## The Sudoku Satisfaction Tour

In the next three posts, I introduce Sudoku Satisfaction  by Richard Nicholas Seemel, by inviting sysudokies to attend a tour for Satisfaction readers. The tour will highlight differences between  two systems that agree on basic solving approach, but not on its fundamental procedures.

Last November I was delighted to receive and examine an autographed copy of Rick’s Sudoku Satisfaction. Rick is a retired engineer(civil), and clearly values the human engineering of Sudoku solving.  This is the first opportunity I’ve had, after Hidden Logic, to review this book.  Rick understands what I do, and has the generous spirit to encourage me to do it with his book. My review will be in the form of a tour for Satisfaction readers, explaining what they can do with the basic solving knowledge and experience gained from Sudoku Satisfaction.

Before the Satisfaction people arrive, a word about their book.

Sudoku Satisfaction is thin on the shelf, but packed with definitions and examples, mostly on basic solving.  Like another one-of-a-kind, Carol Vorderman’s  Master Sudoku, Satisfaction does not acknowledge advanced  techniques based on linking relationships between the remaining candidates(canos), the techniques I have spent so much of your time on.

A mark of Rick’s independent approach to Sudoku is a barrage of coined terms for many basic  concepts. I cope here by placing Rick’s term after my customary one where it first occurs, and outside of that, adding quotes around the Satisfaction coins, as in “canos” above.

Satisfaction has an Order of Battle (the guideline), somewhat like Sysudoku basic, with phases that are followed systematically.” The “guideline” is designed to find easy clues (unos) before number scanning(inscribing) the remaining candidates into cells(squares). Scans are done repeatedly, consisting of an “inspection” to identify the most promising box, followed by the chosen action. Actions consist of modified slink marking (slotting), box marking (lacing), line filling(completing the count), or a number scan on a cell (crossing). When no further actions seem possible, a full number scan (inscribing) is performed. Slotting leaves aligned slinks and triples in place, for use in inscribing.

The one major difference is that, in Satisfaction, subsets (partnerships) are “advanced”, i.e. defined following “inscription”.  Satisfaction does a form of pencil marking, placing “cano” digits in keypad style. They mark aligned box slinks and triples, calling it “slotting”, and . . . Uh Oh, they’re coming in. Please move back and give them room in front.

WELCOME SATISFACTION FANS!

We’re so happy you could come for a tour of our Sysudoku resolution factory, where we manufacture solution traces and diagrams for the toughest Sudoku puzzles in the world. We’re standing now at our box marking line .  Down there is our puzzle loading bay.

We’re starting the tour by walking through a Sysudoku box marking of your 4-1 example puzzle, looking at both grids and traces.  Box marking “flow” is by increasing number, so here we’re missing Satisfaction’s 9 run and resulting 1 run, but on completing the 4’s, we are making progress, with “uno”s and “slots” on the grid.

Actually the pencil marks are not exactly slots. Most are aligned strong links defined by boxes.

Candidates of a number in a unit form a strong link when there are exactly two of them in the unit. If one is found to be false, the other must be true. That’s the logical definition of a strong link.  Like Rick, Sysudoku uses selfie names for important concepts. To us, strong links are slinks.

We also mark triple candidates in a slot as in Box 6.  I should tell you, to us, Box 6 is the East box, or E. Boxes are named for compass points, with C in the center. So E appears in traces, not MB RT (Middle Band, Right Tier), or B6.

Now let’s look at the corresponding box marking trace. This is how it starts:

The trace has a list of marking effects for each number. I know you’re used to scanning combined effects of numbers, one box at a time. We look for “lacing” effects of clues and slinks on all boxes, for one number at a time. When they sweep into boxes along a bank or tier, we call it a double line exclusion, or dublex. When they come from two directions, it’s a crosshatch. But we seldom use these terms. Here’s why:

In Sysudoku traces, every effect is shown, so we must be brief.  Compared to Satisfaction, we save tons of space by reporting the “what”, but not the “why”.  In Sysudoku basic, the “why”  is supplied by the reader. They know, but don’t particularly care, whether it’s a dublex or a crosshatch.

Each effect depends on the state of the grid at that moment, so looking at the grid above, you need to know the state it was in as you read every effect. For that reason, you read a trace by starting with the grid of givens, and filling it out as you read. Also, the trace leaves the exact cell (square) of the box unspecified.  Of course, you have to know some simple abbreviations as well. The “m” stands for slink “marks”, “t” is “triple”, “np” is “naked pair” (twin pair). A number alone marks a “uno”. The “m” with no number means it’s the list number.

Sysudoku traces show cause and effect, and the order of solving, what you know as “the flow”. Causes have their effects listed beneath them, indented to the right.  When there are multiple effects from a cause, the list of effects is in parentheses. Causes are slid to the right to create space for their effects beneath them.

In the trace, Sysudoku flow is therefore left to right, and depth first going down. Every effect from a cause is explored before the next effect on the list becomes a cause. The 5: trace illustrates all of this well. Now it’s time to get out the handout on trace reading.  The grid is already posted for lists 1 through 4, check this out for a minute, and we’ll follow the roller coaster on list 5. . . .

Ready?  After the box slink in NE, a triple in C makes a small run. Next, we post SW5, and its four effects. Only S3 continues the run. Do you have a good eraser? OK then, in the list of S3 effects, post the S9 and S8 as pencil marks in the center of the cell (square). You can replace them with full size digits when they become causes. It’s to keep track of where you are. Meanwhile you have the SE3m effects to post, with small font SE3, unless you anticipate that NE8m has no effects.

C3 ends the run, and we go up to promote S9 to full size, then S8. These font size changes are less messy for me, because I do it all in ©PowerPoint.

That’s another point I wanted to make. Sysudoku is for tough puzzles. Pencil and paper is fine for easy puzzles or casual solving. But the art of tough solving is detailed and error prone. ©PowerPoint is a great pallet, tracking system and record book. Many resolutions go on,  sheet after sheet.  The sysudokie focus on tough puzzles explains the special machinery on the floor here. We display selected information and construct candidate (cano) networks to enhance the vision of the human solver, and minimize ineffective searching.

I see that everybody gets the idea, and most of you finished posting the handout grid, while I was rambling on. Here’s what it should look like now, less a few smudges.

Rick’s run of the 9’s in Satisfaction 4-1 shows up in two places. At SE7 we had an hidden single c9 for a NE9, but when I looked on the trace  for the last move that enabled it, I discover that it was there in the givens! You can do that kind of thing with a trace. In the previous grid, we had another earlier cause for the single NW9 from a line marking (c-u-c) on c3, but I just left it in reserve for the 9: list. I do that for numbers higher than the current list, except when the unit filled had three unresolved (blank) cells (squares) or less.

Question from the back? . . .

Yes, you see the 8r8c6, and what happened to the crossing that found it in Satisfaction? Well, we don’t do number scans(crossings) in box marking, simply because it’s harder than box marking, and we can do it easier later. Number scans are done a line at the time, in line marking, the major stage after box marking.  There, we take advantage of box marking result, and common fill needs of remaining free cells on the same line.

That brings me to the other major difference in basic solving between Sysudoku and Satisfaction. I mentioned the strong link being important enough for a coined name in Sysudoku. Another type of link between candidates has one, the weak link, or to us, the wink.

The logical connection between wink partner candidates is, well, weaker. If one is proved true, the other is false. They can both be true, or both false, but they cannot both be true. All candidates of the same number in a unit are weakly linked.  Another term used for winks is “seeing”. Wink partners “see” each other.  The slink is stronger because, if another candidate “sees” either partner, it is doomed.

Seeing is the essence of the melting of partnerships illustrated in Satisfaction.  It is also the essence of commonality and crossing square patterns. A square “sees” like numbered candidates in its CSP. Sysudoku concentrates more on the logical properties of candidate links, because many advanced methods depend on winks and on chains of candidates that alternate slinks and winks to extend seeing across the grid.

I’m hearing that lunch is ready, so I’ll just say that 4-1 collapses in marking the “6:” list. The trace gets you well into the collapse. Here is the solution, in case you need it. On the way  to lunch, please wash your hands

After lunch (and to be reported next week), we’ll demonstrate the slink marking bypass, and line  marking, a more efficient inscribing procedure, and how “partnerships” are handled in Sysudoku basic, not after it.