Definitely Extreme 304

This post encounters what seems to be a monster in Castillo’s Only Extreme 304. A stingy basic leaves a near monster cloud of candidates resistant to the ordinary advanced repertoire. Following a theme of this review, a small coloring cluster is extended across the grid by not-both trials. It takes two more trials in the next post to defeat 304.  Or perhaps you can find a less extreme path.

The ordinary looking basic trace

leaves this formidable grid to navigate:

There is a Type 1 UR and a resulting box/line to start, but then I find nothing else.








In the swath of bv cells across the middle, I latch onto a tight little XY-chain intersecting a very modest coloring.

The potential for  coloring the XY-chain is enhanced by an AIC with numbers common to both the cluster and the xy chain.

If blue 8r4c2 and 8r3c3 are not both true, then 8r3c3 is green, and working back 7r3c3 is blue, 7r2c2 is green, and 2r2c2 is blue.

Testing terminal 8’s on the subchain from r4c2 is a start. The 8’s are not both true, along with blue,  because this forces both 3 and 8 in r1c7.






The cluster expansion removes four candidates. Clearly, a further expansion to 3r3c1 does further damage.

Again the not-both trial, testing blue + 3r3c1, is required for the extension.






If both terminals of the X-chain are true, c6 gets no  3’s.  Not acceptable.








The expansion turns 8r3c1 blue, generating three traps that expand the XY-chain further.








The final not-both trial to extend coloring over the XY-chain determines that 3r3c7 and 4r6c7 are not both true. If they are, 1,3, and 7 are removed from r2c5, and 1 and 3 are removed from r9c4, leaving two 4’s in c5.

Unless you have found a less extreme path, let’s see how you would continue with the fully colored XY-chain.  My finish of Only Extreme 304 comes next week.






Posted in Extreme Solving, Puzzle Reviews | Tagged , , , | Leave a comment

Pattern Coloring Not-Both on Only Extreme 261

On this post of the Manuel Castillo Only Extreme review, Only Extreme 261 justifies its “extreme” label. After limited advanced moves, a pattern based coloring suggests an extension via a not-both trial on a long AIC strong link. The not-both trial rejects the coloring by reaching the solution. A counter trial assures that this unexpected result does not signal a multiple solution.

First, the basic trace. Simple to follow, but leaving a distracting host of candidates, and not many clues, on the grid.



My first advanced nibble is a 7-chain and extended chain (red) for two almost nice removals in c8.









One of them enables an irregular 562 wing. The weak link attaching the 26 wing is a 6-chain, lining 2’s up for the victim.


It was a bad day for fishing on the X-panel, but 7-freeforms from the West side were only three.  By assigning colors by starting point, and coloring only where all patterns of a color cross, a blue/green cluster is created. Only the blue or the green candidates in common, can be true.




Applying this coloring to the grid, where several AIC  chains had been fruitless,  the conflict between the blue and solid green patterns at r4c7 has a counterpart. The coloring of candidate 7r4c7 is also the issue in the Not-Both condition for extending the cluster over two more candidates of the AIC slink .

It’s getting creepy, how  AIC  slink coloring  keeps coming up. The color of the East 7’s is not decisive either way, but seriously affects the solution path.

Before the trial, however, there’s a cheap removal to take.  In a red/orange coloring  of 8-freeforms from West to East, the ending candidate on the same row will have different colors. We don’t have to enumerate the freeforms for the trap.



In the trial, if both 7r9c4 and 7r4c7 are true, green is confirmed. The red/orange cluster explodes. There is no color wrap, but red forces two 5’s in column 5. Orange gives an immediate solution of Only Extreme 261.





This unexpected success leaves us needing to see if the AIC slink coloring, making 7r4c7 blue, brings more solutions. From the freeforms 7-panel above, the blue 7-pattern is confirmed in that case, and both green patterns are false. A trial trace makes it easy to demonstrate that no more solutions exist.  Blue implies red (E6) and forces two 2’s in c6. Time to move on to Only Extreme 304.



Posted in Extreme Solving, Puzzle Reviews | Tagged , , , , , , | Leave a comment

Only Extreme 218 by SASdC Trial

This post demonstrates the Single Alternate Sue de Coq with Castillo’s Only Extreme 218. The opportunity for this kind of trial is spotted early in the bv scan, but is best deferred until it is needed as a last resort. Only Extreme puzzles certainly qualify as possible candidates for the SASdC.

Sue de Coq is based on a logical description of a chute as three factors, one a clue and two binary factors, the alternates. In classic Sue de Coq there are two ALS in the box and line remainders of the chute, each ALS matching the two numbers of an alternate factor. The true candidate must be in the factor or in the matching ALS, and can be removed from any other remainder location.

In the single alternate form, only one of the alternate factors is matched by an ALS.  This match allows only one of the matching number to be in the chute.   If one is indeed present in the chute, one position is left for the two unmatched numbers, and removals of the matched numbers can be made in the remainders. A trial determines if both matched numbers are missing.

We pick up the solving of 218 right after basic, in the scan for APE and Sue de Coq. You could be on the lookout for ALS-XZ and BARN as well.

In SEc9, the possible contents are 9(5+7)(1+6) + 9(16+61), the first term being the classic Sue de Coq with the alternate (5+7) present, and the second, its contents with alternate values 5 and 7 missing. The SASdC trial follows up what happens if the alternate values are missing. If this trial reaches a contradiction, then the regular Sue de Coq is in force, removing 5r1c9 in this case.

What happens is a bit unusual. Instead of a contradiction or a collapse to the solution, the trial makes some updates, and stalls. We must continue from there


We look up to realize the “missing alternate” being tested has placed the 8’s and added bv and slinks to open up coloring. We dutifully add another tan/yellow cluster to take up the slack, and look for overlaps for bridging and merging of clusters.



It’s easy to conclude that if

not(orange and violet) and not(red and violet) then not violet.

Yellow quickly confirms both orange and blue, and the solution pours out.

The trial of missing matched numbers in the SASdC is often decisive.  I think you would agree, that logic based trials are far better than arbitrary guesses, or abandoning the puzzle.  Done too early, trials risk concealment of advanced logic and put a cap on learning.

As a last resort, a trial temporarily concedes that the puzzle is extreme.

Next we take another leap of faith, to Only Extreme 261. Four to go.

Posted in Extreme Solving, Puzzle Reviews | Tagged , , , | Leave a comment

Only Extreme 218 Straight Up

Barely escaping the bypass, Manuel Castillo’s Only Extreme 218 gets tough, and brings out some seldom used methods. An alternative trial path by Single Alternative Sue de Coq, normally held in reserve,  follows in a second post.

The bypass filled in the center band and tower, leaving very little action for box or line marking stages.


Then 218 announced its intentions with irregular 457-wings.  First, consider the SE 57 wing winked to the NE hinge by a lumped 5-chain. Two regularly attached 47 wings pair with it to generate removals. In black, a lumped 5-chain hitches a ride on one link of the irregular 457 wink. One ANL victim requires 5-chain vision to see one of the toxic terminals. The SW 5’s provide a slink (orange) for the chain and a wink  (green)for the victim.

I don’t look for these things. They happen. We use slinks for chain winks all the time, but it’s rare to see two candidates slink and wink at for different removals simultaneously.

It was a glorious, but very short story. Nothing else on the bv scan or panels.  Adding some coloring and AIC hinges, I stumble on an ALS-XZ. The AIC builds itself into a nice loop, extending the red/orange cluster around the loop.  The loop then extends, through r7c2, carrying red/orange into blue green.




Looking for a bridge wrap,

not(green and red)

implies blue or orange. A candidate seeing both colors is out.

No takers on that, but an important  fact is illustrated. Coloring extends with AIC extensions of nice loop colorings, in this instance merging blue and red, green and orange.

In the first step, if 5r7c2 is true, red 5r7c7 is false, green 4 is true and blue2r8c7 is false, proving not-both and extending red/orange over blue green.

There is also  a 7-chain ANL.

As the AIC scaffolding is hauled away to the dump, 218 breaks down with an orange wrap in r7. Manuel’s solution emerges. What a nice advanced ride!

Next week, , a reminder of what to do when you’re stuck, as I expected to be here. We’ll do a deferred trial introduced in Sysudoku, the Single Alternate Sue de Coq, on 218.

Its on the line marked grid. Can you find it and run the trial?





Posted in Advanced Solving, Puzzle Reviews | Tagged , , , , , | Leave a comment

The Akron 2017 Championship Sudoku

This is another Sysudoku analysis of the championship puzzle of the Sudoku tournament put on by the Akron-Summit Public Library. It’s an annual tournament of four rounds, the last being a three person solve – off on poster board grids, participants in earlier rounds of 3, 2, and 1 puzzles looking on. All four rounds were 20 minute solving sessions. The puzzles are unidentified selections from Will Shortz books, with his kind permission.

This walkthrough Sysudoku analysis of the final round puzzle is especially for the 2017 tournament participants like me, who were bumfuzzled by it on Saturday.

Here is the grid after the first stage of Sysudoku basic reaches a second 3-fill. That’s three unresolved cells in a line or box. The first one is resolved. The second is not, so a line marking fill string is left a reminder

To accurately follow the basic steps, mark them on a fresh grid, as you follow the traces.

Here is the first trace. Read from left to right, but also down the cause-and-effects steps. Multiple effects are lists inside (). Brackets {} mark 3-fills. The first one is resolved, but we’ve gotten to the N7 effects only.

On the grid, we have arrived at a second 3-fill, in c1. I’m looking for two of 1, 2 and 6 clues seeing a cell, one number seeing two cells. It doesn’t happen, so I leave the fill string, and move on.

The bypass trace ends with C7 on the top line, and another unresolved 3-fill to fill 1, 6, 9 into c6. The full name is the slink marking bypass. What it bypasses is the writing down of strong links that are used to generate the clues we have written in.

Now we write down the box slinks and wall triples to complete box marking. Here you see what they are.

Box slinks are exactly two candidates of the same value in a box. Why write them down now? Because strong links are central to advanced methods. We add line slinks later, but box slinks are distinguished by marking them in the top of the cell. Pencil marks are spaced on my grid template to allow three. I’ve never needed more.

I trace box marking as number labeled lists, and generate them 1 through 9. For comparing your lists with mine, attack boxes in left to right, then top down, order.

Effects of a marking are indented below, and may include clues and slinks of other numbers.

Line slinks and all remaining candidates are added in the third stage of Sysudoku basic, the line marking. Cells are marked one line at a time, in increasing order of free cells. A free cell of a line is one not resolved as a clue or a member of a closed subset.

Naturally, we start with three free cells, the unresolved 3-fills. In r6 we marked a bv and 1-slink. In c1, the line slinks are box slinks. They actually preclude other 1 and 2-candidates in the SW box, because of their required presence in c1. That’s a box/line.  I mark them as a naked triple to keep from adding them to SW as I line mark five other lines. This leaves only 3 and 9 missing in the box.

Next is a list of 4-fills. On r3, I make up 1268 as a fill string of numbers missing from at least one box segment, and copy it into each cell. Deleting numbers seeing the true number in a box or column. What’s left goes into the middle line of the cell. When the line is filled, I check the fill string numbers for slinks, and reposition slink partners not in box slinks to the bottom left corner.

In the 5-fills, the naked triple limits 2 and 6 placements in c2. We’re on the watch for matching slinks on parallel lines, to catch X-wings. In c9, I cut my fill string to 268 by spotting the 1-slink, and the 7 box slinks. The 7 slinks are there, in c8 and c9, but amount to a dead 7-wing. I’m rewarded by a naked single.

The detailed marking of the naked single is where you need to follow the trace to see how it guides the marking process to leave nothing out.

All the effects of a cause are handled before the next cause on the list is processed. When a list is exhausted, the last cause on the next earlier list is processed. As a further bookkeeping aid, I keep a deferred clue in pencil mark form until it is processed as a cause.

Of course, this careful processing is as unsuited to a speed contest as it is necessary for our task here, rating a puzzle against a prescribed order of battle.

We have one column to fill, as opposed to three rows, so we choose the column, but that does not finish line marking. We still have to carry out the marking of row slinks, and the checking for matching slinks defining X-wings. Of course, we have been checking for subsets as lines and boxes get fully marked. Championship 2017 has made it to Sysudoku advanced.

That starts with a check of aligned bv for unique rectangles. Then it’s a quick check for Sue de Coq or APE. Quick because the cupboard is bare.

But there are plenty of bv and three value cells, and a systematic search uncovers a regular 698-wing. The victim 8r5c5 is removed because it sees the toxic set of 8’s in the XYZ hinge and the XZ and YZ wings.

In Sysudoku, weak links are marked with dashes; removals, by diamonds. In a weak link, if one partner is true, the other partner is false. In the wing, one of the toxic 8’s has to be true. An outsider 8 seeing all three is toast.



I use a visual aid to look for XYZ-wings. Here is my XYZ map after the search. To the bv map, which is for enumerating XY-chains, I add 3 and 4-value cells with XYZ and WXYZ wings. The hinges without connected wings or without victims are crossed out. Note the 489 hinge not crossed out.

It leads to this wild picture, an irregular 498-wing. I claim the irregular XYZ, or iXYZ, as an Akron innovation made practical by the XYZ map. The wing is irregular when attaching winks of one or both wings are ER or forcing chain weak links. Here, the 9-wink of the 98 wing is a grouped 9-chain. This one has an irregular victim, seeing one of the toxic 8’s (the hinge 8) by a grouped 8-chain

The removal of the i498-wing is decisive. When I get to coloring after finding no fish or X-chains on my X-panels, the removal creates the 8-slink in r8 that completes this cluster.

The power of Medusa coloring is well illustrated here. Either the blue or the green army is true. The grey square marks a unique rectangle in the center bank. Blue forces 69 in all four corners, an obvious double solution. It is too late to reject blue for this reason, because the double solution is completed. And green gives a third solution. 

In 2017 Sysudoku demonstrated another possibility. Computer solvers, by ignoring the slink and coloring networks used in this derivation, can reveal additional solutions not derivable by these fundamental forms of logic.

Congrats to Deb, assistants and participants for a fun event.

OK, regular readers, we now return to our normal broadcast, and the case of Manuel Castillo’s Only Extreme 218.





Posted in Advanced Solving, Basic Solving Procedures, Shortz | Tagged , , , | Leave a comment

Almost Extreme 175 Tags Five Advanced Bases

This post reaches the halfway point in the review of Manuel Castillo’s Only Extreme collection, with Only Extreme 175. A double UR, a regular Sue de Coq and irregular XYZ-wing prepare the bv field for coloring, and an XY chain coloring wrap.

A challenging Sysudoku basic,

leads to a busy, unbalanced grid.  Advanced work begins with a Type 1 unique rectangle with two removals.  Neither victim can be present if an obvious multiplicity is to be avoided.





A rare treat is the Sue de Coq hidden in the brambles, that removes seven marks and triggers a box/line removing four more.






Manuel’s Halloween treats continue with an irregular 784 -wing.  The 7 wink attaching the 47-wing is an ER 7-chain.

Also irregular is the  4r9c2 victim seeing two of the toxic 4’s by grouped 4-chain.



The X-panels are less generous, so after a quick survey of the bv field, I get out the crayons.

My usual blue/green starting cluster is surrounded by a red/orange one when it stalls.  There are two traps.


More tellingly, in this clash of clusters, it turns out that blue and orange are incompatible. Going a little further, so are blue and red.  Since we must have red or orange, blue must go.

In logical expression this computes as:

Not(blue and orange) and not(blue and red) = (green or red) and (green or orange)

                                                                                = green and (red or orange) = green

 Two wrongs don’t make a right, but these two mismatches do make a wrap.

 Looking at the revised bv map,  there is  a long XY chain with four  removals, including a red 3.     This is a wrap by XY chain, always a possibility with coloring.    Here it starts an immediate collapse.

Next time, 43 Extreme Sudoku later, it would be Only Extreme 218, but this review is interrupted for breaking news, a report on the Akron 2017 Sudoku Tournament.  Watch this space. 


Posted in Advanced Solving, Puzzle Reviews | Tagged , , , , , , | Leave a comment

Only Extreme 132 Joins the Extreme Team

Another payoff for expansion of a limited coloring network via AIC slink. It’s an extreme tactic that, after six years of blogging, I finally blundered my way into.  This collection illustrates the not-both trial thoroughly.

Please comment if you know of anyone else that has introduced it.

My 132  basic trace:



And here is the line marked grid , fill strings attached:

Maybe these Sudoku are not as hard as I think.  What can you find?

My bv scan came up with a regular 475-wing, for one more bv cell. No XY  trains running on the railroad.





My constructive inclinations now call for the crayons.  Coloring produces an isolated cluster.

An AIC slink extension of blue/green looks like a promising break out.  




Testing the not-both is arduous, but 9r1c3 and 7r1c8 are finally proved guilty of something, in this case, a conspiracy to force two 5’s in r6.

Yes, it’s a trial. Trials justify the Sysudoku “extreme” label.    You can demote the puzzle by finding a combination of advanced moves that win the solution without  a trial.

With  its not-both papers signed, 132 traps an interfering 4, allowing a long XY chain to make an indecisive removal.

In the clutter of AIC hinges and chains, there is an ANL, but it only gains two clues.



I post all removals to the X-panel when the action stalls, repeating the scan for chains, fish and pattern restrictions.


This time,  a simplified 7-panel revealed a single freeform descending from the now blue 7r1c4. Here, note the failure of an alternative path (red) to reach r5.  So either the green army or the blue 7-pattern, is true. To test the latter, we add the blue candidates in the blue/green cluster to the freeform candidates.

And this time, the test is easy. The 6 marks are removed from r8 and c8 by 6r7c2 and 7r8c8.

Marking continues with green candidates, plus the blue freeform candidates not seeing a green candidate. These candidates are eligible to be in a green pattern.

In this case, the collapse of Only Extreme 132 is immediate, and we can continue next post with Only Extreme 175






Posted in Extreme Solving, Puzzle Reviews | Tagged , , , , , , | Leave a comment