Coloring KDST 5 10 5 is Too Easy

The bypass almost finishes KrazyDad Super-Tough v.5, b.10, #5, whether or not you start with the 4-fill and two 3-fills. Here’s my 4-fill version.

Line marking is minimal, and coloring on the few candidates remaining wraps green in r6.

With the current Basic process, we found the KrazyDad Super-Toughs much easier, compared to the  KrazyDad Insanes.

I’m incorporating 4-fills into the Systematic Sudoku Basic. They can be quickly bypassed as they arise if none of the missing values see two unfilled cells, and no missing value sees three. The disadvantage of adding 4-fills is having yet another rule to follow, and possibly overlook, in laying out a reproduceable path for newcomers, and for Sysudoku vets seeking to compare solutions.

Next I embark on possibly be my last collection review. You gotta’ stop sometime. It will be on the corresponding left pages of Heine’s Sudoku ultrahardcore 1. We’ll start with UHC 1 and follow the same skip by 44 pattern for 12 left pages.  

Your bad if you didn’t order the Sefan Heine’s Sudoku ultrahardcore 1 book for the right page review. Here’s the first left page puzzle, UHC 1.

I’m doing the left page review because of Stefan’s warning about the intractability of his right page puzzles. Maybe you’d like one before deciding if you want to tackle Heine ultrahardcores. I’ll be leaning on, and sometimes bypassing, my same two widely available solvers, and seeking, among other things, a better approach to avoiding the sheer drudgery of exhaustive ALS analysis.

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A KDST 595 Hidden Weakness

In KrazyDad SuperTough v.5, b.9, n.5, an almost naked triple is concealed, awaiting a single elimination. It’s not something reasonable to search for, but two systematic constructions get you there.

An otherwise anemic bypass fills the NorthEast box, but slink marking claims no more cells. Technically, the eliminations occur in the close of c5, the next line. The naked triple is a subset of c5 alone.

 NWc1 offers a Single Alternate Sue de Coq trial,  NWc1 = 1(2+3)(7+8) + 817, which was deferred.

No easy bv scan removals  but there is a skyscraper 6 chain that could have been spotted on the r5 line marking, before the naked triple eliminations.

If not, it can be picked out in the crowd on the 6-panel, or instead you might see this finned 6-wing. The basic follow up on either  of these finish Super-Tough 595

Both collapse traces feature a second, decisive  naked triple in c2, and a knot breaking hidden dublex Chdx6. Here is the skyscraper trace and its naked triple.

The finned 6-wing follow up trace has a different shape.

Next time, KrazyDad Super-Tough voume 5, book 10, number 5 finishes the updated review.

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KDST 585 Favors the Bypass and Coloring

In spite of a big bypass, Krazydad Super-Tough v.5, b.8, #5 requires some work. An extensive XY railroad looks good, but a comparison with Medusa coloring favors the latter. This brings an opportunity to show unusual coloring resolutions, one involving dead fish.

In a quick bypass, starting with two 3-fills,  KDST 585 fills the second one as an effect of the first one.

Basic ends with a naked quad and three more bv.

Down at the railway station, a nice loop (black) and two ANL (red) collect more bv. There is an interlocking nice loop around two more bv, but it makes no more removals. We could use the interlocking loops for coloring, which looks inevitable anyway.

After a little follow up

We do that.  The nice loops would have generated most of the cluster, but not the 9 removals.

Two full color traps, and the new bv brings expansion.

The expansion produces a  boyfriend trap. 9r1c3 is caught in a cell with the wrong color. It loses regardless of which is true, girlfriend blue or guilty companion green.

The new naked pair removes 3r9c3, and we get a super tough cluster to resolve.

One route is to work on the cluster directly, with lite coloring.  The first probe works. 2r2c8 is blue lite, trapping 2r9c8, making 1r9c8 green, trapping 1r2c8, confirming the blue lite 2 and therefore, confirming blue.

Another route is to use an independent means to removing or confirming a blue or green. The 3-panel has a dead swordfish and a dead jellyfish, and the finned 3-wing here, with a victim in the same box as the fin, 3r2c9.

The expansion puts green 3r1c9 in with green 9r1c9, another boyfriend trap wrapping green, and KDST 585.

Just two more Super-Toughs, with 595 next. Look it up on

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KDST 575 Highlights Box Marking

Box marking gets to shine in the redo of Super-Tough, volume 5, book 7, #5.

Here is the grid after the relatively modest bypass. The fill strings show where 4-fills were examined, but only one was found.

In this snapshot, box marking is just beginning to pay off,  as the C box is claimed and the 23 pair slice up the center 2 candidates.

Below is the trace up to that point.

Here’s the entire 9’s box marking and the line marking.. It’s my best example of box marking slinks taking space and generating clues.  Typically box marking generates no clues.

In the final line marked grid, I could color now, but let’s see if some old friends show up first.

On the left, a hidden unique rectangle. We look for pairs on rectangle corners. The slinks say that if UR candidate 9r6c2 is true, it’s corner 6 is false, placing 6 in both adjacent corners.  The bv corner then forces the opposite corner to 9,  and that solution on the rectangle can interchange UR partners and become a second solution.

On the right, an irregular 139-wing. One of the hinge or wing Z candidates is true. 9r6c8 sees the hinge and one wing via column 8. It sees the other Z via 9-chain.

Then on our regular visit to the railroad station, two XY ANL confirm 1r9c3 and 9r9c5. That’s enough for a quick collapse, but .  .  .

coloring gets the same results easier and faster, trapping 9r1c3 and 3r1c5 and wrapping green in c4 and c5. A consistent result.

For next week, look up KrazyDad Super-Tough v.5, b.8, number 5.

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Super-Tough 565 Wrapped Twice

In this post, KrazyDad Super-Tough v.5, b.6, #5 survives a wrap of one coloring cluster, only to fall to a second.

The bypass starts with two 3-fills, one resolved. Then in line marking, there’s an outbreak of naked pairs.

Here is the hard won line marked grid.

Would you go with the Super Tough experience and start a coloring cluster?


How about on the C box diagonal and column 4?

Going on to the bv map, there’s a tight little XY ANL.

It’s not a little spur in an XY  railway, it’s the only XY chain in town, and a simple one at that. Agree?

Moving on to the XYZ map, we get one of those unworkable rectangular XYZ-wings. But wait, it is workable. 3r9c9 sees two of the three toxic set 3’s You could dispense with the forcing chain. If you see blue 3r9c6, you see blue 3r5c5.  You don’t even need 3r9c6. Seeing 3r4c1 does the same thing. It’s an ER, or a 3-chain, or a shortcut i583-wing.

Not to be outdone, two X-panels step in with X-chain ANL. The 2-chain gets a bv partner for a clue, but the 3-chain tops that by wrapping blue.

Surprisingly, KDST 565 hangs on after (W2, W9, green), and a second cluster traps two, wrapping red, and triggering a quick collapse.

Surprisingly, KDST 565 hangs on after (W2, W9, green), and a second cluster traps two, wrapping red, and triggering a quick collapse.

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KrazyDad Super-Tough 555

This post’s  basic trace on Super-Tough v. 5, b. 5, #5 illustrates the full use of 3-fills in the bypass, and closes with a six node remote pair.

On the grid as the bypass is completed, S9 is marked as a naked single by hidden dublex. Since box marking hasn’t started, the slinks defining the hidden dublex are not yet marked. Can you supply them?

In the box marking trace, the slinks are listed by the boxes containing them.

That’s all you need when following the trace. In line marking, two cells are claimed by a naked pair, and a naked single C5,

to another naked pair.  Now don’t scroll down until you find the remote pair,

that makes Super-Tough 555 melt away. It’s rare to see a six node remote pair.

Next week, in KDST 565, another challenging Basic is answered by coloring. Again, that’s Super Tough, volume 5, book 6, number 5 on

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Krazydad Super-Tough 545 Wraps Up Fast

It’s mostly in Basic with Super-Tough v. 5, b.4, # 5. The post of March 26, 2013 reports a long XY chain, followed by two remarkable irregular XYZ-wings, then two finned swordfish. However, this update shows that the generous bv field can be exploited more immediately.

Here is the grid as line marking. Is completed.  You notice first the large number of bi-value cells, the bv. Now scan over the field to see how well they are connected. There’s an extensive XY Railroad in there for sure.

But you can throw a coloring cluster on the bv field much faster than drawing a railroad, and if the cluster does nothing, still it won’t interfere with the bv scan, or the railroad.

Do that while I report  the Basic trace.  Starting with blue 1r1c3 cross every strong link, changing the color on every one. A slink requires exactly two candidates of a value in every row or column, or exactly two candidates of two values in a cell.

Here’s exactly how the two 4-fills came up in the bypass, and how a hidden dublex claimed 6 more cells in box marking. Also, the trace shows that three rows were left when candidates were all identified. Did you know that’s what those chicken scratches were about? You can follow every move, find my mistakes, and question my tactics. We both win.

You don’t need to read explanations on the traces page. Just follow along with your grid, do what comes to you and see if and why every move is justified, and how those moves are described.

Now back at your colorful grid, what did you do for 3r8c4? 3r3c4 and 3r7c6 say “color it green” while 3r8c7 says “color it blue. It’s not majority rule here. It’s that blue or green is true, and 3r8c4 sees both blue  and green 3’s. It is removed, leaving a blue clue. All blues are true, and all greens false.

Next week its Super-Tough v.5, b.5, #5. Get the puzzle at

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KDST 535 Trips on a Basic X-Wing

The X-wing is the easiest fish to spot. So easy, that the process of line marking finds it if you’re paying attention. KrazyDad’s Super-Tough v.5, b.3, #5 demonstrates.

The last line marked was r1, because it had the most free cells. When two 9 candidates line up with two already marked in r3, the new 9-wing rips through the bv.

In the basic trace,  the bypass starts with a naked pair and resolves two 3-fills. It’s a good one to read through.  Box marking reserves three cells. The 9-wing  removal triggers a steep collapse, before we close the columns.

Next week, it’s KrazyDad Super-Tough v. 5, b.4, #5,  on

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KrazyDad Super-Tough 525 Review Update

This post has an updated solution of KDST 525, starting with a 3-fill and a rare remote pair. The bv scan has an irregular XYZ-wing, and the 6-panel features a  long XY nice loop that illustrates the XY Railroad on the SysudokuTools page. An easy coloring wrap finishes.

In the bypass, the 3-fill up front is soon filled, but many await line marking.

On the line marked grid, you likely see the naked triple first, but there is a Sue de Coq where Sr9 contains 2(3+4)(6+7)  and r8c4 has to supply the 6 or 7 and r8c5 can only supply the 3 or 4. That fills out the remote pair. The hidden unique rectangle is signaled by the corner 18 values and the sling along one side. Think of the inference from 8 being true in a corner being carried by the slink. It doesn’t work from 8r4c3.

Another hidden UR follows with two slinked sides and diagonal extra values. Actually,, there’s two. If the other UR value in the slink corner is true, the slink value is carried to the adjacent corners, wiping out the extra values in both.

Now the XYZ-map yields an irregular grouped 476-wing. 6r4c8 sees two toxic 6’s already, and is helped to the third with a grouped 6-chain.

Then the aforementioned nice loop, over the remote pair territory, adds two more bv.

The crayons come out, and the 6 removals turn 6r9c6 blue, and 4r9c6 green, trapping 4r1c6, wrapping blue.

Shut off the lights when you leave. Next week, it’s KrazyDad Super-Tough v.5, b.2, #5.

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KrazyDad Super-Tougn 515 Starts a Review Update

This post begins the update review of the Super-Tough collection available on with volume 5, book 1, number 5.

The Super tough collection was first reviewed in March 2013, but that was one of the first reviews on Sysudoku, and only four posts were devoted to it. That review is updated here, with the full basic trace and all significant diagrams. The KrazyDad Insane collection is also reviewed on Sysudoku (see Titles). Both Super-Tough and Insane are huge collections, 20 volumes of 100 books, each with 8 puzzles.

My KDST 515 bypass starts with two 4-fills. In c2. NW1 and S1 together see three cells, leaving one for W1. You probably see the 5 clues in c2 first, then note the missing values 1456, then look for one of them boxed with two free cells. Find the second 4-fill, and confirm it in the basic trace.

On the line marked grid, a naked pair 28 signals a possible unique rectangle. With a floor to ceiling slink, the opposite rectangle candidate in the ceiling has to go.  It 8r5c5 is true, so is 2r2c5 and 8r2c4, making 2r2c4 false. The slink makes 2r5c4 true. Rectangle values 2 and 8 can then be interchanged for a second solution.

A second boxed naked pair gives up a second hidden rectangle of the same type. Same rule. Trace this one out.

Two clusters cover most of the bv. They are bridged in c9 by

not(green and orange) => blue or red or both.  

Beeby finds a 1-way that expands the blue/green cluster to a second blue 3 in r6. Green then wraps orange r9c9.

A second way to wrap blue and orange is this  AIC  ANL with two green terminals. Absent the blue victim seeing both terminals, blue is wrapped because at least one terminal of an ANL is true.

But these are AIC building moves.

By construction, and much easier is, in the bv scan,

using the Sue de Coq restrictions of

 Cr5 = 2(3+8)(5+6)


Cr6 = 1(3+9)(5+6)

to show that

blue =>  9 in Cr6

=> 3 in Cr5

=> 5 in CR6

 => orange, merging the clusters

Then a couple of lite traps wrap blue.

 First, 4r3c2 blue lites 3 r3c5, trapping 3r7c5. That allows 4r7c1 to blue lite 8 r7c5, which blue lites 8r2c4, trapping 8r4c4. In c4, C4 does the wrap.

Collapse is just as immediate.

For the volume 5, book 2, number 5 puzzle we do next week, see


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