This post introduces a new technique based on limited pattern overlay (LPO). I call it pattern slicing, or more whimsically, pink olive analysis. In pattern slicing, strong links between candidates are chosen to divide enumerated patterns into disjoint sets. In this blog, two colors mark the candidates known to belong to patterns in these sets. The technique can find LPO orphans and extend Medusa clusters. The puzzle started in the previous post, Insane 425, illustrates the technique. It was pre-selected for my review of KrazyDad’s Insane collection found on www.krazydad.com .
Last post I invited those readers of the sysudokie persuasion to examine the 1-patterns and 7-patterns of Insane 425 at the stage of solving reached at that time via an LPO aided Medusa coloring cluster merge.
In the left 1-panel below, note that slinks in r8 and r9 divide the patterns into two sets, the pinks and the olives. The colors mark the cells known to be contained by the pink and olive patterns. I choose pink and olive as colors distinct from the ones I normally use for Medusa coloring, hence the label “pink olive analysis.
In the middle panel, we color the remaining cells to show a resulting distribution of patterns across cells. The pink candidates can belong only to pink patterns; the olive candidates, to olive patterns. In c6, all of the olive patterns must include r6c6. In c5, however, the pink patterns may pass through three separate cells. The coloring helps us completely enumerate the patterns.
In the right panel, we enumerate the olive patterns, finding that the patterns containing r5c7 cannot be completed. In fact, all olive patterns cross r2c7 and all pink ones cross r2c1. This gives us four candidates included in all olive patterns, and three orphans omitted from all patterns. We also realize that all pink patterns end at r1c9, making r6c9 a fourth orphan.
On the grid, two of the olive patterns include r3c9, which has a blue Medusa coloring 1-candidate. Even though we cannot say that blue is true, we can say that candidates exclusive to these two patterns are blue! Cluster extension by removing the orphans and coloring these 1-candidates blue traps two, and generates naked pairs np26 and np79 in c4.
We now have more slinks among the cloud of 7-candidates, and returning to the updated 7-panel, we start freeforming from the right, discovering that no green pattern exists. This proves that blue is true for all numbers! Can you believe it? A pink olive martini !
Even this stroke does not resolve the puzzle. I tried to exploit the remaining bv with a red/orange Medusa cluster.
The SW box can satisfy the red candidates, and red candidates bring on an instant collapse.
Rest in peace, Insane 425. My hat is safe for another week, but I still feel on the brink of losing my challenge to this collection.
Next up is Insane 435, if you have the time and fortitude, try it and anticipate next week’s less demanding post.