Begin With the Bypass

Sysudoku Basic starts with the slink marking bypass, so called because it defers the marking of strong links to later Basic stages. Strong links?  A strong link is a link between two candidates, so first, what is a candidate?  A candidate is a possible number value to become the true value, that is, to be assigned to the cell in the solution. Sudoku means “number placement”.

Candidates are marked by small numbers placed in the cell, the pencil marks,  to represent currently possible placements. A strong link means that at least one of the linked candidates is true, i.e., is in the solution. In solving it is essential to recognize the strong links. Here we talk about them so much, we call them slinks.

Slinks are seen and used extensively in the bypass, but in Sysudoku, we don’t  pencil mark most of them until later. Many Sudoku systems fill the cells with all the candidates the puzzle defining clues allow, before making any placement.  That’s poor human engineering. In human tasks, detail that is not currently helpful is clutter. And actually many slinks are quite visible in the structure of the given clues. Sysudoku starts by using those slinks, but marking  only those that hold sets of cells in reserve for certain values. Clues and subsets are marked in the bypass, a subset being a set of n cells reserved for n values.

The bypass is a systematic process, concentrated on simple tasks at the right times.  Most of the resources of the bypass you will discover by your own experience with it, but you can accelerate the process by reading detailed traces on puzzles reviewed on this blog.  This page takes you through a detailed bypass of a 5-star Dave Green puzzle, to its collapse point. The walkthrough explains how you read a bypass trace, by describing the writing of one.  For that, here is a briefing on grid geography in Sysudoku.

Here is how boxes and lines are named. 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 and subsets restrict  a value placement in 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:

beginners-dublexOne 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.

beginners-crosshatchThe other bypass mainstay move is the crosshatch. Clues of the same value 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. These pages will show you many advantages of tracing, when dealing with hard puzzles.  In Sysudoku traces, space is saved by not saying why or exactly where in the box the change occurs. Instead, the trace reader knows, or figures 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 a 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.

Starting with 1, we look at the crosshatch targets NE and S. Just this once, sweeps are denoted by arrows. Four NE cells can contain 1. In the S box, two candidates form a 1 -slink. Since one of these candidates is true, the aligned slink joins c4 in a dublex confining C1 to the intersection Cc6. Three cells, and we move on. We’ll write in the slinks in box marking.

Now check for clues and slinks for the value 2. There’s more than two, so you check the incoming on every box not containing 2. Cover this and compare your results with NE:  2, W: 3, C:2, SW: 4, SE3.  That’s the order of the scan for Sysudoku traces.

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.  Now for the record,



we can start the bypass trace with NW3 as 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  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 Sysudoku traces will make you a Sysudoku Basic expert.

The trace is a trace writer’s bookkeeper. It contains every effect that has not been used as a cause, and the solver knows exactly where the next cause is in the trace. Writing traces will enable you to track down and correct your mistakes.

The effects list should include any effects on earlier values, in this case, values 1 and 2. Effects on later values are can be left to show up in later lists. No need to check for the same event twice.

Note that W3 is posted above in pencil mark size. That marks it as an effect not yet used as a cause.

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 values. In Sysudoku it’s called 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 values in square brackets 

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[148], and the given 4 seeing two of its cells.  We jump on the two remaining free cells of r9, where N1 places the missing 1.

Here is trace to this point.  How would you continue it?  Where does the S1 and S8 go? Who is the cause of the two-cell squeeze that now produces S7 and S3?

It will help if you write your own trace as well as maintaining your own grid. Sysudoku Basic is easy to do but is too organized and graphic to be easily conveyed in words.

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. Follow that verbiage with your trace extension.  Check yourself out on the next full trace panel.

This exercise illustrates some of the advantages of solving and tracing with an office tool like ©PowerPoint. This advantage is even more striking when we get to doing the Advanced graphics you have been enjoying in the blog.

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.

It’s a subset known as a naked pair. The two cells are reserved for 4 and 8 and these candidates will be the only two candidates of these two values in the box. Pencil marks are added at the top of the two cells because we have two box slinks.

In the trace, the products of a 3-fill resolution are listed as its effects. From this list, W1 produces a 3-fill in c3, and NW48 resolves the N box 3-fill, for five clues. Imagine all that, then check yourself below.

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 useful 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.  In the bypass, you use the  6-slink to exclude 6 from c2, and write it  in box marking. 


Let’s end with a basic method that occurs rarely in the bypass, but frequently in all further Sysudoku stages, the hidden dublex. It’s at work in this grid, taken from the review of Moito i-4  posted January 9, 2018. The trace reads Whdx2, telling us that a hidden dublex is placing 2 in the West box. Can you figure out what a hidden dublex is, and where in W the 2 goes? Check your answer in the plaque at the end.

If you came out all right with the Moito bypass hidden dublex, and the hdx definition plaque ending this page, you’re ready for this one, a trace reading challenge from the Tom Sheldon Master Class review.

You’re reading through the bypass trace of Master Class 50 in the post of 8/20/19. You’ve just put SW5 and S1 on the grid and the trace says that

SW5 = > NEhdx5,

Where in NE does NE5 go, and why does it go there?




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 marking skills to follow up every removal or clue.

Next on the Guide path to advanced puzzles are the pages on box marking and line marking, but you might want to master the bypass first. After all, there are hundreds of bypass traces from collection reviews that you can walk through with your own grid, pinning down the logic of each bypass step.

The bypass begins every basic trace. You can select puzzles by the number of value placements made in the bypass, or whether or not the puzzle collapses in the bypass. Look in Reviews/Review Tables for interesting puzzles, and the Titles/Collections for their posting dates, then use the archive calendar on the right to find the posts.  No telling what you might notice along the way.

Here is an example, the review table of Chamberlain’s Super Fiendish Sudoku:

On the left are the puzzle numbers. The Gv column tells the number of givens, and the BY column is the number of clue and subset bypass placements. The blank symbol — signals a  collapse in the bypass. This is where you get examples of the Sysudoku  follow through designed to leave no asset overlooked.

Again, an understanding of this page, and its Sysudoku Basic examples, is sufficient for mastery of most newspaper and magazine puzzles, up to a 5-star level.

When you have confirmed this, you’ll be ready to try your bypass skills on this example, from a review of A.D. Ardson’s Sudoku Diabolical.  It’s puzzle 350. Trace your solution and compare with the trace posted on 2/13/2018.

This page is the first of a series of pages on Sysudoku Basic, Advanced, and Extreme methods.

After the bypass, the goal of Sysudoku Basic is to prepare for Advanced methods, and for puzzles fairly labeled as Hard, Very Hard, Tough, Super Tough, Diabolical, Extreme, etc. Collections of such puzzles are available in books and websites.  Many collections are review Reviews page on Find It, and in the Titles page, or on the category sidebar.

You may be looking for:

The W2 is placed in r4c3. The dublex is hidden because the bypass starts with a series of 3-fills and the dublex is apparent before the Basic reaches 2 in box marking.


10 Responses to Begin With the Bypass

  1. Roger says:

    Hi, I’m definatly an amateur when I comes to Suduko. I approach the puzzles with a different goal in mind – use an Ink pen and don’t put anything down on paper but the answer. While this eliminates me from the more advanced puzzles, it has helped me to exersize my mind and memory – which was my primary goal.

    • Sudent says:

      Thanks for the comment, Roger. You would enjoy The Nikoli puzzle books distributed in U.S. by Workman Publishers NY. Your strategy is probably one that computers use on all puzzles, backtracking trial and error. You go further than most of us can, and it does sharpen the mind. Let me know if you ever get pulled into sysudokie land, the subject of my blog. It’s a different world, equally fasinating.

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      Jeffrey, my theme is the WordPress default theme Twenty Ten. Most of the graphics come from the templates described on the Solving Templates page, with PowerPoint graphics shapes and tables added. My header is a slice from my travel photos. I’m happy you like the effect.

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