Pattern Coloring

Pattern Coloring is a form of pattern analysis that combines coloring with freeform pattern mapping.  

Every unsolved value has a single pattern of true candidates.  When coloring clusters are present on the grid, each cluster represents candidates of two opposing colors, candidates of one color being true, and those of the opposing color being false. The true pattern cannot mix opposing colors of a cluster of its value, because all of its candidates are true. Pattern coloring is based on this fact. We start with one or more freeform starting lines consistent with a starting cluster, and use coloring, regular and lite, to expand the cluster to lines across the grid.

In Sysudoku, pink and olive colors are used as pattern colors to distinguish them from candidate cluster colors, so the technique is called the “pink/olive”, or PO.

Pink/olive was introduced in the post of 7/30/13, on KrazyDad Insane 425. In a post revision of 12/25/18, a beginning cluster starts pink and olive South to North freeforms on two starting rows r6 and r4, with a color link in c3 to r2c3.

We turn to lite coloring to expand the cluster and extend the freeforms. We an arrow to represent the weak link/strong link sequence for : if a is true, b is true. Here it means, if 3r3c3 is olive, so is 3r1c7. Also if 3r2c3 is true, 3r3c2 is false, making 3r3c5 true.  We’re building an olive network.

And a  pink network with it.  We can shade r2c7 pink in c7, trapping 3r2c5, and appointing N3 to delete 3r3c2.

This leaves two connected patterns you could call a pattern slink. One pattern is entirely false and the other is true.

In this case, lite coloring was applied on the grid to expand the cluster to other values, eventually confirming the olive candidates.  This is reported on the Guide’s Lite Coloring page Advanced Sysudoku/Lite Coloring.

The 6-panel in Insane 445 offers a similar example.

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

The slink in starting line r7 is color linked to the slink in c3. Then two more olive cells are identified by lite coloring, linking in the slink in c7. South to North freeforms define one pink and two olive patterns.

The two removals are useful, but pattern trials end it quickly. The pink pattern reaches a contradiction on the third clue. And a trial of the 4 olive cells common to the two olive patterns reaches the solution.

Insane 455 demonstrates more ways to use pattern coloring. One is lite pink olive X-panel traps.

On the 5-panel PO compatible rows r157,  the c1 slink traps 5r3c3. 

On the 8-panel, coordination of c2 and c6 traps two in r1.

On the 4-panel. Lite coloring links r4 and c2 for another trap.

West to East freeforms find 3 possible pink patterns with three common cells, and 2 possible olive patterns, with 5 common cells for trial. No olive includes r5c5.

Here is the Insane 455 grid with 4 common pink and 5 common olive 4-candidates highlighted.

Treating the 9 cells common across  the pink and olive patterns as a coloring cluster is valid. One color is true and the other is false. But here it’s ineffective.

The 5 common olive cells make a decisive trial. A failure would reject all olive 4-candidates and confirm the common pink 4-candidates.

The olive trial succeeds, leaving a much cleaner grid,

ready for regular coloring.

Starting the red/orange cluster on the unresolved olive pattern cells, orange is confirmed by the NE trap.

The solution mixes pattern and regular coloring.