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.


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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.





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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.








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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.


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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.


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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.



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An Orphan Takes Down Nakamoto Extreme 163

In this post, AIC building is replaced by BARN’s, conventional chains, coloring, and a noteworthy pattern analysis result.

Nakex 163 basic starts with a 3-fill. The bypass contains six more. Two resolve into clue and naked pair, and one, into three bv.

We include the first advanced move, a unique rectangle, on the line marked grid.

The signpost for the UR is the r8 naked pair.  Then we examine the extra candidates. In this case, the extras complete a naked pair.   A DIY rationale is that, if either 5 or 6 is true, the bv will force both values out of the ceiling corners of the rectangle.

Nakex 163 goes 143 one better, by responding to the bv scan, with BARN’s as well as XY chains.

BARN’s are difficult to spot. The signpost is the naked appearance of four values in a bent region, likely noticed in scans for Sue de Coq or XYZ-wings.

The long XY ANL puts itself together on the bv map XY railway.

In the follow up marking, railway ANL removing 2r3c7 and 8r9c8, are overtaken.

That was so nice,

how about another BARN and long XY combination? It’s a 4-BARN 1579 before the ANL, or a 3-BARN 159, leaving out r8c3, after.







The ANL removal 7r9c3 brings Sudokuwiki  a WXYZ, which we insist on calling a BARN. The bent region is Sr1 and just the right selection of cells is required to make it work. The long 1-chain removing 1r6c4 is followed by an 8-chain eliminating 8r6c5.

Sudokuwiki finds a slink chain branching off the 1-chain, and removing 1r6c6, which it interprets as a red/orange simple coloring.

Row 2 has blue seeing red, showing that not(blue and red)  implies green or orange.

On top of all this, the 9-panel has a slink network we can express as a blue/green cluster. Can we expand this cluster by pattern analysis?

Looking at the West to East freeforms, we can say that if blue is true, 9r1c3 and 9r7c1 are true. But this isn’t enough to extend the cluster to them, because blue may be false. If green is true, the green candidates  in c1 and c3 are not determined. The blue extension is not valid because there is a green freeform that reaches r1c3 and r7c1.

Fair is fair, so let’s try a freeform expansion on the red/orange cluster.  If orange is true, the orange candidate is determined in columns 2, 3 and 4, but none are decided by a red verdict.  In c5, the red candidate is limited to the North box, and the orange candidate to the Center box. That leaves 1r3c4 an orphan. It’s left out regardless of which is true, red or orange.

Take it out along with the removals above, and blue/green takes over.


First N5 => C5. Then the new r1 7-slink enables the 7 – ANL.  Then the orphan 1r3c4 removal triggers a huge expansion of blue/green which we keep going beyond the blue wrap in r7c3 and r9, and the red wrap in c9.

A remarkable wrap up of Nakamoto Extreme 163.

Next is Nakamoto 183, the final review puzzle.

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Nakamoto 143 Avoids Extremes

Nakex 143, the eighth puzzle in the review, avoids AIC building with an outstanding exhibition of advanced techniques, and

three subsets in basic line marking, including this naked triple.

Two more show up in LM closing, the stage that examines unmarked lines after all of those in the opposite direction are marked.


The second subset is this hidden pair as the last line, r6, is closed. Do you see anything else in r6?

There’s two ways to describe it in the basic trace.

Nakamoto Extreme 143 is a show off on advanced moves as well. It couldn’t be just an XY ANL. No, it had to be five ANL with three terminals. We count the almost nice loop for every victim, because each is the meeting of a different pair of winks.



The swordfish shows up on the 7-panel, after the 3-chain and its SWc2 boxline 3r4c2 removal. The Sudokuwiki gets the same results from a simple blue/green cluster, and a Wc3 boxline.





A  rare classic WXYZ and an XY ANL are enabled by the 3r7c3 removal.  Also the swordfish breaks the 7-panel into two complementary dead swordfish in a complete color linked field that becomes the backbone of a new  red/orange cluster.


Cells r4c7 and r9c8 demonstrate

not (green and orange) => blue or red,

springing the r9c2 traps that imply green or orange,  trapping  r4c7 and r9c8.

Now SE4 => NE6, and a 6–ANL wraps orange in c7, confirming green in r9c8. It’s a red sunset with a green flash for Nakamoto Extreme 143.


Next up is Nakex 163.





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Nakamoto Extreme 123 Is, Briefly

Nakex 123 limps into AIC building briefly,  then succumbs to Sudokuwiki XY chains, simple coloring traps,  a coloring bridge and an outstanding BARN.

Here is the grid at the end of a bypass exceptional among Nakamoto Extreme puzzles.

The slink marking bypass is a human engineering feature that replaces the burdensome candidate identification task most experts cede to the computer, with an enjoyable challenge.



Beyond the naked pairs that claim cells in the bypass, strong link and subset marking are completed in two more systematic stages: box marking and line marking.


Short of AIC building, Sudokuwiki finds only this simple XY ANL, shown here on the line marked grid.






In AIC building, the new c2 7-slink allows an ALS bv boomerang.






That proves enough to get constructive methods going again.

The new r2 7-slink allows another XY.








The new bv prompts a Sudokuwiki simple coloring trap. In the trap, 5r4c8 is removed by green and by blue.  Leave the cluster to possibly expand.

Update the 5-panel, but also look to see what the removal does. Here it creates a grouped slink for a 5-chain ANL.



After W2 and E2,

Sudokuwiki opens a second simple cluster for a trap.







The trap expands red/orange to show:

not                  (blue and range) =>                  green or red

It also enables an XY ANL removing 8 and bringing 7 into red/orange.



a 347-wing and a very striking BARN.


The expansion wraps red in r5c3, and recall that red or green must be true, so orange and green are confirmed.

Next, its Nakamoto Extreme 143.



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A Pattern Analysis Attack on Nakex 103

This post reports an alternative Sysudoku solution to Nakamoto Extreme 103, starting with a pattern analysis signaled on an X-panel. The analysis develops and exploits a coloring cluster to accelerate the solution.





The starting cluster is expanded when West to East freeforms reveal that any pattern including 4r1c1 also includes 4r3c7. In other words, if blue 4r5c1 is false, then 4r3c7 is true, defining a slink carrying the colors across the grid to trap 4r1c3.




After this expansion, West to East freeforms for blue confine it to a single pattern, and the cluster wraps green, as two green 4’s are forced into c3, with follow up:



Now  AIC building is unnecessary. First  comes an XY-chain removing 6r6c4.

Then another for 7r4c5:


After a third ANL triggers a SEr9 boxline,





a large second cluster can be  added, just in time for a shortcut confirming ANL.









This sets up the identical confirming ANL from the Sudokuwiki path, but this time, for the collapse, as orange 9r5c5 wraps red.




The collapse trace and color version of the solution are below.



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