A Bracket Busting Dave Green 4-Star

Here’s the  basic trace on the Saturday Dave Green 4-star shown at the end of last week’s post. It survived the three Sysudoku Basic  phases: bypass, box marking and line marking. It’s the first I remember.

Let’s talk through the Sysudoku marking of the bypass. It’s short enough to bring up every attention point, but it’s best to read it as you mark your own grid.

In the 1 scan, the NW crosshatch has 3 cells for 1, the E dublex 2, and the S dublex 2. We’ll mark the box slinks in box marking. The 2 scan will create slinks in 4 boxes. Then for 3, a crosshatch into SW creates a slink and dublex to complete a wall with NW3 and a 4-fill in c3. We follow the slinks in NE and E, and return to scout the new NW wall.  What new dublex will it create? The value 7 is not in the wall, and the limited crosshatch produces NW7.

The 1 crosshatch into NW now leaves one cell for NW1. Now there’s a NW 3-fill, missing 5, 6 and 9. No sweepers, so we continue the 3 scan with cross hatches into E and SW. Slinks are bypassed for 4 and 5. The single 6 can take no action.

In the 7 scan, first a slink in W, and then clue C7 generating a double crosshatch for W7. Now looking in the other direction, a new 4-fill in c5. As we go, more and more 3 and 4-fills occur. Look to see if values in the side lines are missing in other boxes. Values 1 and 7 are not missing. The N6m slink is noted.

On every new clue, an automatic check for a 3-fill. W7 yields c3[689]. The rule is two hits on a cell  or two values on two cells. When a line 3-fill is not immediate, we post a fill string reminder.  Continuing the 7 scan, the last box is double crosshatched for SE7, Two 8 crosshatches for nought. On the 9 value, the NE crosshatch dublexes SE9, which supplies that second 9 seeing the 3-fill cells. We put the effects list in brackets to say it resolves a 3-fill.

Box marking is a routine posting of the slinks we saw in the bypass, until we get to the SE box on the 6: list.  As the 6 slink is added, my count verifies the match of cells and values. With no more additions possible, 5r8c9 is obviously true.  But the more direct analysis seizes on the new hidden pair 16, and two accompanying clues.

The effects of that list is extensive, but somehow the 4-star survives. Maybe there’s a side effect overlooked along the way. Read it out on your grid and if so, let me know.

Another  possibility is a slip up in line marking. Here’s my line marked grid after the close. Did I miss a subset?

Now from here, you can enter advanced in several ways.




My choice is unique rectangles, because a readily spotted pattern can be looked up in a table for corresponding eliminations. Here we have a type 3 where the extra contents of the ceiling corners forms a hidden pair eliminating 8r6c9, and a type 1 where either 6r1c9 or 6r7c8 eliminates 6r1c8 to create a double solution rectangle that Dave Green would certainly not publish.  The collapse from (E6, E8, NE1, SE1) is immediate.

Now advanced readers have waited long enough. The review of Stefan Heine’s Sudoku ultrahardcore 1 begins next post, with the ultra 3 shown in the previous post.

In his book of 500 puzzles, Stefan informs us, puzzles on the left page can only be solved with the most complicated methods. But no one will find a logical way through even one of the 250 on the right. To me, this sounds like a perfect setting in which to explore the quite logical Sysudoku concept of trials, so I’ve  committed  to 10 from the collection of upper right page puzzles.

In his subtitle “Intuition schlagt Logik”,  what does Stefan mean by “intuition”?  The term lacks the objectivity of “logic”.  In Sysudoku, “intuition” is not taken to mean “trial and error”, the repeated trials of largely arbitrary choices, confirmed only by the contradictions reached by alternatives. This technique does, in time, solve the most difficult of puzzles, but without insight into any puzzle’s logic.

Instead, we’ll take “intuition” of ordinary meaning to have a role in what has been identified as trials, and seldom invoked, in the blog.  A trial is two mutually exclusive partial solutions, one of which must be true and the other false. In a trial, intuition guides the decisions that our methods are not enough, and how we will construct a trial. Experience refines our intuition as to when a trial is going to be decisive. We want enough evidence on both sides, for the contradiction of the wrong choice to come soon, and the right choice to go all the way.

Sysudoku employs a different  trace method for trials. The normal trace is depth first, the squirrel going as far out as possible before turning back to a branching limb. A trial trace is breath first, an army of squirrels advancing out in inference lock step, until a contradiction is reached. Breadth first tracing provides a measure of just how obvious the contradiction is.  Also in trial tracing, when we get a solution but suspect there may be more, we try the alternative. There are several instances o occurring here.

After the coming long review, you’ll have 240 more ultrahardcore right page Ratsel to refine your intuition. We’re not saying that a solution by trial is as good as a logical solution without trial. On the other hand, when right page ultrahardcores fall by Sysudoku trial, we don’t expect to hear that logic has been somehow defeated.

Posted in Basic Solving Procedures, Puzzle Reviews, Green | Tagged , , , , | Leave a comment

Puzzleproof’s Sudoku Extreme Is Good Basic

Finishing with no advanced moves, the Extreme Sudoku 2 collection proves less than extreme. However, the collection, including the last three selected puzzles, 154, 175 and 196, have many worthwhile examples of basic slink marking in action.

In the Pzlpfx2 154 bypass, a column 3-fill steps in front of a box 3-fill. You can read that in the basic trace,





but here you have the hidden triple Cht389 that brings a quick collapse in box marking.

You needn’t search for these. Just be aware of the count of box slinks against the free cells.


As 9 arrives, three slinks are confined to three cells, so only two cells are free. The missing value 1 is only allowed in r4c4, leaving only r6c4 for the 6 value.  At this time you may be watching the SE box for any confinement of the missing 2 value. The hidden triple doesn’t allow time for that to happen.

Here is the grid after the bypass in Puzzleproof Extreme 175.



Everything seems to come along as needed, as it traces out the typical Puzzleproof Extreme path.

The last to leave, but the first to go, among the Puzzleproof Extreme 2 review puzzles, is 196.

The wrap up in the bypass is aided by the c7s57pair, due to the East box filling and values 5 and 7 being forced into the two cells by their candidate positions in NE.

The bypass trace shows this effect of the E5 cause is third in line, but quick to act. The steep collapse includes  a hidden dublex.

So the Puzzleproof Extreme Sudoku 2 rating is newspaper 5-star. However, provides  many basic happenings of entertaining value to human solvers. Admittedly, several of these were only discovered in my second reading, guided by a trace of the first solving.

Also worth noting is that many bypass breakthroughs actually come to my attention afterwards, in box marking and  line marking. They are presented as bypass effects because Sysudoku is not about my accuracy, but the humanly friendly methods that sysudokies seek.

Next post ends this series of basic level puzzles with a long sought Dave Green Conceptis, one that breaks the line marking barrier. This Akron Beacon Journal Saturday May 2 4-star defied me on newsprint, and got into Sysudoku Advanced with a pair of unique rectangles. Or maybe I missed the basic move that proves otherwise.  If so, inform us with your comment.


Also, it’s time to announce that Stephan Heine’s Sudoku ultrahardcore 1 collection of 500 puzzles,(see post 5/5/20)  is in the house, and review will begin June 9 with 3+44n, n = 0, 1, . . ., 9  selected for analysis.  Expect these puzzles to take multiple posts. The first one is ultra 3, at left.


Posted in Basic Solving Procedures, Puzzle Reviews | Tagged , , | Leave a comment

Double Sweep Lessons From 112 and 133

Two rare double sweeps in the bypass show up this post. In Puzzleproof Extreme 122, it’s a 5-fill line; in 133, a 5-fill box. In each, 5 cells are free and two are claimed by two values, leaving a 3-fill.  Both puzzles are finished in box marking.

How do you prepare to spot this start of basic on Pzlpfx2 112? Two cells to fill in c4 and two values in the South box forced to fill them.

There are many effects from this 4-fill before the list of value effects begins in the bypass.  Is that what happened in your trace?

And how did you represent it in your trace. It’s a 5-fill, but c4[34579]?

I went with a subset pair here, but later added a line to announce the 4-fill in the South box.

If you don’t spot the double sweep 5-fill or the 4-fill, they get resolved later.





Here is the grid as the 9: list starts. Here you note the missing 2 and 9 to see both SW48 effects. It’s interesting to follow the collapse from here.

The hidden dublex is easy to spot because the two 9 slinks that create it are added together.



Instead of the hdx, let’s close with the placement ambiguity that remains just before the decisive NW4, in the “after ellipse” resolution normally omitted. Maybe that lasting ambiguity explains the Puzzleproof claim that this collection is somehow “extreme”.

You think?


Moving on to Pzlpfx2 133, the basic trace reveals a crippling bypass, with many unresolved 3-fills.




First is this double sweep N59, leaving Nc5 to fill.  Then the resulting N4 adds the second slink in c6 that joins the one in Ec8 for the hidden dublex Whdx4.

The box marking collapse is straightforward, but if you solve on after the ellipse, you see how long it takes to pin down placements of some values, particularly 3.

Next, the review of Puzzleproof Extreme 2 is completed with 154, 175 and 196.





Posted in Basic Solving Procedures, Puzzle Reviews | Tagged , , | Leave a comment

Can Box Marking Be Extreme?

This post continues the Sysudoku Basic review of Puzzleproof Extreme Sudoku 2, with reports on 70 and 91.

In the basic trace of Pzlpf2 70, there is the typical heavy bypass, and collapse in the 9: box marking list. The first box marking clue comes as the 9 value partners with the earlier 7 value for a hidden pair C79, squeeze out for C8.


Then we watch as N5 restricts N8 placement for the hidden dublex clue NEhdx8.


Trace conventions intervene shortly after, as one of the hidden dublex effects, a 3-fill in c9, can be resolved immediately, but is third on the effects list. The resolution falls instead to NE6m, the second hdx effect.  All effects of NE6m are listed ahead of any effects of c9[679].


The conventions help trace writers compare traces, but sometimes produce surprising results.

The next Puzzleproof Extreme 2 for review is 91. An explosive collapse is triggered when 7- slinks in C and S generate the hidden dublex Nhdx7.






This time, the 3-fill  r3[689] is immediately resolved, and the first effect NE6 places N6, and N3 as well, leaving only two N cells.


The pair N29 is resolved by given 9r7c6, and causes N2 and N9  are held in reserve as N3 generates decisive effects.



This is a primary feature of basic traces, to use effects like clues, slinks and unresolved  3-fills,

but also to hold them in reserve as causes, bringing them up after effects of earlier causes are thoroughly explored.

Next we report on Puzzleproof Extreme 2 puzzles 112 and 133.








Posted in Basic Solving Procedures, Puzzle Reviews | Tagged , , , , | Leave a comment

Puzzleproof’s Extreme 2 is Box Marking Level

This begins a four post review of Puzzleproof’s Extreme Sudoku 2. The pre-selected puzzles are every 23rd puzzle starting with 7. All of the puzzles are solved in the bypass or in box marking. The review provides full tracing, and highlights some Sysudoku Basic moves. This post covers review puzzles 7, 28 and 49.

On Pzpfx2 7, suppose this is your reading grid as the trace tells you that W7 => (E7, E5), and you add 7r5c7. E7 has no effects, and its up to you figure out where E5 goes and why. As a trace reader, you focus on the W7 placement. What changed? The small square. You review what you do when a small square completes.  Oh yeah. The r5 5-slink, and the c7 5-slink cross hatch E to net E5  at r5c9.

Now look ahead. E5 resolves the r5 4-fill with W1, which works with the small square for W8, and it’s soon over.  Here’s the trace:


Next we look at Puzzleproof Extreme 2 #28. After a bypass flogging, it begins to crumble in box marking on the 7: list. The fatal blow is a 3-fill, whose first cause fills a wall, leaving two clues in reserve.

This shows the effects of this first cause to be four clues, with the collapse continuing from SW8t above.








Puzzleproof Extreme 2 # 49 is a replay of #28, the collapse triggered by the first effects of a 3-fill in the 9: list of box marking.






Here’s the grid after the bypass. Next post, it’s #’s 70 and 91.

Review alert: Soon after Puzzleproof’s Extreme Sudoku 2, I’m expecting to review Stephan Heine’s Sudoku ultrahardcore 1, which, except for the title, is in German. It’s at the suggestion of commenter Alex, who provides links to booksellers for this book at the end of the Reviews page.


Posted in Basic Solving Procedures, Puzzle Reviews | Tagged , , , | Leave a comment

Wrapping Up Nakamoto Extreme With 183

This post completes the review of the Nakamoto Extreme collection. The review table follows the finish of Nakex 183.

A Sudokuwiki assisted solution of Nakex 183 continues with the second APE triggered by the first’s removal of 8r2c9. In this one, both combinations 15 and 85 are contained in the two ALS sharing a unit with  the APE cells.

Independently, another grouped 5-chain ANL eliminates the other APE 5.





The absence of both APE 5’s allows an ALS bv boomer turned confirming ANL, with follow up





Updates on the 1-panel and the bv map are rewarded with a 1 – ANL,





and an XY wing plus boxline.









The Nr1 boxline adds two bv, and encourages a step away from Sudokuwiki with a Medusa coloring cluster. When an XY chain reaches the cluster at 1r2c2, the coloring slink completes a shortcut ANL.

It’s a coloring advantage worth considering.

In fact, coloring is past due, and apart from the blue/green cluster, the remaining bv field begs for another cluster, starting in r2c8. The red/orange cluster is extensive, with two traps, one expanding blue/green.

In r2, a common value establishes the bridge:

not(green and red) =>

blue or orange.

Blue 5r6c4 traps the r46c5 5’s via green r2c5, and 5r4c4 sees blue and orange. That leaves 5r4c2 alone in r4, confirming orange.

Then 2r5c5 => S2 =>SW2, wrapping green and Nakamoto Extreme 183.



J.B. Nakamoto Extreme rates alongside my longtime champion KrazyDad Insane in entertaining difficulty. The following review table confirms that opinion.

We spend May 2020 in Sysudoku Basic, with a collection from Puzzleproof of Coppell, TX, Extreme Sudoku 2.  Despite the title, the review puzzles don’t get beyond box marking, but they   illustrate well the challenging dynamics of Sysudoku Basic, with bypass and slink marking stages.  Why enter advanced solving with subsets and pointing pairs still hidden in a cloud of number scanned candidates?

Here’s the first three Puzzleproof Extreme 2 puzzles 7, 28 and 49 covered in the next post.  If you’re into Sysudoku Basic, and you want puzzles  of posting, you’ll need to order the book.


Posted in Extreme Solving, Nakamoto, Puzzle Reviews | Tagged , , , , , , , , | Leave a comment

Nakex 183 Hides the Keys

The last review puzzle, Nakamoto Extreme 183, follows the collection’s pattern of hiding easier removals behind methods that are very difficult to spot. An effective defense is to maintain bv maps, X-panels, and coloring clusters carefully as more advanced results are obtained.

The basic trace becomes a movie of systematic basic solving as you read it out on your own grid. Compare it to your own basic drill, both process and results.

A spotting note: the required slinks for the hidden unique rectangle Type 1  come from a frequently occurring dead X-wing.




Hidden pairs are more rare.


From the UR, with three 5’s removed, Sudokuwiki moves directly to the 5-panel for a grouped ANL.












there is a 4-BARN that might be spotted in the wake of the dead 2145-wing .  The wing’s 5 value set is toxic, but no 5 sees the whole set. The alternative 15 wing does no better.

Next ,  Nakex 183 enters AIC building with a bv boomer from 3r3c5, making a confirming ANL

N3 enables the APE below. The ALS outlined in red exclude 8 of the 15 combinations in cells r12c9.








It’s the common values with  the two ALS that make r12c9 a good candidate for an APE.  List the surviving (r1c9, r2c9) combinations: 13+16+21+23+26+53+61+62+68+83 and note that no x5 or x8 is listed. Listing in opposite order, we scan  16+31+35+38+61+62+68 with no 5x or 8x listed. Maybe you  would notice that 3 missing from the two ALS would make the second list shorter.

The next Sudokuwiki move is a second APE, made possible by this one.  Can you spot it? Next post will have that, the finish of Nakex 183, and the review table for Nakamoto Extreme.



Posted in Extreme Solving, Nakamoto, Puzzle Reviews | Tagged , , , , , , | Leave a comment