Pattern Slicing

Pattern Slicing is a form of pattern analysis that combines coloring with freeform pattern mapping. The technique divides a value’s patterns into two sets, sometimes identifying the true pattern of a value, or identifying candidates to represent one set in a trial.

For every value, all candidates of the true pattern are true. Of the two colors of a coloring cluster, candidates of one color are true, and those of the other color are false. Before we know which cluster color is true, we do know that cluster colors cannot mix on the true pattern.

In pattern slicing, we start with a line having exactly two candidates of a value, and assign opposing colors to them. Often it is possible to extend these colors to additional lines in both directions. We can then use this line to start freeforms in the crossing direction. Freeforms that include candidates of both colors can be discarded.. In Sysudoku, pink and olive cluster colors are used as pattern slicing colors to distinguish them from normal cluster colors, so the technique is referred to as the “pink-olive”.

Pattern slicing was introduced in the post of 7/30/13, on KrazyDad Insane 425. South to North freeforms are divided into two sets compatible with rows r6 and r4. We’re looking for freeforms consistent with coloring of the starting line and remaining parallel lines.. The cells that can only be in one set are shaded pink or olive. We call them collectors. Cell r1c7 is an olive collector because r42 is one. Two pink collectors are caused by olive collectors.

South to North freeforms are restricted to three. One olive or two pinks.  The dashed pink pattern mixes colors, and can’t be the true pattern. When it is removed, 3r2c5 and 3r3c2 are orphaned, and N3 is confirmed.

The remaining two freeforms are strongly linked. On each line, two candidates are color linked. They can be given regular cluster colors and be part of a coloring cluster. We call it a pattern slink, because one of the 3 patterns is true, and all candidates of the other are false.

In this case, lite coloring was applied to expand the cluster and eventually wrapped the pink candidates for a solution, using several traps unique to lite coloring.  This is reported on the Guide’s lite coloring page Advanced Sysudoku/Lite Coloring.

Pattern slinks are often decisive in a trial, with a contradiction of one confirming the other.

In this example of the monster Fata Morgana, posted 7/7/15, a slink chain c2-r5-c9 divides the patterns into two pinks and 4 olives

Then  a decisive trial of the pinks, test the 3 common candidates,  leading to the solution.  Note the orphan and two failed pinks. The 3 common candidates of the olives were tested, just to show they would reach a contradiction.