An AndrewsMcMeel  6-Star Sample 4-fills Out

Scroll back for the givens grid. After the fourth 4-fill, we never get back to the three unresolved 3-fills in the bypass trace.

Here is the grid, just before SE6 (halfway down) wipes out the naked pairs.

The Sysudoku basic level close down is complete. Many basic level example traces are reached by scrolling back.  For each example, the givens grid is one post further back.

Earlier basic level examples, and advanced examples, can be located by date on Titles, and found by the monthly archive.

Next Tuesday’s post is the home page, with news of continuing updates.

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A Filling USA Today Weekend 5-Star

Starting with a 2-fill, two 3-fills, and a 4-fill near collapse, there’s value by value action left in the bypass for only one value. Scroll back for the givens and trace out the bypass.

An x-fill lists the values to be filled in the line. The square bracketed effects are the clues and subsets placed in the line

Here’s the grid you take into box marking.

Box marking adds all candidates which are members of box slinks, strong links due to having exactly two of the same value in a box. Box slinks are marked in the same position at the tops of cells.

Some slinks are already marked. They are subsets, naked pairs, two values in two cells in a box or line. Column 3, c3, has a line slink.  Its position is bottom right because the line is a column.

You can follow this trace on your same grid into box marking. The box marking trace is a list of boxes having box slinks for each value. There is no list for 5 or 8 because all value 5 and 8 clues are placed. The naked pair 69 in the NE box is the result of the value 9 slink combining with the earlier 6 slink, and the pair overwrites a 1 candidate, placing the other 1 in the NE box.

The follow up is fatal, but tracing is suspended because order of placements no longer matters.

Here is the grid at that point, when many naked pair subsets remain.

This week after x-fills, only the value 8 remained to complete the bypass. The week before that, the Kampelmann Hard 109 bypass reached a solution on x-fills alone. I was waiting for the next Washington Post 6-star when my Sudoku expert pal Gordon Fick suggested I look at the WP puzzle supplier AndrewsMcMeel’s website. Turns out, the site has a sample 6-star. What could be more typical of their 6-stars, for a last weekly post?  So here it is. Do the x-fills first.

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A Kampelmann Hard With Bypass Coloring

Ever have a Sudoku fail to tie down a solution? Hard 109 of last post seems to fail to do so without a trial. Coloring, which has found many multiple solutions, defines the unique solution for this one.

Starting with 4-fills, r2 has  no clue seeing two box cells.   But c2 places NW2 and leaves a 3-fill for later.

Then in c6, we get a 4-fill bonus. It’s not practical to look for naked singles in every cell, but as you check a 4-fill you already have five values seeing the four cells. Does any cell have three more? Three more see r1c8, but only  5 is absent from c6. Two absentees see r4c6, and two see r8c6, but r6c5 has three more!

Because unresolved 4-fills are so few in number, it’s worth it to scan their free cells for naked singles.

Now on your own or following the trace, the bypass continues:

Eventually you get a near BUG, but with two cells of three values. What is the solution? By trial, one works and one doesn’t.

Instead, we add coloring. Ignoring column 9, the cluster wraps green, with two green 9’s forced in r8.

The solution is the blue army, plus an uncolored 9r8c9.

Waiting for the next Washington Post 6-star, I went to the library and copied this USA Today Weekend 5-star. It’s almost bypassed by 2, 3 and 4-fills, and holds out through box marking. Well, almost.

Do the x-fills first. It’s the low hanging line marking fruit available in the bypass.

If you’re new, look in The Guide/Bypass for x-fill finding.

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A Washington Post ****** Basic

Scroll back one for the reason for the change in plans, but this is the first of several weekend puzzles from the Washington Post, added at the last minute for additional illustrations of Sysudoku Basic solving.  

Basic starts with a 2-fill and moves smartly to this point. What happens on value 6?

If you’re reading the trace, you only need to figure out the reason for W26.

Going on, the trace continues with the effect of cause C8 being c6(129). That’s a signal that you could have seen the new 3-fill. But that means there was a 4-fill in c7 before C8. Did we miss it?

No, the values 4, 6 and 7 were all present in c7 before C8 made it a 3-fill.  Resolving 3-fill c6(129, 1 and 9 in r6 places C2, leaving the naked pair 19 to be resolved by N1 and a naked pair 35 in r5.

The bypass finishes on value 9, with np67 adding a np35, and a 3-fill in r5 resolving into three bv.

If you’re reading  the traces, notice how the box 3-fill (W) and the bv refill (r5) are marked. In the box marking trace, the naked pair SW45 leaves a 3-fill, resolved to a clue and pair. SW1m is marking a strong link on 1. The link is marked by “m” inside the trace of a different value, 5. Next in this trace, 6 and 9 in r1 force the 3-fill r8[369] and NE7.

Now we’re ready for line marking. It requires care to avoid using candidates covered by unmarked lines. It helps to designate bv where they are really defined.

The collapse on the second line is quick,

but building the cluster to a wrap of blue is even easier.

For next week, we’ll throw in Kampelmann Hard 109 that turned out to be much worse than hard. See if you get far enough to see what I mean.

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A Harder Kampbelmann, Barely Basic

Hard 143 starts with a stingy bypass, and requires box marking and some line marking.

In the bypass, a r9 3-fill resolves  into SW8and the naked pair 36. W8 then follows, either from the 8’s dublex, or  from the West box 3-fill’s naked pair W12.

The full Basic trace shows three clues in the bypass, and one in box marking. The box marking trace identifies the boxes in which box slinks, and line triplets (“t”) occur, for each value. In the box marking event NE3m, the “m”, standing for slink “marks”, is added because the slink occurs on the 6: list, rather than the 3: list.

Each trace follow up is a left to right sequence of nested lists of effect, indented below their causes. This bypass trace here begins with two resolve 3-fills. After resolved n-fills, bypass  traces normally start with clues for  values 1 through 9.  Next is the box marking trace, a  list by value of box slinks (strong links).

The line fill list identifies filled lines at each level of free cells. In this case, two lines with 3 free cells, is followed by five lines with 4 cells, then two lines with 5 cells. The follow up trace leaves an unfilled line of 3 cells, and two with 4 cells.

The trace reaches a stage where the follow up is obvious without a trace, marked by . . .

The bar menu links to a page of explanation of traces, but the best way to learn how to read them is to decide what effect you would mark after each cause, and then note how and where it is described in the trace. At that level, we all think alike.

 I filled in the solution from there with pencil marks, but some of the pencil marks  are effects that never got to be causes. 

Next week’s post was going to be the home page, with navigation information, and a brief report on recent updates in the blog. But on a family visit I discovered that the Washington Post now has what they rate as 6-stars on Saturdays. I’m not talking about the puzzles in the interactive games section, but the Andrews McMeel Syndication puzzles you do on newsprint or on your PowerPoint template.  So I’ll defer closing weekly posts to include several from the Post. Here is next week’s 6-star, from last Saturday, 6/4/22.

Is there another weekend newspaper series that you’d like to sample like this, before Tuesday posts are suspended? Send grids of givens with dates and newspaper identification to, and I’ll squeeze them in to your credit.

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Naked Pairs Carry the Ball in Hard 134

A second Kampbelmann Hard is tough on paper, but  gives way routinely to a systematic bypass.

Here is the grid well into the bypass, with a large number of cells held in reserve by box filling naked pairs.

In the trace, we’re at value 9, just before r5[258] is resolved.

The rest is routine follow up.

Next week, the third and last Kampbelmann,  Hard 143, is harder, carrying into line marking, after giving an opportunity to show a box 3-fill (West) in the trace.

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A Hard, But Bypassed Kampbelmann 50

My Basic bypass starts with a resolved 4-fill. Did yours? 

The final collapse begins with the value 8 scan resolving the naked pair left from the resolution of 3-fill c2[258].

In the bypass trace, you can discover when the previous 8 clues were found.

That was a very productive 4-fill. Here is the collapse trace, and solution.

Next week, another Kampbelmann Hard, 134, offers a 3-fill among the givens. Take it first. If it does not resolve immediately, you at least get a fill string to help later.

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Box Marking Subsets Maintain a CREATORS Collapse

Sysudoku weekly posts will soon be ending. This post may be the last one from the Akron Beacon Journal CREATORS series. In this one, Sysudoku box marking rescues us from a very stingy bypass, in ABJ Creators of 4/20/22.

The bypass trace, shows no 4-fills or 3-fills.  The two 4-fills created by the bypass, c2[1234] and c5[2578], are not marked on the trace or the grid because they don’t resolve immediately. The spotting check: in c2, values 578 that see two fill cells are not missing. In c5, 3 and 6 are not missing, and 8 does not see a third fill cell. Value 5 sees three fill cells in 5-fills r6 and r7, one short.

Box marking is almost complete, when the 8 slink joins the 2-slink in the North box for a naked pair N28 to start a collapse.

The collapse carries to the solution,

when NW3 creates the second naked pair NE36.

Weekly posts continue with three Basic level puzzles from Hard Sudoku for Adults, by Kampbelmann , dated without copyright notice April 2020, among the toughest I tried on paper without tracing and full 3 and 4 fill analysis.

Next is Kampbelmann 50, which can be solved in Sysudoku Basic bypass.

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An ABJ Bronze With Many 4-Fill Bypass Traces

This post demonstrates the type of bypass you get by following up every resolvable 4-fill as it appears, in a less difficult puzzle. Bronze is the least difficult level announced by ABJ Creators. A similar solution path is started on any of four other 4-fills on the CREATORS Chrome of Sunday, April 3, 2022 givens grid, that immediately resolve.

On the 4-fill r1[2479], NW2 and NW4 see two free cells in r1, and E4 sees a third, placing NE4 in r1c7. Now on the trace, you can mark the 3-fill r1[279] left in r1, or be assured that the trace reader will note that SW7 sees a second 7 left in r1, placing NW7. That leaves two r1 cells for 2 and 9 and NW2 sees one of them, placing both values. The same effects list, in a different order, happens if you notice the 7 placement first.

That’s the way it goes.  It’s easier to check for a resolution of a 4-fill before entering it in the trace. Just check the clues in boxes with two free cells for missing values. Follow up on the missing value by checking for a third free cell seeing it.  A hit signals a resolution. It’s even easier with a 3-cell box. Just place the missing value in the outside cell.

Can you use the missing value rule to spot the other 4-fills that start the bypass with a resolution? You can compare your survey results with the full report at the end of this post.

In the final grid the pencil mark values were placed as effects, but were never used as causes, so they represent an over-supply of information for the solution.

This is how the other four 4-fills start the trace.

Next week, diligent spotting yields no  bypass 4-fills and there is not much of anything else, but box marking brings in the solution.

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Backing up to a 5-fill

Here is the Akron Beacon Journal CREATORS of 3/30/22 at the end of tracing the follow up of a 5-fill. Scanning for 5-fills is not productive. Too many, and they almost always fail.

But this time, 4 of the 5 free cells of c7 see a given 2. It’s a 5-fill with a clue. From here at C5, the solution places itself.

The follow up trace has three more 4-fills and five resolved 3-fills.

Next week’s  ABJ Creators Gold gives a choice of 4-fills for a bypass solution. We might not pick the same one.

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