An Unexpected Challenge from TV Times

Sysudokie Sunday breakfasts were shaken up February 4 by the Sudoku in the TV Times, which unaccountably defied the bypass. Accustomed to dusting this one off as a warm up, many wound up with an unwelcomed cloud on the amply sized grid, and spending surprising amount of time getting to a solution.

Forget about 3-fills. Starting with the grid in the previous post, the scan of numbers produces a trace of

SW1, C9,

and this grid.

Now you have to recognize that the c5 5-fill gives a hidden single 8.  Put that in and rescan 1 – 9, for three more clues.


  Here is the trace, . . .


. . . and the grid at the naked single point of collapse.  Who would’a thought?








We’re spending some in March with Rebecca Bean’s Extremely Hard Sudoku, v.10, and you’re invited to the preview, with her second highest rated puzzle I-34.

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Ardson’s Toughest, Even Slightly Diabolical, 310

This post fleshes out the review table entry, and checkpoints the two week homework assignment of the Ardson Sudoku Diabolical v.1. The early coloring typical of the review is helpful, but not decisive.

In the bypass, the 3-fill menace is resisted, and there are two very unsystematic hidden singles you are forgiven for missing, 4r4c3 and 8r4c7. You may be mystified until you see the causes in the trace. Now I don’t know how I spotted them.




The remainder of basic is routine.





With no grid scanning prospects, the North bank bv field looks ripe for coloring.  A cluster is started, yielding a trap that nets naked pair N15, expanding the cluster.

To follow up on that, I added two more limited clusters, but return to systematic city with the XYZ map


A right angle XYZ is usually useless, but this 381-wing shows that in the AIC seeing world, the right angle is a plan for a construction project. Just look for a potential victim seeing two Z’s, and see if it can possibly see the third one.

You’d never search for such an AIC without a specific target.



The added clusters come with possible bridges:

In c4, not(orange and maroon) => red or grey.

In r7, not(blue and orange) => green or red.

On the 1-panel , a finned swordfish extends blue/green, and sets up a coloring bridge. In r6c3,

not (green and grey) => blue or maroon.

That bridge traps 1r9c1, expanding maroon/grey, . . .




. . . into the South box, where another bridge emerges:

not(grey and orange) =>maroon or red

=> red and

(maroon or grey)

=> red.




The resulting maroon/grey expansion wraps grey in the South box.

Then maroon wraps blue.

That pretty much wraps up Diabolical 310 and the review. If it really takes the irregular 381-wing, the finned swordfish and the multiple wraps, I’ll concede that diabolical puzzles can be found in A.D. Ardson’s Sudoku Diabolical v.1 .

Next, we detail the solution path for the 2/04/18 Sudoku in my TV Times magazine. It’s basic level, but may have generated complaints from readers unable to get a toe hold on a Sudoku they are accustomed to solving. For me, box marking revealed two inferences it takes a more talented  sysudokie to spot in the bypass. Are you one of those?

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The Bypass 3-Fill Smacks Diabolical 350

This post starts with a trace of the merciless 3-fill pounding of Ardson’s Sudoku Diabolical 350 in the bypass. Highlight grids from adv2 110 and 190 then follow.

The 3-fill brings on the unit fill phase of basic solving, when fills take precedence over number order, much sooner. The challenge is to avoid overlooking 3-fill opportunities. Writing out the 3-fill strings in the trace is effective for me, but you may find that I have overlooked a few.

 After the effects of NW1 are explored, the main list resumes with N3.

 Here is the grid near the end of the first leg, after C3. Single pencil marks indicate effects not yet explored as causes.







Diabolical 110 offers another kind of highlight, a near-BUG right out of the bypass. Filling in the 3-fills where possible, and coloring, you get traps and a blue wrap in the SE box, and a green solution.




In case you’d like to watch this happen, here’s the basic trace.




Sudoku Diabolical 190 is also reduced to a bv sandbox by the 3-fill. After these bypass actions,

and easy box and line marking, 190 is vulnerable to the two bv predators, XY chains and coloring clusters.

First, two XY- chains make three removals. One is removed by boxline as well.








Then coloring is decisive as two blue candidates are forced in r4c2.

Next week, a full backup of your solution on Sudoku Diabolical 310. In this review, it’s saving the best for last.

Be kind to your Valentine.

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A.D. Ardson’s Sudoku Diabolical

This post begins a brief review of A.D. Ardson’s Sudoku Diabolical, with a review table and analysis of the first of a pre-selected series 30, 70, . . . , 390. Ardson’s Sudoku Very Hard Puzzles, volume 2, very similar in format, was reviewed in April through July of 2017.

In comparison to Very Hard v.2, Ardson’s Diabolical v.2 appears from my sample to be less consistent, and certainly not more diabolical. Four of ten collapse in basic, two in the bypass.  Among the advanced level puzzles, a generous bv field invites coloring, and with consistent success.

Your homework, Dbv1 30, got the Diabolical review off to a good start with me. The 3-fills made a big splash in the bypass, and line marking featured a nice naked triple, and an 8-wing at the end of the close.


The 8-wing in two columns is not available until all rows are marked. It is spotted in closing as the c7 8-slink gets marked, and the other columns are scanned for a matching slink. It’s a sysudokie bonus of line marking

Besides coloring, another benefit of a generous bv field is an extensive XY railway. Here, three XY chains yield five almost nice loops (ANL), one for each victim.

After this, there is not much for the X-panels to work on.

But coloring is well supported, and the first cluster has four traps. Among them, the 5r7c1 removal creates r7np37, removing a green 7, wrapping green.




As blue dominated dbv1 30 fights on, a new cluster is added. The modified XY railway nets two ANL to  wrap red, for the orange finish.

Next, a trace of the bypass collapse of Sudoku Diabolical 350, a showpiece for the 3-fill.

Try it out. The starting grid is at the end of the Guide page Begin with the Bypass.

Also next post,  I’ll have highlight grids from dbv1 110 and 190.

The Diabolical review will conclude with a full report on dbv1 310. Shown here. You have two weeks to mull it over, then compare details.

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Coloring Bails Out Basic on III-34

In this last post of Moito’s Sudoku Road to Mastery, Basic drives the 0.91 rated III-34  into a near BUG blind alley with a flurry of subsets and boxlines, then hands off to coloring for a quick score.

A tight bypass resolves one 3-fill and leaves one. Then box and line marking go routinely until I prefer two 7f: final rows over a gaggle of columns, and finish the rows on r6.

The grid at that point  has the first subset, a modest naked pair. The pair removes four 8’s, but one of those removals brings more than a clue.





What happens is that C4 removes 4’s to create naked quad in r4 and a naked pair in c3.







The quad generates two boxline slinks, but the naked pair starts a collapse, which . . .



. . . stalls one cell short of a BUG. But no problem. Coloring reveals in c8 that green is impossible.








Next post begins a review of A.D Ardson’s Sudoku Diabolical, with # 30, shown here. Let’s compare solutions.

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Coloring Dominates Very Hard III-15

The review of Moito’s Road to Mastery Sudoku continues with another example of early coloring and its cooperative interactions with the X-panel. The advanced path is similar to that of Very Hard I-35 two posts back, but this time coloring dominates the action.

When a first cluster stalls, a second one bids for attention by completely coloring the 8-panel, and delivers a column of traps.  Very Hard III-15 toughs it out as this dominant cluster grows, merging with its stalled predecessor. Finally,  the wrap of a third cluster chooses a side and its over. Sideshows to this drama are an irregular XYZ-wing and a finned X-wing that traps its own fin.

The bypass starts with a 3-fill, but then succeeds only in closing out the 9 placements. With one exception we’ve noted, Moito’s yield very little in the bypass, but tend to give up plenty of bv in basic.




A potential 57 UR in the North bank is prevented when the 4’s insist on a place in one of the roof corners. A second possible UR is erased by the r7 naked triple.




Next, the XYZ map reveals an irregular 675-wing. The 75 wing is attached with an 7-chain, in which two slinks function as winks for the team.

As Very Hard I-35 suggested, it’s a good idea to start coloring clusters when bv are abundant. On the ©PowerPoint grid template they don’t interfere and later unrelated removals can bring traps or wraps in the clusters.



The finned 6-wing removes 6r4c4, making 4r5c4 and 6r4c4 red, trapping the 6-wing’s fin, 6r6c4. That’s the advantage of having a coloring network in place. And it is so easily done.

Two more traps and green merges into red, blue into orange.


One more trap and we are dangerously close to a BUG, a double solution certified by unanimous bv.

One final cluster saves the day, as 4r8c2 is trapped, seeing orange and red, wrapping Aqua. Lavender sees orange, so red wins.



While Moito’s Road to Mastery is not consistently advanced in practice, or in protection from multiples, it has provided many entertaining challenges. I think it deserves to finish out the January posts. So let’s do Very Hard III-34 next time.

The Guide pages now cover Sysudoku Basic. If you’re a beginner, it’s all you need for know, for now.

Stay tuned, the Sysudoku Advanced header page is completed. The Unique Rectangles methods page  is next.



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How Not to Find a Multiple on Moito’s Road

After a jaw dropping irregular XYZ-wing, a marking mistake reveals an unavoidable UR and two solutions of Very Hard IV-6, then the correction leads to an even more remarkable, but no less unavoidable uniqueness violation. Coloring reveals the logical path to all four solutions, no errors required.

In Sysudoku Basic, a very stingy bypass and a routine box marking lead to a demanding line marking. It was tough, but our reward is an irregular XYZ for the trophy case.



The hinge of the 345-wing is r3c7. The 45 regular wing is attached in the . . . , well, regular way. The 35 weak link is a grouped 3-chain. The 5r6c7 removal is regular, its winks to the square marked toxic set, being unit weak links. The 5r6c7 sees the irregularly attached Z through a grouped 5-chain.

Have to ask how such a crazy wing is ever spotted?  It becomes possible with the XYZ Map, a derivative of the bv map. The map is where you can view all the XYZ-wing ingredients and examine the grid for the enabling AIC.

What happens next is embarrassing to admit, but is one of my more instructive mistakes.  I follow the two effects of the irregular removal, the 3r3c3 removal by the disrobed pair c7np39, and the boxline Wbxl5m removal of 5r6c2. But somehow I miss 5r5c2 and take the removal as a boxline, removing two 5’s to produce NW47.

A quick collapse came to a very strange end, when I reached a deadly rectangle on the very last removal. No chance to identify a preventing action. 

Then a check with Moito’s IV-6 solution matched neither of these two. 




Going back to the boxline removal above, and scratching my head over its mistaken effect, I had a much better alternative, a double Type 1 UR. Sorry, extra candidates are in one corner, and it must be reserved for one of them. Rectangle candidates are asked to leave quietly.

The 9r5c2 removal is an effect of the r5np39 naked pair created by the 5r5c7 removal. The 5r2c2 removal comes from NE3, and its c1np25 effect.

OK, back on track, and knowing we have a multiple, we naturally go to our customary multiple tracking bloodhound,  the coloring trials.







The green trial gives us a 6-node remote pair loop. Like the earlier deadly rectangle, it arrives too late to be avoided at the puzzle’s expense. Moito’s solution is the orange side.

Like too many composers, Moito doesn’t run its solver long enough to avoid multiples.

I was a little surprised to find that blue is just as decisive, and leads to the deadly rectangle I encountered first. That means there are exactly four logically derivable solutions. Does your favorite solver agree? If not, I’d like to know.

This is the first time I’ve seen a UR multiple solution formations turn up with all other placements decided. The occurrence doesn’t affect the dispute  I have with the UR detractors who say that use of UR is an additional assumption of uniqueness that we should not make. It is not that. It is nothing more than a belief that the puzzle was published with adequate processing and rudimentary proof reading.

Suppose the remote pair loop or the UR had occurred earlier, and we took avoiding action, then became stuck. That would have proved nothing, because, what can you expect from a known multiple? It has already given up claim to the rules of Sudoku.

Next time, the review continues with a walk through of Moito Very Hard III-15, shown here. It’s another example of coloring/ X-panel cooperation.

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