Systematic Sudoku

This post concludes that Manual Castillo’s Only Hard Sudoku book is for those sysudokies who enjoy the bypass challenge, and are not expecting a to get to many advanced techniques.

So many puzzle books, so little time. This relatively recent 2014 release by Manuel Castillo, lives up to it’s name, in that it does not venture beyond a simple “hard”. It is varied and active in basic operations, and sometimes challenging, but the collapse usually comes before all candidates are corralled for advanced solving. I preselected one every 40, starting with Only Hard 2. Here is the standard Sysudoku review table.

Plenty of Wayne Gould “no pencil marks” runs, and plenty of hidden singles and naked pairs and triples. Any “Only” that makes it into advanced solving will come with plenty of bv cells, and I would not expect any to survive the bv scan.

Here is the checkpoint line marked grid for the one taking up the most space in the review table, Only Hard 82, with fill strings still attached.

To get to this rather spectacular line marking, my bypass was short but tricky, requiring some of that backup from box marking that is convincing me to do box marking on the same sheet. Said line marking was a series of naked singles, each playing out where I had come to expect a collapse.

Note how thoroughly and compactly the complex, systematic shredding of Only Hard 82 is documented by the sysudokie trace.   The 8-wing on the line marked grid appeared in the marking of line r5 when the naked single E6 led to the NE1 clue, removing 8r1c1. The wing icons stayed on the grid through the remainder of line marking, and kept the 8 off the fill string for c6.

The close procedure yielded a naked quintuple, and on the last line, a naked triple. And did you notice how the row 8 naked triple removes a candidate in row 7? This had no chance to impact, however, as the quint marks to a collapse.

Too bad, but the naked quint erased this Type 4 UR. My approach is to spot it first by the extra candidates 4 and 9, then look around for somebody to get rid of them both. Of course that somebody, 4r1c4 in this case, becomes the victim of the UR. Or you can use the Type 4 drill procedure, taking extra candidates 4 and 9 as contents of a cell on r1, completing a mental naked triple that forces out the offending 4.

Again, Manuel’s Only Hard Sudoku collection is an active basic marking challenge, with an occasional surprise.

Next time, another Unsolvable 190, which offers me and JC an exocet which, with some effort, I refuse.

This post illustrates a sysudokie human solver technique, the exocet chute lettering table, for the second time in the Unsolvable series. The method was applied to the double exocet of Unsolvable 181 in the post of February 18. Unsolvable 186 is a single exocet. As before, the exocet was first spotted and resolved by JC Van Hay. Here we duplicate in detail his result, as reported in his brief comment in the Weekly Unsolveable page of Andrew Stuart’s site.

The basic solving trace for Unsolvable 186 is short but not sweet. The bypass closes out the 4’s, but no more Mr. Nice Guy in a clueless box marking and a very tough line marking,

leading to

and the question of “Why are we doing this?” I got nowhere with the X-panels, looking to nibble away at a few orphans. But the practiced eye of Van Hay found an exocet in the West stack. I’m hoping JC will send in a comment on how he spots these things so quickly.

Let’s see that exocet stack, alongside a lettering table which enumerates the four different ways that the outsider digits 3 and 8 are arranged in the 9 chutes of the stack, around the exocet base and targets. This is an essential element of the chute table technique.

It may take longer to figure this out than it took to draw it up, but it’s worth it. In this table, the contents of the 9 chutes aligned with the two base cells result from the four different ways that 3 and 8 can occur in the NorthWest box. The arrangements in NW determine the arrangements in the other 6 chutes of the western stack.

We designate the base solution as digits a and b. Actually, placing the 4 and other givens in the table helps us navigate in the table.

The presence of 3 and 8 determines whether each chute requires zero, one or two exocet digits.

The table reveals that fortunately, only the arrangement of the top table allows ‘a’ in one target and ‘b’ in the other, the qualifying condition for a solution via the exocet.

Within that single arrangement, are you wondering if you can interchange c and d in the middle column c2 and have both possibilities to test?   One gold star for alertness, but no, you then have to exchange them in row 2 as well, arriving at the same arrangement with interchanged letters. From the lettering, Weekly Unsolvable readers can connect the dots to JC Van Hay’s comments that

“A solution of D2 or E2 excludes the same digit from AC1 and GH3” and

“DE2=ab -> -(ab)AC1.GH3 “ .

So what do you make of “and 0 solution via singles except if ab=95”?

First, let me say that “via singles” does not mean there is a solution requiring only naked singles if DE2 (r45c2) = 95. “Singles” is just guru speak for the puzzle collapsing without notable advanced techniques.

And if you read it to mean that 95 is the only combination of digits, one from {2,7,9} and one from {5,7,9} that brings a collapse, you’re on to what JC is saying. So here is the grid with the NW 3 and 8 candidates in their courtroom seats for the exocet trials. How many trials? Well, 2 combines with {5, 7, 9} in three ways, 5 with 7 and 9 in two more. Then if we are lucky, we get a verdict from a naked pair np79 in r45c2.

Expect three on average, but it could be six.

I leave it for now, half expecting a more diligent student of sudoku to give us a citation to additional conditions that at least limit the testing this particular exocet. But to complete the message of this post, here is a challenge for sysudokie readers:

Here is the Unsolvable grid conditioned for the ab = 59 trial announced by JC Van Hay. Below is a trial trace. It follows the breath first “singles” track of the Sysudoku trial trace, which is the appropriate form for a trial in which you expect a contradiction. The purpose is to document the contradiction graphically on the starting grid with the shortest inference paths.

In case you decide to follow the trace, or duplicate it on your own for a checkpoint, at left is the 3-node XY chain or XY-wing, that is there when the”singles” give out.

Your challenge is to send in a comment with a Sysudoku trial trace of another ab combination that has not already been documented in a comment. You must state the contradiction and document its location. Ties will be credited to all.

Next is another brief review, on Manuel Castillo’s Only Hard Sudoku. It’s a “no nonsense” puzzle’s only book of 400 puzzles, but the only challenge is how much you can get out of the bypass. Only one will be traced all the way, so if you do ‘em before reading about it, here it is, Only Hard 82.

This is a single post review of a book of very few words, Djape’s Hard Sudoku Book.   The book is a good size, the paper is good quality, and grids are clearly printed, with adequate margins. There’s no commentary inside, but the cover does provide good advice: “Remember: do not guess!

It’s just puzzles, 200 of them, divided into three sections. The first 64 are labeled “BRAIN”, the next 86 are “IQ” and the last 50, are “INSANE”. I decided to include 5 Insane’s , starting with 151, and taking every ninth. Thinking that a bit thin, I then worked back through the IQ’s, and left out the Brains. Stop that giggling. Anyway, here is the customary review table.

On average, it does appear that the puzzles are properly placed in IQ vs. INSANE. Four of five don’t survive sysudokie basic. But the one that does, gets beyond the bv scan to a beautiful kraken jelly. The unhyped title, Hard Sudoku, is appropriate.

You might want to see if you can bring it to heel sooner.   The givens are still in place on the jelly grid, after the Sue de Coq in SWc2 removes 3r1c2, leaving a hidden pair or naked triple in c2.

Two of the kraken jelly’s victims escape, but one of them betrays a peer in c8 by participating in a forcing chain to the fin. It could be a poster for kraken analysis.

The preselected INSANE examples are less advanced, and rather sane.

Here is the unique rectangle of INSANE 151. It’s a Type 4, in which the extra candidates of the slink corners are treated as a single cell forming a naked pair to take out 6r7c8. The same result can also be spotted by asking if 6r7c8, which clearly removes the 6’s, can get the 1 as well, leading to the forcing chain doing the job.

INSANE 178 got a little further in the SOM with this four cell BARN and WXYZ-wing. The bent region is outlined in blue. Three of the four wings are in the same unit as the victim and the hinge. The victims needs a grouped forcing chain to see the fourth.

Actually,  there also a sneaky little 186-wing eliminating a 6 from the other cell of the Cbox’s conjugate pair, again, by forcing chain vision.

I’m not even going to show it to you. It spoils my nice panoramic of the BARN.

That’s it for advanced level highlights, but if you enjoy challenging basic solving as much as  I do, you can wind your way through IQ 133, with its double X-wings and naked triple ending. In case you don’t have this Hard Sudoku Book yet, here is the starting grid. You may wind up getting one.

Next post is the third Unsolvable of the Sysudoku review series. It’s a chute table analysis of a single exocet in Unsolvable 186. To get there first, look back at the double exocet post on Unsolvable 181.

In this post, two distinctly Sysudoku techniques have roles in a pattern trial of an Andrew Stuart Unsolvable, this time #183 of January 16, 2016. First, pattern (template) analysis on two numbers finds compatible partial patterns for a coloring trial. A perturbing property of freeform pattern analysis is explored, with a little help from a friend. Then in the trial, an attempt to construct an irregular XYZ wing reveals a particularly influential candidate that brings the puzzle to a collapse.

A special welcome to Weekly UnSolvable enthusiasts. This is the second post in a series intended to highlight tools and techniques enabling human solvers to resolve these puzzles logically, without arbitrary T&E probes, and if they prefer, using computer solvers, including Andrew’s, only for backup checkpoints. For me, the Unsolvable series is the Sysudoku monster for 2016. These puzzles are monstrous, having survived Andrew’s solver. Sysudoku is out to prove that sound methods, calm nerves, and a patient, focused hand can defeat them. The series started with the double exocet of Unsolvable 181, three posts back on February 18, where the chute table was introduced as a tool for exocet trials.

Here is the Sysudoku slink marked grid of 183. I’m sure that UnSolvable veterans can quickly grasp the basic solving technique and pencil marking from this example. Slinks are strong links. Box slink candidates are marked at the top, row slink candidates at the bottom left, and column slink candidates at the bottom right of the cell. Slinks and subsets are marked in the process of finding all remaining candidates, a process I call basic solving.

Basic solving is summarized in this basic trace:

It’s untypically drab.

W3 is the entire result of the slink marking bypass, a clue in the West box. You read a trace by filling in the grid, and by seeing where the 3 goes, with the puzzle in this state. The bypass is an optional first phase of discovering clues by mentally imposing slink marking without writing in the pencil marks. It’s a warm up for the very systematic processes of box marking, traced in the first line. One number at a time, The claims on a box are interpreted to write in the slinks(m), aligned triples (t), and for less stingy puzzles, clues.

Now don’t be lazy. Getting this down will enable you to closely observe sysudokie solving in these Unsolvable posts. So get out a grid, copy the clues, put in the W3, and verify why the box marking is what it is. Which in 183, isn’t much.

Now we come to line marking on your grid. All we’ve got here is the order in which lines are filled. But as you go along you can verify if it’s reasonable sequence to fill the easier lines first. Sorry Unsolvabrights. I do r1, r2, r3, . . . and not A,B, C . . . Usually the count of free cells (6f) starts low from 3f and builds up, but this is 183. On each line fill, build a string of possible fill digits, then apply them across the line. There’s usually a lot more to do in line marking. Close in the trace is the extraction of line slinks on lines not marked when one grid side is covered. We also mark the bi-value cells (bv) and X-wings in line marking, with green boxes. See it? Also, if you’re into AIC, forget it. Not a single AIC hinge.

When faced with such an overwhelming fog of candidates, sysudokies skip the bv scanning methods and go directly to X-panels . These are 9 by 9 tables showing only the candidates of a single number. They cut the fog by ignoring clues and ‘other’ candidates. X-panels are good for fishing and the search for X-chains on a first pass, but in a case like this, we circle back through the X-panels for pattern analysis.

Here is the 2-panel with the 183 trophy fish. Removing the fin (f) leaves a column swordfish with the victims shown as question marks. In a very tough kraken analysis, every one of the potential victims(?) escapes by not ‘seeing’ the fin. Try it out this easy way. Copy the panel into a ©PowerPoint table. Starting with a “victim” wipe out every 2 it sees. If any singles or fish remain wipe out their victims. In all of these victims, the fin remains. I’m not going to checkpoint these surprising results. If Virginia can do it, so can you.

Here the X-panels yield no X-chains, to me at least, grouped or otherwise. So we move on to pattern analysis. The solving public has been warned to stay away from pattern or template analysis, based on the mistaken notion left by the Pattern Overlay Method (POM) that every pattern of every number must be known, so that elimination of every pattern that conflicts with all others will leave just one for each number. Obviously a job for computers only. Sysudoku has demonstrated that human solvers can take advantage of weakly patterned numbers to find candidates in no patterns (orphans), and use partial patterns on some numbers to extend coloring clusters and formulate trials. The effort was inspired by Andrew’s treatment, in The Logic of Sudoku.

You may need another update here. What is a sysudokie trial? It is a logically derived set of candidates that are all true together. The coloring trial is the most widely known example, but Sysudoku introduces the single alternate Sue de Coq and the nice loop coloring extension as well.  In the most useful trials, the set is all false together as well. The larger the set, the more decisive the trial. The solver uncovers puzzle logic either way.

Unsolvable 183 is weakly patterned in the South band and East stack. A freeform analysis of the 1-panel gives up that toehold. In MS graphics for ©PowerPoint and ©Word, a freeform is an inserted shape, a string of line segments, each completed by a click. Each freeform across the grid and hitting every line and box just once defines a possible pattern(template). It’s easy to prove.

To make pattern analysis humanly practical, it’s necessary to choose the battlefield carefully. In 183, the South band and the East stack both divide freeforms naturally into two groups. In the original post, I had freeforms South to North. Here, in a little more detail, are the blue group freeforms.

I had the freeforms of the left panel, and concluded that r7c3 was a blue orphan. But shortly after the post came out, I got a gentle alert from Andrew to look again. Back on the freeform drawing board, I came up with the right panel forms, these going through the supposed orphan. But even worse, now I had only one cell on all the blue patterns.

I have hard knocks experience that freeforms don’t capture every subtlety of pattern constraints, and it is possible to get differing results from differing directions. Here are my East to West freeforms, and you’re welcome to weigh in for Andrew if I mess it up again.

Green freeforms are consistent, but at r3c7, the blue ones have 2 c1 targets and 3 c2 targets to hit. At c4, both paths must skip r7c3 to hit a line not represented in the next column. The alternative red form thru r1c6 has already used all ending targets at c4. A very similar problem constrains the r1c7 forms. Both patterns must skip r7c3, and the red r3c6 form has no c1 target left. The 1-orphan, and more importantly, the four 1-pattern nodes, are there after all.

Also promising is the 3-panel.  There are only four possible 3-patterns, two of them are consistent with 1r9c8. One of these, the short dashed blue one, comes with the finned 2-swordfish eliminations, because it erases the fin.  If it fails, the trial leaves two possible 3-chains, one with grouped ends.

We’ll do the trial. The hope is to make progress, regardless.

The trial begins with these advantages, but it is still just a trial. On a grid copy, we post the trial clues, noting eliminations, and track the marking with a trial trace. New clues are centered, but kept at pencil mark size. Only the exclusively green candidates are eliminated from the green freeforms.

Note that 1 and 3 patterns are not decisively interlocked, but quickly found contradictions may uncover an “obvious” merge that I don’t yet see. It starts off nicely with a 8-chain ANL, due to the trial placement of 3r3c5.

Making use of the newly trial acquired bv, I was looking for a forcing chain wink (weak link) to attach the 25 wing to the 257 hinge for a 572-wing, when I noticed the surprising influence of 5r8c2, and decided to use it as a continuation leg of the trial.

Yes, it’s getting close to a cheap bv trial, and you are free to look for better evidence, but this post better end soon.

Of course, I copied the slide, to be able to come back, and continue the trial with 2r8c2. This backstage admission alone could convince you to use ©PowerPoint for this backtrack ability.

Well, there was no backtrack. In case you’d like to follow the Sysudoku trial trace, here is the collapse:

A page on traces explains them in detail, but with an updated grid in hand, you can figure it out faster: lists are completed all at once, then left to right, each cause’s effects are turned loose to race downhill.

Thanks for following the comment and coming by.  We’ll continue with selected Unsolvables down the road. How could a sysudokie pass them up? But in return, I’m expecting to see some sysudokie tricks in your comments in Andrew’s Unsolveables. OK?

Next is a brief review of the IQ and Insane puzzles in Djape’s self published Hard Sudoku book.

This post considers Carol Vorderman’s “difficult” collection as a practice field for the Sysudoku bypass. Carol’s tips for solving are described, and sysudokie homework on the walkthough “difficult” example is checkpointed. The review of Master Sudoku is concluded with Vorderman solving tips and a report on the Master Sudoku “super difficult” collection.

Your homework assignment shows that Carol Vorderman’s “difficult” techniques carry you through on puzzles solved by the bypass, making the collection of 50 puzzles a nice challenge for your sysudokie bypass techniques, and your Wayne Gould attitude. My evidence for this is the following trace. I hope you got that far with the bypass, but if not, follow the trace for some instructive moments.

When I followed Carol’s walkthrough in Master Sudoku, her first pass 6 through 9 went as expected, with an “only one fits” on 8, and a “missing numbers” on 9. But from that point, moves came in no order I could identify.

The primary skill in the bypass is to react immediately to dublex, hidden dublex, “walls”, “squares”, and to clue and naked pair opportunities created by 3 free cells or less in units. With a blog trace as demanding as the above, I can expect to have to start over where I missed one.

The solver’s immediate reaction is not urged in Carol’s book, and rightly so. It is not important in basic solving to find and store away every bit of unused information. It is valuable for stretching the bypass a