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.

For 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. You can figure out most of it by following along, and nail it down with references pages later.  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.

I 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.

So 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.

N9 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.

When 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.

Now 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.

In 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 Popular Culture Department, our own Akron Tournament Director, has my email.

The blog’s 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.