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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Sudokuwiki’s Nakamoto Extreme 103

After Sysudoku Basic, this post describes the Sudokuwiki advanced and AIC solution path on Nakex 103. The next post reports an alternative path shortened significantly by a freeform pattern analysis.

Nakex 103 starts a little differently, with some bypass success:

Also untypical in Nakamoto Extreme is an X-wing in the third stage of basic line marking.

The 5-wing appears when the two 5’s in r6 are seen to match columns with the naked pair of r8. The fish icons are left to affect the line marking of c2, c5, and the closure rows.




The basic trace of Nakex 103:

The first Sudokuwiki move on this grid is an APE in which an 5-value ALS eliminates combination 31 and a bv, the 41.


How is such a large APE partner ALS  suggested? Other than the bv, 1r3c9 has only one combination with r3c7, 31 in r3c8. Now from r3c8, you stretch the ALS boundaries along r3 to get one ALS containing 31.

With that, Sudokuwiki now enters AIC building, missing the pink/olive pattern analysis on the 4-panel to be shown in the next post. Will your version of that ready for comparison?

For this  AIC confirming ANL, you might start with the r4 4-slink from 4r4c6, noticing the AIC wink to the W grouped 3-slink. The wink to 3r5c9 and AIC wink gets you to the 4-chain leading around to the C grouped slink closing the ANL. C4=> S4, and the “bunny rabbit” just happened.

The next just happening is an AIC nice loop. 5r5c3 is a good start for a boomer, and Medusa XY  cells carry the ball, but the 4-slink back into the starting cell closes the nice loop.  The same description applies to a boomer start from 4r5c3.

Then an alternate path from 4r5c1 achieves boomerang 1.









Independently, a second boomer, from 5r6c5, re-traces a section of boomer 1.






Any emerging slink, however long, is eligible to start a boomerang. Here, the grouping creates the r6 slink necessary to get back to the starting cell of boomer 3.

Sudokuwiki labels boomer 4, in black, as a digit forcing chain, removing 2r9c4 regardless of 4r3c7 being true or false. But arriving at that conclusion by choosing a candidate in the boomer is blind luck. The boomer starts with the 6-slink from r9c4, and the cluster supports the shortcut in red.

The boomer 4 removal enables this confirming AIC ANL, starting from either slink from  9r1c3.  The NW9 placement removes 2r1c3, allowing an extensive cluster to develop. This cluster is an immediate result of the 4-panel pattern analysis to be covered next post.




In fact, the next Sudokuwiki move is an AIC confirming ANL that is also the final move in the shortened solution path next week.

But not here.  After the follow up






Sudokwiki continues with a hidden unique rectangle, Type 2b. and an XY ANL.









Next, three moves on a grid. First , the West BARN 3467 removes 6r6c1. This  removes 7r5c1, by the naked triplw 178, or by turning 6r5c1 green for a trap.   The 7 chain stands alone with one elimination 7r9c3, which enables the purple BARN 1238.




Ending this Sudukowiki display in a Sysudoku way, a bv boomer from 6r1c1 wraps green.





Even so, it still leaves a 273-wing to put Nakamoto 103 away.

But not until next week, when you compare your shorter version to the one appearing here.

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A Nakex 83 BARN Storming Finish

This post details the unusual finish of Nakamoto Extreme 83, with three more interdependent BARN’s, well assisted by Medusa coloring.

From the first cluster trap and BARN, further expansion and the aligned triple continue to move Nakamoto Extreme 83 towards the exit door.






In particular, the second aligned triple’s 4r8c1 removal brings a second BARN, and its expansion traps below


The follow up   






brings a third BARN, and that BARN’s removals set up

a fourth.








Then after a shortcut XY ANL (left) expands the cluster for three more traps










the next expansion wraps green in c6, for the immediate collapse of Nakamoto Extreme 83.

Next time, it’s Nakamoto Extreme 103.








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A Nakex 83 BARN Challenge

Nakamoto 83 earns its Extreme badge by an extremely tough Basic, and resistance to anything short of AIC building. It ends with an expanding cluster, accelerated by a series of BARNs. This post brings you to the first one, and leaves it to you to find the rest, before the March 10 post.

The line marked grid is evidence of the extremely tough basic phase, with many long line fill lists and cells of four and five candidates.

The basic trace reports no concessions.

Heavy lifting continues as Nakex 83 requires immediate AIC building. Here is AIC boomer 1 turned confirming ANL, from 2r1c3. It ties 2 and 3-chains together with AIC winks.





A second confirming ANL follows the same spotting pattern, two converging slinks, starting as a boomerang from 3r3c1.





After the follow up



the naked pair C47 removes two 7’s from the C box, the aligned triple W7t removes 7r8c2, and an XY ANL removes two 4’s.




Now, starting from the new 7-slink in the r5s57 pair, an ALS node and XY segment lead back to the starting 7 for a nice loop.

Nakex 83 is showing that boomer search is a basis for all AIC building, and there is good reason to keep up with bv scanning data.



a budding cluster nets a trap, and an XY ANL, to which Sudokuwiki adds a BARN.

For newcomers, a BARN is a Bent Almost Restricted n-set.









An n-set is n cells containing only n values. In this and most cases, n = 4. “Restricted” here means confined to one unit, box or line. “Almost” refers to one of the values being bent to share two units, a bent region. In a BARN the bent value is toxic. It  includes a true value.

From here, Nakamoto Extreme 83 finishes with coloring expansions and traps, generating a series of three more BARNs and two shortcut ANL. Using Sudokuwiki, I missed out on finding them, but you don’t have to. It’s laid out next week.




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Sudokuwiki Ends Nakex 63 On Its Own

This post picks up on the Sudokuwiki/Sysudoku resolution of Nakamoto Extreme 63 where it was overtaken by pattern analysis and coloring, and finishes it in two ways, one humanly practical and one not.

Sudokuwiki doesn’t maintain coloring clusters between moves, or use pattern analysis to expand them.  After the 785-wing in the solution of the previous post,  Sudokuwiki continued with a two solution paths  too instructive to pass up.

The first continues with an Andrew Stuart cell forcing chain. The idea is to remove a candidate that forces all candidates in some cell to be false. It takes a modern computer very little time to determine what a single candidate forces out, but how many such examinations fail between cell forcing chain successes? Way too many for human tolerance.

But here’s one. 3r1c9 forces 7r8c2 off via 3-chain and 7-chain. The ALS forces 1r8c1 on, 15r8c1 off. Is that a peacock or a swan?

The 3r1c9 removal enables a confirming ANL enlisting a UR slink and an ALS node. What is a UR slink? The rectangle r89c16 presents a multiple solution if both 3r8c1 and 6r9c1 are false. Therefore, If one is false, the other must be true. A strong link in the ANL.

Now, after a simple BARN,





two hidden unique rectangles, Type 2.



Next, an APE, in which the ALS excludes 15, and the bv at r4c1, 35, as placement combinations in the aligned cells.

Then an ALS AIC nice loop expands the cluster to trap 9r6c3 and bring in C8.




The further expansion traps four candidates and repeats the XY-wing of the last post.

The follow up to E5 proves green to finish Nakamoto 63 the Sudokuwiki way.






Andrew Stuart’s Sudokuwiki solver has an option to bypass specific methods. When Stuart’s cell forcing chain is bypassed, the next method after boomer 7 and the 785-wing is this ALS toxic pair. 3r9c1 is eliminated because it sees all 3’s in both ALS. Since only one ALS can have a 7, all values are locked in one of the ALS, including one of those 3’s. The toxic pair takes the place of the cell forcing chain in the Sudokuwiki solution path.

But a second elimination, of 9r6c3, Sudokuwiki  attributes to “rule 2”, saying 2,4,9 are unique to the orange ALS. We need to know what  prevents 9r6c3, and therefore blue, from being true, and leaving the ALS placements 2, 3,4, and 7?

In Stuart’s Sudokuwiki strategies, “rule 2”  is attributed to forum guru David Bird, but not explained. A clue to rule 2 is the fact that 9r6c3 forces both shared 3’s in the SW box to be true. That is because it forces 9 out, and 7 into the orange ALS, along with 3 and 2.

In general terms, this effect can be described this way:

The reason is, when an unshared value is removed, it forces the common value into its ALS,  removing the common value from the other ALS, and leaving both ALS locked. In the above example, 9r6c3 must go because single 3’s in both ALS share a box and can’t both be true.

It’s not that that the outside candidate can’t be true, removing a value set. It’s that the effect that has in this case violates Sudoku placement restrictions.

Next week, we consider what Sudokuwiki can do with Nakamoto Extreme 83. You must have the book by now. Are you using another human oriented solver? If so, tell us about it.

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