Bypass & Tracing

Here is the bypassed grid of the Washington Post Saturday 6-star of June 11, 2022. The Bradley hand writing type font distinguishes the derived clues from the givens. The naked pair 47 in column is its only subset so far.

The moves in Sysudoku are reported in full detail by means of its basic and follow up trace. Here is the trace leading to the grid above. You could place the givens on your puzzle grid and follow the grid state on every bypass move.

The trace is a two dimensional cause and effect map. Indented under each cause is an effect or list of effects. Lists of effects are fully posted on the grid, but listed effects become causes one by one, left to right. All descendant effects of a cause are posted before the next listed effect becomes a cause. So for example, the traced bypass causal sequence is

, where “=>” is read as “causes”, and “,” is read as “and”.

For trace readability, Sysudoku uses compass direction names for boxes, instead of conventional box numbering. The center box C is the compass “you are here”. Lines and cells are alphabetic lower case, numbered left to right, and top to bottom.

In the trace, a clue is marked by box and value. The cell location, and the reason the new clue is there, is omitted. That makes the exact trace compact and practical to publish. But reading it requires writing the moves on your own grid, so you have the puzzle state on each move. Such trace reading is valuable for any Sudoku beginner.

The Sysudoku Basic bypass is a two – front attack. On one front, outside clues and aligned strong links “see” into a box, limiting the box cells available for that value. Meanwhile, as clues and subsets are placed, the fewer remaining free cells can be filled with missing values.

In the bypass, the objective is to limit to a single cell, a new clue. Or maybe two values limit the box to the same two values. Two tactics apply. Going to the trace above,  NW4 is, in Sysudoku Speak, a cross hatch.  NE4 and SW4 lines cross and leave only NW4 for 4. Why did we start with 4? We didn’t. After we look at all the basic tactics, you can verify that no earlier start was available.

In the frontal attack, new placements are made when the unit, the line or box is limited to a single cell or when two cells are left for two clues or a naked pair. Meanwhile on the second front, lines with 3 free cells, the 3-fills, can often be resolved to place clues or pairs. Or more rarely, the 4-fills resolve into clues or pairs.

According to the above trace, the new clue NW4 causes W4. Why is that? It’s an instance of the second frontal tactic. The new NW4 and the given SW4 exclude 4 from two lines crossing the W box, and given C4 excludes 4 from r4c2.  In Sysudoku Speak, the second tactic is named a double line exclusion. It’s handy to remember that name for your first few encounters, but we soon shorten it to dublex. W4 is a cross hatch of a given and a dublex. Both front line tactics are so common, we soon don’t mention them anymore.

Two tactics work together on the frontal attack.  Starting the trace above,  NW4 is, in Sysudoku Speak, a cross hatch.  NE4 and SW4 see 4 cells as they cross examine the NW box and leave only one free cell for NW4.

Why did we start with 4? We didn’t. After we look at all the basic tactics, you can verify that no earlier start was available.

According to the trace above, the new clue NW4 causes W4. Why is that? And where is clue W4? 

In the other frontal tactic, a double line exclusion in Sysudoku speak, the new NW4 and the given SW4 exclude W4 from two lines crossing the W box, confining W4 to the line c2. But C4 sees one of the free W cells on that line, leaving only one for W4. You can call it a cross hatch of a clue with a double line exclusion.

 It’s handy to remember that name for your first few encounters, but we soon shorten it to dublex. Both front line tactics are so common, we soon don’t mention them anymore.

Let’s take another look at the first leg of the trace, and give some attention to that second front of attack I mentioned earlier. The trace identifies two W4 effects, E4 and W5 in a list.  We see the cross hatch of the r5 dublex and hard working NE4 for E4, and how the c2  dublex on 5 brings in W5.

On the grid, we pencil mark W5, because E4 has two effects which are in line as causes, before W5 becomes a cause and gets its effects get worked out.

That other front in the bypass attack is to look ahead, as clues and subsets come in, to see when free cells get few enough that we can directly place values in them. Sysudoku has spotting rules and procedures for doing that.

We start lookng when we’re down to 4 free cells. Such a line we call a 4-fill. 4-fills often fail to resolve, so we don’t mark them on the grid until they do.

Of course, some puzzles start with 4-fills. If one starts with 3-fills, we try to resolve them before doing the 1 – 9 scan of values. So on the current grid, we actually started with a 4-fill, and added one with E4 and two more with W5.

Here’s something remarkable, though. Imagine if clue NW5 is to its right on r3, so the c2 dublex on 5 doesn’t happen. We get W5 anyway, as a resolved 5-fill. Four of the five free cells in c2 see a 5.  But as you can also imagine, this doesn’t happen often enough to be looking at 5-fills, or even looking for a 3 out of 4 resolution in 4-fills.

Instead for 4-fills, the bypass takes advantage of the higher  probability of 4-fill resolution with a 4-fill meeting this test. Looking at the starting grid 4-fill in c5, we have two cases of 2 cells in a box, but in both, the value the box sharing value is not missing. You can check the other three 4-fills seen so far.

On E4, another cross hatch of clue and dublex gets SE4.  The way the trace works, C3 is included on the grid as SE4 takes effect. So why C3?

The bypass uses slinks to find clues, without stopping to mark them.  The 4-cell square in SE creates two  3-slinks. You quickly learn to see them in the corridors of the uncluttered grid. See these two? Given S3 puts a 3-slink in Sec7.  We mark it for advanced work when we get to box marking, but right now we’re free wheeling, and that slink clears 3 from Ec7, to generate the 3-slink in Er7 that makes a dublex with W3 to place C3. It takes a little practice to see and use slinks before marking them, but this is why Sysudoku DIY’ers like the clear grid slink fighting of the bypass. It also helps to have a big laptop puzzle template and (c)PowerPoint graphics.


Now, before before all of its other effects are known,  C3 creates a wall in Cr6, so when W5 becomes a cause, it will use slink in Cr5 to place E5 and we’ll have a 2-flll in r6. But first, we need to figure out where the trace’s S2 goes.

We don’t even have a given 2 clue. The c5 4-fill must have something to do with it.

Indeed it does. 4-fills tie in with naked singles.

Naked singles?  Cells seeing all values but one. Ordinarily its impractical to check every  cell’s box, row and column for naked single’s. Too many looks for too little reward. But an unresolved 4-fill cell sees five 4-fill values already. If a free cell’s crossing line has three more, it’s a naked single. 

R9 has 4,5 and 7. Place the Sns2 in r9c5, and you have the trace’s c5 3-fill to resolve. The trace marks an n-fill with square brackets, and resolves it into an effects list. The c5s47 says “subset 47 in c5”.

The Guide offers two ways to resolve a 3-fill. In this case, free cell r1c5 sees missing values 4 and 7, placing 5.

S2 also makes r9 a 4-fill, but the trace says it doesn’t resolve. For the Cell/Box check above, SW4 is not missing. The 4-fill rule we just used for the 3-fill would require a free cell to see three of the missing values r9[1369].

Reading the bypass trace, we return up the indented steps to C3, promoting it to a cause, and place E5 and the r5 2-fill. W2 leaves an unresolved 4-fill in c1. C3 effects recorded, we promote W5, and have two 4-fills to check.  The 4-fills fail and we move on to the next list value.

At this point we have the 5-9 values to scan for the S6, NE9 of the bypass trace, but I would probably do a quick check of 1-4 first, for anything overlooked. NE9 brings an unresolved 3-fill.  I like to mark these with fill strings (see line marking).  On your reading grid, you should have the bypass grid we began with.

This example continues in Box Marking, off  About Sysudoku.