a clue. If two cells, then you have a line slink. In r3, 2 is such a number, so we pull the 2’s down to the left corners of their cells to mark a row slink. That’s a little harder with pencil and paper.

Why bother with line slinks? The most immediate payoff is, if you get a matching one on another row, you’ll have an X-wing. That means we look at other rows as we pull the numbers down. We do the same with columns.

akron 14 LM trNow that you’re aboard the line marking train, just follow the trace and check your grid with the one below. Check your selection of rows and columns, and your slink marking. Note my priority to box marks over line marks on the same candidates.

akron 14 LM gridIn line marking r5, we got a new naked pair, taking 4 and 6 from the other r5 cells, and leaving a 1-clue. This triggers a collapse of the puzzle, but be very careful as you handle cells not covered by line marking. In this case, the four free cells of r6. The ‘5’s appear only in the W box, but cell r6c2 is not necessarily a bv, and 1, 2, 8, and 9 are ‘maybe’s. Stay aware of that. It’s safer to line mark r6 first, then follow the collapse.

We haven’t touched on all of basic solving here. You may want to consult early posts on naked and hidden subsets, X-wings, the hidden dublex, and boxline restrictions. And if you live in the Akron area, you could even ask the library to have me do a live session demonstrating how all this is done with PowerPoint and Sysudoku templates. Deb in the Cultural Arts department, our own Akron Tournament Director, has my email.

mensa xwing 13The basic solving clinic is over. Turning our attention back to advanced solving techniques, next post continues the review of Peter Gordon’s Mensa® Sudoku Guide, with its advanced instruction. Peter begins with fishing. I suggest you re-enter Gordon’s world by taking on his first advanced example, demonstrating the X-wing.

No, I’m not asking you to do it as Peter would, by “scanning” as far as you can, then doing a number scan on the remaining cells to get the remaining candidates, and to pick up the remaining “one- choice” and “elimination” opportunities. Just use the dublex bypass, and search among the candidates for the X-wing. It has to show up in line marking if you don’t see it earlier.

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The Fiendish 100 BUG-gy Maze


Bad news for Su Doku Master Wayne Gould. Fiendish 100, the only “Fiendish” of our Train Your Brain Su Doku Fiendish review to survive line marking, is found to have at least 15 solutions. The solutions are revealed in multiple BUGS, an irony in itself, since a BUG can be expressed only with the pencil marks that Wayne urges us to do without.

fiendish 100 DBTo begin the Fiendish 100 report, here are the dublex bypass and box marking traces, followed by the resulting grid.

 

fiendish 100 BM tr

 

 

 

fiendish 100 BM grid

fiendish 100 LM trLine marking depends on two naked singles, and deals with many triples.

fiendish 100 LM gridWould you want to do it without pencil marks?

I didn’t think so.

 

 

 

 

 

 

 

fiendish 100 SdCThere is not much for advanced techniques to do, but to start, I find a potential  Sue de Coq in

Nr2=6(1+5)(2+7)

+627 +672.

fiendish 100 veriBUG trTo eliminate 5r2c2, I have to verify it, by proving that 15 is not missing, leaving Nr2 = 627 +672.

The trial trace runs right into a Bi-value Universal Grave. I color the two solutions immediately.

fiendish 100 blue greenDespite the name, a BUG is not a death sentence for the composer, but it is a big black mark. It’s not supposed to happen. Some “experts” recommend solver eliminations that prevent an iminent BUG on the theory that the composer could not possibly have foisted a multiple solution puzzle on the public.

I have found that, instead, composers sometimes do that. We should expose composers who do not fully employ readily available computer technology to prevent multiple solutions. Note that I am not talking about unique rectangle eliminations, but complex BUGs such as this one.

When a multiple solution is encountered, it signals a slippery region of puzzle logic that accommodates multiple inputs and gives the solver no logical toe holds to climb on. In this case, the faulty Sue de Coq verification BUG left me with the suspicion that more solutions may be lurking in beyond the failed Sue de Coq’s 5r2c2 elimination. It turned out to be at least 15 solutions.

I decided not to post the seven additional grids necessary to show how the solutions are derived, but those interested can ask at sysudoku@gmail.com  for the PowerPoint solution file for Fiendish 100.  The search follows a pattern I’ve used before. Use the Find It page above to find them.

The NPM challenge was fun, but it won’t be continued in the Order of Battle. I believe this collection was tailored for NPM, in tune with Wayne’s beliefs. We have adjusted Sysudoku basic solving toward NPM, by including a dublex bypass in box marking. I believe the combination is a little more efficient than box marking alone, on average, and adds a challenge .

The Fiendish puzzles are a treat for basic solvers, NPM or not. On a road trip, my grandson Daniel and I had a solving contest with them. He won.

Before I begin the review of Peter Gordan’s advanced solving instruction, ending the basic clinic, I’ll be posting my annual report on the Akron Sudoku Tournament, put on by the Akron-Summit Public Library, with the support of Will Shortz. The puzzleakron 14 champs are basic level. You will learn how my dublex bypass for timed contests would have fared in the hands of the rapidly thinking winners, as opposed to me, in whose hands it failed decisively.

Participants who have the puzzles will be able to get sysudokie traces for all the puzzles by request on sysudoku@gmail.com. In the post, I’ll have a review table including all tournament puzzles, and a full trace of the championship puzzle shown here.

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Fiendish NPM Wins and Loses


The NPM collapse of Fiendish 130 is checkpointed, with regular slink marking backup on the solving logic. Then slink marking reveals the more demanding mental task necessary for NPM solving of Fiendish 145.

Your “No Pencil Marks” trace to a collapse of Fiendish 130 could look like this:

fiendish 130 npm tr

If you got stuck, this corresponding regular slink marking will reveal what you missed:

fiendish 130 reg trIt is longer, isn’t it?  And the point is, we won’t be needing those slink marks.

fiendish 145 npm gridTurning now to Fiendish 145, the win streak ends. on my first attempt, I managed only four NPM clues. The anemic trace was

NPM: W3, N6, C7, C4

Going back to slink marking, it became evident that I had missed something. Do you see it in the “2:” marking?

When the naked pair 12 closing chute Cc6 is noticed, the NPM trace becomes

fiendish 145 npm trA little better, but note, that in this trace, the causes of (C4, C7), SE6, and E8 are hidden. This is not a good feature of a solving trace,  another reason to reject the notion that “no pencil marks” is a superior mode of solving. Pencil marking and tracing the naked pairs, as in dublex bypass tracing, would at least track the state of locked sets and uncommitted cells.

fiendish 145 BM gridHere is the full result of box marking Fiendish 145. It comes with another strike against NPM. This puzzle requires extensive line marking. Would you want to do it without these pencil marks? Why?

I believe what the NPM solvers would actually do is begin trial and error probing, starting with the naked pair. I hope not. If the answer is more important than the logic leading to the solution, I say just look in the back.

And by the way, in line marking, do line strings count as pencil marks? Do we have to give them up as well, in order to be enlightened?

Outside of the preselected review puzzles, I ran across Fiendish 41, a puzzle that raises an army of naked pairs. For this one, NPM is like blindfold chess.

fiendish 41 gridBut the dublex bypass, just by pencil marking the cells locked by the naked pairs, keeps the parade going. From this bypass grid, you can recover the given clues and walk through the trace below to experience this remarkable solving effect. Following the bypass, box marking, line marking and solution are easy.

 

 

fiendish 41 trBottom line, there is no reason to forgo pencil marks in solving advanced and extreme puzzles. Wayne Gould, and others that claim otherwise can provide no evidence on puzzles not fashioned for NPM. Puzzle publishing is up to its hips in hypoku, and favored labels like “fiendish”, and “no pencil marks” admonitions are equally naive.

fiendish 100Next time, I’ll derive and display the multiple solutions of Fiendish 100. Want to try your own technique first? You have one week.

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Gould’s Not So Fiendish


This post begins a review of Wayne Gould’s Fiendish collection in his Train Your Brain Su Doku. The review is an opportunity to take up an important issue in basic solving, the use of pencil marks. For the ten preselected puzzles of the Fiendish review, instead of the dublex bypass of recent posts, I begin box marking without pencil marks. I checkpoint it in a separate trace, labeled “No pencil marks”, or NPM. This Wayne Gould review concludes my series of posts on basic level collections, and my clinic on basic solving.

fiendish 85 npm trHalloween is over, but was Fiendish 85 a trick or a treat? I was surprised that NPM carried me to a solution. Here is my 2-D trace.

Read it by filling the grid as you go and supplying your own reason for each effect, given the cause and the state of the puzzle at that point. Except that with NPM you have to remember candidates of that state.

Actually, my trace follows the same path as the usual slink marking. Without pencil marks, however, you have to remain aware of the slinks and naked subsets you are not allowed to write in. A good example is 6: S3. This necessary “marks memory” is also responsible for N7.

Any remaining mysteries should be resolved by following the regular slink marking 2-D trace. I carry it below to a point where it is no longer necessary to keep marks and closed sets in mind,

fiendish 85 bm tr

fiendish 85 slinks gridwith the grid now looking like this:

I know several Sudoku solvers who operate without pencil marks, but I haven’t investigated how they do it. The Fiendish 85 example illustrates how a sysudokie, accustomed to slink marking and closed subset marking, could do it on a basic level puzzle.

 

 

For the review, I preselected every 15th puzzle starting with Fiendish 10. The table includes the number clues I was able to add in the NPM phase, with a reasonable effort. Let’s consider it an average sysudokie performance, with many of my readers doing better.

fiendish review table

For two puzzles, the collapse (—-) was reached in the NPM phase of box marking. With one exception, there were very few clues added in box marking after NPM, suggesting that the NPM clues are those normally found in box marking anyway. The exception is definitely an outlier, being a multiple solution puzzle.

Another very noticeable feature of the collection is that it is definitely basic level. Line marking is generally easy, when it is necessary. Fiendish? Hardly.

Wayne Gould is a very successful purveyor of a computer solver, and a long standing supplier of daily puzzles to newspapers. Peter Gordon, again in his Mensa Guide to Solving Sudoku, relates how Wayne became well known in Sudoku history. It wasn’t his knowledge of human solving, or his opinions of pencil marking, as quoted in Train Your Brain Su Doku Fiendish. Wayne says:

“If you are writing too many pencil marks, it means you are not understanding how the puzzle works. You may be relying too much on mechanical procedures, without appreciating the underlying logic.“

At first I was aghast at this proclamation, until I realized that nowhere did Wayne specify what “too many” means. Maybe he wasn’t dissing slink and subset marking at all. He could have been making a valid criticism of the inefficient, mechanical process of finding candidates by number scanning that we have called out expert after expert for advocating. Number scanning is indeed a mindless operation that does indeed generate too many candidates, and too many pencil marks.

But then Wayne goes further, with “If, in time, you can shake yourself free of written pencil marks, you will see the Su Doku puzzle for what it is – a thing of beauty!” By the special spelling we are to understand that Wayne means his puzzles

Now that’s going way too far! Here Wayne must mean all pencil marks. And only if you go without them, can you behold the beauty of his puzzles. That’s ridiculous. I agree that keeping the marks in mind, and not on paper, is good mental exercise, but it’s going to expose less logical truth, not more. Take my own results in this post, for example. In the review, my NPM home runs were 2 of 10, but my basic collapses by slink marking were 10 of 10.

And what about advanced methods? Are you prepared to remember all viable candidates so you can do the advanced repertoire blindfolded?

Wayne’s opinions on underlying Sudoku logic will get more respect when he demonstrates  genuinely advanced and extreme level Sudoku solving.

What’s your opinion on solving without pencil marks? And do you think those who do it, on very tough puzzles, are really solving? Or could they be doing simple trial and error? That can be a mental challenge, but it is not solving by the Sysudoku definition.

As to the Fiendish collection, I have several tasks in mind to do, all bearing on the pencil marking issue.

fiendish 130First, I’ll checkpoint Fiendish 130  the same as I did 85, giving readers another shot at one for which a legitimate NPM collapse is within reach.  That will be next post .

Then I’ll examine one with which I had the least NPM success, Fiendish 145. I intend to use the successful regular slink marking to show what mental gymnastics would be necessary for NPM there.

Next, I’ll demonstrate a puzzle for which the difference between NPM and the dublex bypass is stark, Fiendish 41. It’s not a review puzzle, but one I encountered in the car service department waiting room.

Finally, you may be interested in the analysis discovering the 12 solutions of Fiendish 100.

If you have Train Your Brain Fiendish, you can go on ahead and start uncovering all of these fiendish secrets. Meet me at the passes.

 

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Just One More Dave Green


Here we savor one more basic solving 5-star gem by Dave Green, appearing in my paper, the Akron Beacon Journal, October 19, 2014.

My plan was to conclude the Dave Green portion of the Sysudoku basic solving clinic with the white knuckle 6/19/14 offering of the previous post. But a writing pen encounter with the newsprint version of Green 10/19 had me believing this one was going to escape Dave’s controlled delivery and get into advanced territory. A careful PowerPoint solving session brought relief, and was very entertaining, so I squeezed it into the blog schedule.

The checkpoints of the Green puzzles represents very well my current thinking on basic solving, including the latest innovation in the basic clinic. If you are a new reader, I recommend you work through the early posts on basic solving, then follow traces of the clinic, catching up on advanced solving later.

green 1019 DBMy dublex bypass took respectable advantage of Dave’s four “wells” in 10/19.

green 1019 DB tr

 

 

The DB clues speeded up the very productive box marking.

 

green 1019 BM tr

 

 

 

 

green 1019 BM

Line marking is tough, starting at 4 free cells and going to 7 at r8, when . . .

green 1019 LM grid

a naked quad triggers the collapse.

fiendish 85 So here’s to Dave. Maybe someday I’ll review his 6-stars or higher. Right now, I want to continue the Sysudoku basic solving clinic by reviewing a collection of New York Post puzzles by Wayne Gould, the well known composer. Wayne made some intemperate remarks about pencil marking in his Train Your Brain Su Doku Fiendish Edition. I’m going to do what I can to refute them, as I review this collection.

You can get a jump on the review by tackling one of his “fiendish” puzzles, # 85. Before box marking, I’m going to do as Wayne suggests, and find as many clues as I reasonably can with no pencil marks( NPM).

NPM is very close to the recently introduced sublex bypass, excepting only that the naked pairs are remembered, not written. Try it NPM, and I’ll back you up with checkpoint tracing. As in the bypass, I won’t be listing NPM effects in separate lists by number.

There’s always a chance we might learn something new, don’t you think?

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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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