This post finishes the solution of KD Insane 425 review with pattern slicing, a technique also referred to as the pink olive. Before that, we attempt to answer the homework question by using patterns to merge the clusters. That doesn’t quite work here.

The question posed in the last post was, can the blue/green and red/orange clusters, with the common value 3, be merged by pattern analysis. Since red and green 3’s appear in the same line, blue or orange, or both, are true.

Here are some relevant facts about coloring and patterns: Cluster candidates of one color are true; those of the opposing color, false. Only one pattern is true. All candidates of the true pattern are true. All other patterns contain false candidates. A candidate in all patterns is true. A candidate in no patterns is false.

And here are some inferences about patterns and coloring:

1. A pattern containing both colors of any cluster is false.
2. Cluster colors of the true pattern must merge.
3. Any false candidate or color in the pattern makes it false.

On the question about merging the clusters, shading the freeform 3-panel with the cluster colors, the solid freeform r6c3 pattern is orange and green, the r6c3 dashed freeform is orange and blue, and the r6c9 freeform is red and blue. All are compatible with orange or blue. The enumerated patterns place no restrictions on the coloring.

The stage is set for something new, and that is to select starting lines that divide freeforms into disjoint sets, and then to mark crossing cells for the freeforms  to continue the division over the remaining lines.

The analysis divides patterns into two sets, and will be called pattern slicing. Two colors are used to mark the sets, not on the candidate text boxes, but as shading on the X-panel cells, as in the panel above. To avoid possible confusion, the colors used for pattern slicing, pink and olive, are never used for Medusa coloring. For that reason pattern slicing with pink and olive coloring is pink/olive analysis, or just the pink/olive.

Pattern slicing has several objectives, depending on the level of pattern restriction. It may limit the value to a single pattern, or a pair of patterns.  Or it may simply decrease the number of these.

When promising starting lines are available, the corresponding freeform division can be mapped on the panel before freeforms are drawn. In the Insane 425 3-panel, rows 6 and 4 are selected as starting lines, then the freeform crossing cells that must be the opposite slicing color are marked. That includes columns 2 and 3 and the West box.

Now secondary restrictions are mapped along crossing lines to keep pink and olive freeforms in disjoint sets. The idea is that no freeform of mixed colors, and therefore inconsistent with those first two rows, can represent the true pattern.

As freeforms are drawn over the pink/olive mapping, it is clear that only the olive 3-pattern is possible

Later pink/olive examples of this review illustrate how pink/olive analysis often must go farther, setting up alternative mappings with corresponding pairs of patterns for trials.

Back on the grid,

the collapse is immediate:

My hat is safe for another week, but I still feel like I’m going to lose 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.