This post finishes the solution of Insane 425 in the KrazyDad Insane review by introducing a new technique in pattern analysis, pattern slicing. Or more whimsically, the pink olive. In this case, pattern slicing wraps a coloring cluster merge, finishing Insane 425.
As a preliminary in Insane 425, let’s look at its cluster merge by freeforms.
In the left freeform panel, green and red in the same units imply blue or orange, or both, are true. A green pattern has to include 3r2c7, making 3r1c2 blue and trapping red. That is to say,
green => orange. Green survives if orange is green and red is blue. The candidate 3r1c2 is trapped, confirming 3r1c7.
Now let’s try pattern slicing on the same 3-panel.
In pattern slicing, strong links divide the freeforms on the X-panel into disjoint sets. There being only one true X pattern, at least one of these pattern sets contains the true pattern, and the other doesn’t. In Sysudoku, pink and olive colors are applied to mark the disjoint sets of freeforms. These colors are reserved for pattern slicing. They don’t imply membership in a coloring cluster.
Pattern slicing is available when starting lines determine a pink/olive division, and slinks in remaining units channel the freeforms of the two colors. Pink/olive analysis starts by identification of collectors, cells through which all freeforms of one slicing color must pass. Collectors can be determined before freeforms are drawn. Here, the olive connectors form a single complete freeform. The only possible exception is resolved when r2c7 is rejected as an olive candidate because it takes c7 required for r1.
When the freeforms are drawn, there are two pink patterns, as well as the olive one. Slicing is not perfect, there being mixed cells r17 andr25. However, the combination of slicing with the earlier 3-cluster above is decisive.
The blue/green cluster covers all 3-candidates, so one color is true. The olive freeform includes the blue candidates of the cluster, so of the three patterns it must be the true one, wrapping green.
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.
One more note on Insane 425 pattern slicing. The collapse makes it unnecessary, but a pink/olive analysis of the 1 panel could have immediately extended the confirmation of blue E1 to immediately confirm NE1, S1 and SE1, as well. The red one is a reject. Only the collectors are used.
Next up is Insane 435, if you have the time and fortitude, try it and anticipate next week’s less demanding post.