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.




About Sudent

My real name is John Welch. I'm a happily married, retired professor (computer engineering), timeshare traveling, marathon running father of 3 wonderful daughters and granddad to 7 fabulous grandchildren. The blog is about Sudoku solving. It covers how to start, basic solving to find candidates efficiently, and advanced solving methods in an efficient order of battle. It is about human solving methods, not computer solving.
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