Systematic Sudoku, or Sysudoku, is a human engineered system for solving Sudoku puzzles of all levels of difficulty, and for documenting the solving process. It uses constructions and visual tools in place of exhaustive searching, for a more humanly effective, and enjoyable solving experience.
The parent page Sysudoku Basic explains the human engineering design of Basic, the stage in which candidates are identified. Instead of the traditional keypad display of number scanned candidates, Basic defers the finding of all candidates in favor of using new clues and subsets along with the givens, to keep the number of candidates generated as small as possible. It further supports Advanced methods of solving by marking strong links (slinks), subsets and bi-value cells (bv) on the candidates grid.
Basic starts the solving process with a challenging task of deriving new clues and subsets from the givens and its own results. This is the slink marking bypass, so called because it defers even the marking of slink partners, along with other candidates, to later stages.
The bypass is a human engineering feature. Slinks and other candidates are marked in preparation for advanced methods, but most puzzles of moderate levels of difficulty do not survive an efficient bypass. The bypass challenge makes these puzzles more entertaining for all players, even the most expert.
The bypass is a systematic process, requiring concentration on simple tasks being done at the right time. The bypass on a puzzle can be succinctly recorded in a basic trace, and played back by readers wishing to think it through and master it. Basic traces of review puzzles are available throughout the blog. This page takes you through a detailed bypass of a 5-star Dave Green puzzle, to its collapse point. The walkthrough includes reading the bypass trace.
Here is how boxes and lines are named in Sysudoku. Box names are compass directions from a center box C. Rows are numbered North to South, and columns, West to East.
The bypass works by discovering where outside clues restrict placements inside a box to one cell. A box can contain only one clue of each value. Clues outside the box “sweep” the value from cells in the same line of the box. Outside clues on different lines can coordinate to force a clue in the box, in two ways:
One bread-and-butter move of the bypass is the double line exclusion, or dublex. In the dublex, the same value sweeps two lines of two boxes in the same direction, forcing a placement in the third line of the box they cross.
Of course, new clues join right in, eliminating clues in other boxes. In all Sysudoku diagrams, added clues and pencil marks are in a script font, like the 1 above. Formal script numbers, like the other clues above, are givens, which define the puzzle.
The other bypass mainstay move is the crosshatch. Clues of the same number in two crossing lines simultaneously sweep a box. Here, E (East) and SW (yes, SouthWest) 1’s sweep the W box, leaving only one cell for the W 1-clue, or as we name it in Sysudoku traces, W1. Where is W1?
Did I mention traces? A trace is a record of the solving actions. In Sysudoku traces, space is saved by not saying why or exactly where in the box the change occurs. Instead, the trace readers know, or figure out, why the change occurs. They post each placement to the grid as they read. In this case W1 goes into r6c1. On partial grids, you have to look where it is cut off. Was that your answer?
OK, let’s do the bypass with trace on a 5-star puzzle. This one was offered in Dave Green’s the Akron Beacon Journal on December 10, 2017, a Sunday.
We sweep all boxes of each value 1 through 9 not already containing the value. When there are more than two clues of a number on the grid, we do this box by box, going West to East in each bank, North bank through South bank.
With only two candidates there can only be one dublex or two crosshatches. We need only look at the crosshatch targets NE and S. The S sweeps leaves two aligned candidates, which form a dublex with N1, confining C1 to the intersection of C and c6. This is not enough restriction for a clue, but it shows how aligned candidates can define clues, a very important principle in the bypass. Here the aligned pair is a strong link, and does restrict 1 in C to c6. What makes the aligned pair a slink?
The bypass goes better if we account for the effects of aligned candidates, without marking them on the grid. In the next phase, box marking, we do write them in. In the bypass the objective is sweeps leaving a single cell for a clue. In the grid above, see you can find a 2-clue.
It would be easier without the distraction of sweep arrows, but look at each box not containing a 2-clue, left to right and top to bottom. It doesn’t quite happen. Sorry for the tease, but the search is systematically necessary.
We have better luck with the 3’s, hitting NW3 immediately. Before looking at more boxes, however, we look for the effect of the newest clue. It so happens that NW3 generates NE3 and W3, both by dublex.
We can start the bypass trace.
NW3 is a cause, and indented below are listed its immediate effects. We continue by treating each listed effect as a cause. Each event is described as a clue value in a box. Trace readers are expected to post events to the grid as they read, keeping the grid up to date. Beyond that, the reader supplies the where and why. It’s a very compact record. Reading traces is a great learning tool.
For the effect list, we also check for any new placements of earlier numbers 1 and 2, ignoring effects on later ones, because we will get to them, and it is not efficient to check for the same event twice. Efficiency promotes happiness in Sudoku.
Note that W3 is posted in a pencil mark size. That’s to track that W3 is still a pending cause, as the first effect NE3 becomes a cause. It’s not practical on newsprint, but in a ©PowerPoint template it’s worth it.
What are the NE3 effects? The dublex with E3 leaves two free cells. Two aligned free cells can be significant, but not here. But looking in the other direction, there is something. NE3 leaves three free cells in r1, for three missing numbers. It’s a 3-fill.
A 3-fill is a box or line having only three cells free for placements. Here is the plaque on the Sysudoku office wall governing 3-fills.
Let’s call the first condition, the two-value rule; the second, the two-cell rule. These conditions produce surprising clues. Convince yourself that they work every time.
The 3-fill rule was adopted into Sysudoku basic in 2016, five years into the blog. Why do it? The 3-fill gets to the free cell squeeze sooner. One free cell means a clue, two free cells, a pair of cells reserved for two numbers. The 3-fill was moved into the bypass from the third basic stage, line marking.
You can extend the squeeze further with a 4-cell rule, with a three-number rule and a three-cell rule. That would require much more searching, for much less frequent clues. I think this puzzle tells us that we have the right balance.
In this case, the missing numbers are 4, 8 and 9. Neither condition is met, but what we can do is put a string of the missing numbers next to r1, the 3-fill unit, to alert us to any action that satisfies the 3-fill condition. It is represented in the trace by a 3-fill marker showing the unit and the missing numbers.
Still on the grid above, we turn now to W3, promote it to a cause, and find it has no immediate effects. Continuing the box scan, two free cells are left in C, two in S, and two in SE. On the 4’s, the single W4 has a chance because of the SE “wall”, SEr9 . W4 leaves an unwritten slink in SE. The hidden dublex leaves another in SW.
Going on to the 5’s, a crosshatch N5 leaves a 3-fill in N. Missing numbers are 4, 8 and 9 again. Then as the box scan reaches SW, the SE wall’s unwritten aligned triple dublex/NW5 crosshatch produces SW5, taking one of those free celsl for SE4. You could interpret it as SW5 creating a 3-fill r9, and the given 4 seeing two of its cells. We jump on the two remaining free cells of r9, and N1 places the missing 1.
Here is an unfair pop quiz. Who is the cause of the two-cell squeeze that now produces S7 and S3? The current trace holds the answer.
Now S1 is considered the cause of S7 and S3, because C8 is already posted as an effect when S1 becomes a cause, S3 forms two dublexes for C3 and SE3.
Notice how the trace at this point becomes a guide to the next marking action, in a way that avoids overlooking any effects.
When the C3, SE3 and then S7 bringing no clues, we step back up to the last effect listed, but not examined as a cause. We pull it to the right, where there is space for an effects list, and continue. In this case, S8 is the next cause, and the c4 3-fill is noted, with a fill string on the grid, and a bracketed version in the trace. Since the 3-fill has no immediate effect, the “step up” is actually repeated, with the search for the next “pull out” reaching the top line of the trace, where original causes are added, and we are directed to look to see if SE5 is there yet.
Going to the 6’s, place NW6 in the grid above, and you see three immediate effects, SW6 and 3-fills in NW and NE. The clue of the same number comes first. To list the effects first, then treat them in turn as causes, we list the 3-fills in unexpanded form:
SW6 completes the 6’s and has no effect.
In the NW 3-fill, the first condition of the two-number rule applies, for NW1. This leaves two cells for two missing numbers, 4 and 8, in NW. Whenever this occurs, and the placement are not determined by existing clues, as in the S box here, the cells are reserved for these numbers by writing them in as pencil marks. The marks are placed in the top corners, in a cell marking system called slink marking. More on that in the Basic Overview page.
Pencil marks to reserve cells for missing numbers are allowed in the bypass, when other pencil marks are deferred, because they directly restrict placements.
The N9 effects list ends with a NEr3 3-fill, actually a 3-fill in both NE and r3.
Here is the trace, which you can now follow to the next grid.
We not finished exploring the effects of the SE5 list, and have left behind many unexplored branches of the depth first tree.
As often happens, the 3-fill lists have stretched the trace across the page. Ordinarily, we could abandon the trace and fill in the remaining cells freestyle, but we one this one we may have trouble bridging the blank space in the middle bank.
The trace is continued here to the solution. Bypass generation of causes and effects continues in the same manner, clearly in collapse mode. You can continue solving and tracing from the diagram above, or continue by reading the trace as you post to the grid above.
This Dave Green 5-star featured a box configuration that is helpful to know about – the wall. Sometimes a number builds is own wall by sweeping the single cell missing from it.
As you read Sysudoku basic traces, you’ll become familiar with many more of these memorable box configurations. Here are two more.
A 2 by 2 square of clues creates slinks or clues from sweeps from either direction. Look along the passing row and column for clues or marks of numbers missing from the square. The square may include a pair or triple subset.
A sweep across a four-corner box of clues creates a slink in the other direction.
The Sysudoku Basic bypass is enough to handle newspaper and magazine puzzles, up to a 5-star level. In harder puzzles, you are using bypass skills to follow up every methods removal or confirmation. Next on the Guide path to advanced class puzzles are the pages on box marking and line marking.