A Guide Update and a Funster Kick Off

The threat of a “The World’s Hardest Sudoku” now relieved, this post starts a review of the “extreme” section of Charles Timmermans Funster Hard to Extreme Sudoku. But mostly, it’s a progress report on the Guide, a set of pages on the Sysudoku approach to humanly practical Sudoku solving.

The Guide is a linked set of pages accessed from the bar menu above. The hierarchy of the menu tree organizes solving techniques according to the Sysudoku template tools they use. Free ©PowerPoint and ©Word template files are available from Sysudoku (see Solving Tools above), but solvers can easily construct their own versions on their own systems, on paper, or in their minds.  When completed, the Guide may be available in book and reading tablet format for travel.

Here is the plan for the completed Guide: three primary pages for purely logical solving, and forth for trial methods. On the Sysudoku site, each section is represented by a lead menu page, covering general principles and with side menu links to method descriptions and examples.

Sysudoku Basic

This is about determining possible candidates of every cell, based directly on the given clues, and about slink marking, the explicit marking of strong links by candidate placement within cells. The replacement of the keypad style candidate list of most Sudoku literature is a major feature of Sysudoku. A three stage process incorporates slink pointing, box/lines, and subsets in this task.

Sysudoku Advanced

The lead page summarizes and illustrates elements of advanced methods, including the weak link, alternate inference chains, almost nice loop elimination and confirmation, nice loops, toxic sets, fish, coloring, and patterns.

It’s also the menu page for sections of methods based on the templates used.

Slink Marked Grid

This section includes advanced methods working with the candidate grid enhanced only by slink marking. It includes Uniqueness methods, Sue de Coq, APE, Bent n-set, and ALS methods. A second look at these techniques can occur as AIC hinges are added after coloring.

BV Map

These methods use a table of bv cells taken from the grid, the bv map.  A XY Railway is drawn on one copy. It is a connected set of curves along all possible routes of XY-chains.  The XY-chain is the simplest and most natural form of Alternating Inference Chain (AIC).  A copy of the bv-map isexpanded to accommodate XYZ and WXYZ hinges. This table is combined with the grid to find regular wings, and “irregular” wings constructed with forcing chain weak links and/or having forcing chain “seeing” victims.


X -Panels are 9 by 9 tables showing only the candidates of a single value on the grid. Each panel is examined for X-chains and loops, including grouped nodes, that produce toxic sets.  Then the same panel is examined for regular or finned fish. A fish is a competition between lines, and sometimes boxes, among candidates of the same value, for placement locations. Candidates that prevent resolution of such conflicts are eliminated.

Medusa coloring

Coloring marks each network of strong links, a cluster, by shading its candidates by two colors. Candidates alternately connected on a coloring network logically divide into two colors, one true (in the solution), and the other false (entirely eliminated from the solution).  This property is used to eliminate single candidates that see candidates of both colors (traps) or to eliminate all candidates of one color (a wrap) when the expanded network reaches a contradiction

Pattern Analysis

Pattern analysis eliminates candidates that prevent resolution of another kind of conflict, that like fish, is not directly defined by links between candidates. A pattern is a selection of remaining candidates of the same value and not seeing each other, that leaves one candidate in each box remaining.  The line marked grid generally leaves a large number of possible patterns for each of nine values, but in the solution there is only one pattern for every value. A humanly practical form of pattern analysis,  in Sysudoku named Limited Pattern Overlay, uses X-panels and a graphical freeforms to represent competing patterns.

Second Round AIC

Since advanced methods come in easier and harder-to-spot forms, it makes sense to  invest a reasonable amount of effort on each before intense pursuit of any. Solvers do make subjective decisions about when to move on.  For some methods, the Guide may suggest and illustrate a version “for the second round”, meaning after giving all the methods above a go at it. But in the case of inference chains, there is a second aspect to this.

An important fact that no one seems mention: The role of any link in any method can be filled by an AIC.  A first round example is the XYZ-wing, where wings and victims are made possible by using inference chains for weak links.  Even here, there is room for a second round, because I only looked at grouped X-chains for that purpose. I could use XY-chains and coloring links as well.

To open up possibilities even further, the Guide suggests beginning the second round with a grid enhancement,  the AIC hinge. In every cell, place an explicit wink between every pair of candidates that are slink partners with an outside candidate. That creates a 3-candidate slink chain that can carry a Medusa slink inference in a longer AIC. It allows the bv a second role in AIC.

Trial Methods

A complete guide must address the problem of being stuck. Sysudoku  places no value in guesses which reveal nothing.  However, there are many benefits to trials. A trial is an assembly, by logical means, of a set of candidates that are in the solution or eliminated together. The Sysdudoku trial trace is a way to document which and why.  It can be a safeguard against multiple solution puzzles.  I hope to stay with this long enough to determine for myself if methods in use for monster puzzles are logical methods or trials, but in any case, they are justified.

That’s the plan for the Guide. Thanks for reading through it. I welcome comments.  As of now, Sysudoku Basic, and Sysudoku Advanced through the Slink Marked Grid and the XYZ wing are in the Guide. Next comes the XY chain strong link and its Almost Nice Loop

The most recently added page is on ALS Death Blossoms. The general definition accounts for stems of all sizes, but it’s evident that the stem is rarely above two values. The typical rectangular shape of the DB is illustrated, and the possibility of overlapped petals is addressed as well.

All of the Guide’s DB examples are from a browser search, since I found no comparable examples in the reviews. My problem seems universal among human solvers, since many earlier examples are repeated on different sites.

A notable discovery for me is an ALS DB which eliminates candidates of value other than the common value between the ALS. In this particular example, there is no common value victim. This case was presented as a typical ALS DB, but it is actually a rare special case. For the details, you’ll have to consult the Guide.

Now about that next review. Here’s Funster Extreme 4 in case you don’t have Charles Timmerman’s  Funster Hard to Extreme 400+ Puzzles. The book provides the givens screened candidates, but IMHO you’re better off to ignore them in favor of the bypass and slink marking basic of the Guide. More progress and more fun.

Most of selected funster extremes make it to advanced, but none are truly extreme. There are good, simple examples, so I’ll take a slow leisurely trip through them. There will by good bypass challenges, and you may well find alternatives to share in comments. It looks like a hot summer.

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Painting a World’s Hardest BARN

This post ends the review of World’s Hardest Sudoku Book with its Very Hard 134.  The puzzle is not all that hard, but does allow solution in a very pleasing way, for me, at least.

Right after a basic with many 3-fills in the bypass, and a hidden dublex in box marking, . . .




. . . the 8-candidates in the West box fall victim to the unrestricted 8’s in the BARN at Wr5 via a grouped forcing chain. This removal creates a boxline removing 8’s in the East box.

The BARN, or Bent Almost Restricted n-Set, is a spotting technique for the  Bent n-Set Type 1 (BNS1) now described in the Sysudoku Guide.


Next, the 5-panel gives up an almost nice loop ANL (black) which extends to another ANL (red).








Upon adding a blue/green cluster, a trap of 5r7c2 adds just the right bv to an XY chain linking two green 7-candidates. That in itself would wrap blue,  since at least one green being true means all greens are. But having blue 7’s that see both of the green 7’s makes it more obvious. That’s enough to collapse 134, and the review is done.


Next is a report on the most recent page added to the Guide, illustrating ALS Death Blossoms.


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Two More Basic Losses for the World’s Hardest

This post presents the review table, and basic traces of 46 and 188, two of the top rated ten puzzles of The World’s Hardest Sudoku Book. The puzzles were displayed on the last post.

These two don’t make it to Sysudoku Advanced.  If they did for you, you’re missing something about Sysudoku basic. Read the traces, taking in the traces page first if necessary.  Generate your own grid pictures. If you’re a beginner, the Guide coverage of Sysudoku Basic is there for you. There is absolutely no reason for me to have all the fun.

Basic on 46 is almost done when collapse begins, on the line marking of r6.

A near BUG is squashed at the end by a remote pair.









Worlds Hardest 186 is its second bypass casualty

Here is the review table for World’s Hardest Sudoku Book. When it can be put down, this is nothing like the review table of the world’s hardest is gonna look.  World’s Hardest is basic to advanced in difficulty, with only one selected puzzle, 200, bordering on extreme. That aside,  it’s hard enough to bring out some unusual moves.

Next week, the review closes with a walk through of puzzle 134. You don’t have to follow the review table entry, but it does show where I’m going, if you want to know.


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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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