An Untyped UR Rattles World’s Hardest 188

The review of World’s Hardest Sudoku continues with a quick dispatch of puzzle 188 by a unique rectangle and straightforward coloring. The UR fails its type category, but the examination uncovers an almost accidental chain interpreted after the fact as an AIC dirty rectangle.

Basic is quiet, with a good bypass start, and moderate line marking.





After confirming that the possible UR is not Type 3 or 4, the search is continued on possibility that a candidate eliminating one extra digit can also eliminate another. It happens here to 5r1c1 in a Rube Goldberg chain of events you can mark as an unusual AIC with a naked triple node. Can you draw up a for that?


My version is at the end of the post.

The next move is suggested by many bv and line slinks in values 1 – 4. A coloring is based on the four connecting  slinks of the 4-panel. There is a quick wrap of green in row 3 and collapse is immediate.

World’s Hardest?  Hardly.




Next post in the review traces two more basic solutions. One ends in the bypass, the other, in line marking. The puzzles are 46 at  left, and 186 on the right, both rated 0.90.

This leaves Worlds Hardest 134, and advanced achiever, to finish the review.

There’s a new page in the Sysudoku Guide, on Death Blossoms. The new page is accessed from the side menu of the BV Scan page.

As for the expression of the UR elimination in AIC speak, here’s mine. In addition to regular grouping, we have to isolate the naked triple and treat it as a node on the chain.


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Coloring Wrings Out World’s Hardest 102

World’s 102 starts without ‘1’ givens and with two 3-fill lines. It winds up in a coloring trap expansion into a wrap.

Basic makes progress in all three phases.








Making a hasty bv scan and skipping the XYZ analysis, I go to the bv map and sketch out an extensive railway, for a easy ANL, resulting in a second naked triple.

Why not?





The next greedy move on the 21 bv banquet table is coloring. Starting with  these two traps, a trapping expansion removes 6r6c4, 6r4c5, 6r9c5,and 4r9c1.





Collapse is immediate as SW1 wraps green. Blue mops up.










Next is World’s Hardest 188. When you get to advanced, look for an unconventional unique rectangle.


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World’s Hardest Sudoku 65

Not really hardest, but entertaining. World’s Hardest Sudoku 65 has a UR challenge, a UPE, a finned swordfish, an AIC ANL, and a very different color wrap. It’s also a few cells short of a multiple solution.

Basics are moderate, with 3-fills helping. The “hdxm” is slink marks produced by a hidden double line exclusion.



On the line marked grid, I did look at one possible UR, but couldn’t make it work.

The bv scan turns up an unaligned pair exclusion, a UPE. The pairings of 9 with 1, 3 and 8  in the red target cell are vetoed by the black coated ALS pair.




My next find was late on the X-panels, a 9-chain ANL removing 9r5c9. Then on the same panel, a finned jellyfish demands a bunch of kraken tests. All fail but the 9-chain removal, in the fin box.

Victims of a finned fish “see” the fin. Krakens escape removal if they are outside the fin box, and don’t otherwise see the fin.

An uncoordinated bv field that resists XY-chains also resists coloring. My two clusters share no values. I know that, since blue and red cannot both be true, green or orange is true or both are.

But with nothing else, its time for AIC hinges. At AIC time, you chain anywhere, any way, and look for repeats. I did uncover one ANL.

The panels show little pattern restriction, and next would have been enumeration of ALS. But first, can the aloof coloring clusters get entangled in chains? We follow up on the obvious in r2c2 that

blue => orange.

Blue  creates waves by generating W13, a naked pair, which strips chute Wc7 down to 5 and 8. That denies orange 8r9c3. But wait. Blue can’t confirm and deny orange.  The only conclusion: blue is toast.

Green comes in and takes over. There’s a naked triple, and a handy skyscraper whose removal brings on a finned 8-wing. The collapse is on. I had to follow it down just to make sure that red vs. orange really gets resolved.





It does, but only with one other clue remaining.








At the point of red/orange resolution, orange winning, the grid demonstrates how close 65 comes to a multiple solution.








Next in the World’s Hardest Sudoku review is 102, which gives up too many candidates in line marking, and becomes a tempting target for easy XY chains and coloring. See if it’s that easy for you.

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LPO Knocks Out World’s Hardest 36

A challenge posed by The Worlds Hardest Sudoku Book 36: Is there a route to the solution less advanced than pattern analysis? The puzzle is otherwise distinguished by a BARN right out of line marking, and a notable lack of givens information on the placement of 6’s.

The basic trace is too simple for comfort.




But it is delightful in brain based solving, as it closes with a BARN similar the one in Stuart solver analyzed 200.



Frustration followed, as none of the usual advanced methods advanced the cause, until . . .

looking along the edges of the panels, this elimination emerged from the top down freeforms: no 5-pattern can contain 5r1c9, because no freeform starting there can make it to r8.
Then I noticed the sashimi swordfish claiming the same victim. The finned fish works because the victim is in the fin box.



The resulting NE5 creates to final slink in the 9-chain ANL, and collapse follows.








Next is World’s Hardest 65, another 0.91. World’s Hardest Sudoku is not being hard enough. I’m trying to work in some UPE and ALS where they fit. Tell me what I’m missing.



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A Colorful Ending to World’s Hardest 200

Here we translate into sysudokie notation the XY-chains and coloring that drag off World’s Hardest Sudoku 200, to its sudowiki solver solution. Hopefully you were better able to arrive at your own solution.

First are the new developments on the bv map, where a XY-chain ANL triggers boxline Nr4, which triggers boxline SEr9.







This brings in a naked triple and more XY railway, a 2 eliminating ANL, .  .  .








.  .  . and a 3 eliminating ANL.

The follow up




opens it up for another cluster, and r5:

not(blue and orange) => green or red

sends us looking for a bridge elimination.

Instead, yet another XY-chain expands both clusters, to trap 6r4c5  and wrap orange on r3.

Red leaves a single blue 1 on r4, and there’s nothing left to say.

Except that the review continues, without solver assistance, and with Worlds Hardest 36, with ratings falling to 0.91.



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Andrew’s Solver Tames Worlds 200

This post walks through the “very  hard” part of the solution path taken by  Andrew Stuart’s Solver through puzzle 200 of The World’s Hardest Sudoku Book by authors unknown. This is a remarkable turn of events for a blog devoted to manual solving, but there are reasons, and the results are good.

My interest in Andrew Stuart’s The Logic of Sudoku, now out of print, is renewed as I work on topics for the Sysudoku Guide pages. Although we differ on some topics, Andrew’s is a solver that can be confined to humanly practical methods.  It can serve, therefore, as backup for human solving.

Having made no progress on 200, I reluctantly turned to Andrew’s Solver as a way to include 200’s difficulty in the ongoing review, but also with an eye towards expanding my understanding and gathering telling examples of methods I couldn’t spot.

First in the SysOB is APE r8c12, where 3r8c2 is denied a partner by the 39 bv, and the 13 combination in ALS1356 in r8c567. I missed class the day unaligned APE was covered in The Logic.

Then a BARN or BNS1, a bent 4-set 1 2356 in the Sc4 bent region. The common remainder value is 6. Solver notes still have it as a “WXYZ wing”. There is still room on the grid to show the next in order, an XY-wing ANL.

Also from the XYZ-map, a classic, but dead  Death Blossom Lite (11/29/11) hinged at r6c6.

From the X-panel, a 3-chain ANL (black) extends into a 3-chain ANL confirming SW3.





Even on the 4-panel, the grouping on these almost nice loops is very difficult to see. You might need to bone up on Sudoku group theory.







Consider the next unaligned pair exclusion a reaction to the grouped ANL removals, as the bv r5c5 becomes available as a target cell.  Combinations 45 and 46 are denied the target cells. The removal’s Cr5 box/line terminates 4r6c6.






The solver followed the Sysudoku phasing to this point, but now does the AIC scan prior to coloring. I confirmed that coloring is not effective just yet. The solver does a confirming AIC with a jaw dropping ALS node.

The ALS node

is based on the slinks between candidate groups in an ALS.

The removal of 3r9c9 brings a third ALS to bear on APE target cells r78c9, and 3r7c9 is allowed no partners. The blue/green cluster expands to trap two 4’s. An AIC confirming ANL is cobbled from 1-chain, 4-chain and XY-chain segments.



The solver continues with XY-chains, coloring, and a naked triple. In case you’d like to take it from here, the finish is reported next post.  The parade of diverse advanced methods in the solver solution, many weakly signaled and difficult to spot, justifies an extreme rating.  And it’s not over yet.

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World’s 36 and 200 Basic, and More on 25

In this post, checkpoint traces on World’s Hardest 36 and 200, and a direct comparison with  two Strmckr solutions to Worlds 25. Also, a Gordon Fick contribution to the cause.

Here is Strmckr’s first solution, right out of line marking. It’s an almost nice loop AIC bringing the adjacent winks together to remove 2r1c7.

It looks easy, but it’s not, considering what you have to be looking for, to spot it. There are two multiple value cells and two AIC hinges involved. Strmckr’s “singles” collapse is rapid and complete.

At the point in the SysOB where AIC  hinges are  applied, I have two coloring clusters.

Instead of the pattern analysis and trial, I should have noticed the decisive trap. It’s that both blue and green remove 2r1c7, the same removal as Strmckr’s AIC ANL.


Coloring hastens the collapse as well. The blue/green cluster expands before 6r7c3 wraps green.

The approach towards a BUG explains why 25 can be very hard.

I’ve now released Strmckr’s 4/24/18 comment with his second solution.


It involves a cleverly selected ALS pair. Strmckr takes no credit for that, but instead, ascribes the  removals to “transport”, a forum concept whose definition does not respond to my search.

No worries. With the pair of 2’s as a restricted common, 4r9c7, and 6r7c7 qualify as ALS_XZ victims. Shortly after, 6r4c2 and 2r1c7 follow.

But there’s more.  Sysudoku’s own ALS_XZ expert Gordon Fick responded to the homework challenge and the ALS Partnering idea with an apt alternative.

Working with the bv 28r1c8, try the possible RC with 8r8c8. The r8 row has extra 8’s, but there is an SE ALS with 2 and a single 8.





Now for the checkpoint basic traces. First the basic rout of Very Hard 80, one of two rated second highest by Sudokubooks. Obviously not the monster.

If you’ve never read a trace, filling in the grid as you go, try it out. It took me several tries to get the trace right, and it is very useful. Just give yourself time to know exactly what each move is, and why it is known to work. Read Sysudoku Traces as necessary.

The second trace then, is for a near monster, World’s Hardest 200.

Here is the line marked grid, with fill strings. If you can solve it, tell me how you got it started. I’m sure sysudokie readers will be interested.

Next week, the World’s Hardest review continues with 200.

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