This post begins my review of Jim Bumgardner’s toughest collection, the Insane level, with a demonstration of cluster extension in Medusa coloring, via Limited Pattern Overlay, or LPO. The puzzle is Insane v.4, b.5, n.5. That is to say, volume 4, book 5, number 5. The vast collections on www.krazydad.com requires that kind of puzzle numbering. Please pardon the informality, but I’m calling it Insane 415.
In KrazyDad’s Insane collection, I expect to verify that you will consistently find truly extreme puzzles. Jim says they cannot be solved without guessing. But since the sysudoku definition of solving doesn’t include guessing. I find myself in a friendly contest to find reasonable ways to solve these puzzles within the scope of human solving capability.
So far this blog has revealed refinements and aids for many advanced techniques, but I have labeled only one technique as “extreme” by sysudoku standards. That is my LPO. The subtleties of LPO may play a big role as I explore how far I can get through the Insane Forest without guessing.
I will take up the voume 4, number 5 puzzles from books 1 – 10 in order, and wind up with a review table at the end. Also expect some accounting for the toughness of the Insane collection at the end.
Let’s start with the basic solving on Insane 415. I trust you got the puzzle on www.krazydad.com . Box marking ends with the three middle boxes solved. Line marking is moderately tough, but uneventful, except for the gift of a 5-wing in row closing.
Following the Sysudoku Order of Battle, I marked the AIC hinges and built some AIC tracks, but found nothing productive. The ALS looked unpromising as well. Turning to the prospects for LPO, the imbalance in candidate numbers over the six unsolved boxes prompted me to look at 7-patterns, and extend the blue/green cluster into the 7’s, leading to two traps.
The logic behind this magic is the pattern slink between 5 and 7. Of the four 7-patterns, three converge on r9c2, and one on r9c4. If it is true, the one must be green and the others, blue. Three 7-candidates belong exclusively to the green pattern. No other 7-candidates belong to all patterns of a color.
The pattern slink logic can often be applied to extend the cluster without going into lettering. A candidate can be assigned a cluster color when all patterns of that color include the candidate.
The traps imply SW6=>SW3 =>NW4=>NE1, and resulting blue/green extensions that trap two 4’s in r7 and thereby imply S2 , which, in turn, generates clues N2 and N1,boxline removals, and 7-traps generating NW3.
The coloring party ends with NW3=>NE8=> NEnp36=>NEnp45, leaving an ample cloud of bv for advanced solving.
A grouped forcing chain attaches the 36 wing in r2c9, and the wing removes the 6-candidate in r2c4. The removal generates a boxline in Nc6 removing the 6 in r8c6. This makes 6 in r9c4 blue, removing 3 from the wing hinge. Kind of a boomerang effect.
In sysudoku solving, you don’t actually find these things by searching. Step by step, looking for the next specific item, you discover them.
Maybe you’d like to discover a way to finish off Insane 415 from this point. No guessing of course. I’ll bring one way next time, along with Insane 425 which you may want to tackle first for yourself.
On the way out, here is the trace on Trickiest Beware 141 box marking that I promised to Will Shortz devotees. Master the trace notation, get out a fresh copy of the puzzle, make yourself a movie of sysudokie box marking. You may never go back.