## Core Patterns in the Easter Monster

This post continues the siege of the Easter Monster with a pattern analysis seeking to merge four corner clusters into two. The previous post found patterns supporting a merge of blue and yellow. There are three more merge mappings to examine for enabling patterns.

Now we turn to the possibility of a blue-to-purple cluster merge for the candidate grid of the previous post. Your homework 7-panel blue/purple freeform panel is promising, showing a single pattern in each color, and three orphans.

The 2-panel was less accommodating, with three blues reaching purple and three greens, yellow, and no orphans.

Altogether, there are six 2- patterns voting blue/yellow, and six voting blue/purple. We may have to try it both ways.

If we can merge the red/orange and maroon/grey clusters by the same means, that would make a better first trial. First we enumerate 1 and 6-patterns mapping red into maroon and orange into grey.

In the 1-patterns, we get three going each way, and no orphans.

Turning to the 6-patterns we get much the same, three on a side, and no orphans.
By the way, why do all of these pattern sets have blank corners? It’s a specialty of that monster glaring at us. We are systematically uncovering its weaknesses.

Now a look at a red/grey merge. No cigar, but 6 orphans!

Same answer below.

Three 1-patterns and five 6-patterns support red-to-grey. But four more orphans.

Red-to-grey comes with a lot of baggage.

After all this you may be considering this pattern analysis as difficult as set link graphs by hand. When that thought comes, just remember we are constructing these freeform diagrams, more than searching for them. When you see a set link diagram, there is no accounting of the human effort it takes to find it.

Also, you may be discouraged that we didn’t get a cluster merge pre-trial. Actually, we are winning. We can use the orphan removals in trials, and can take advantage when candidates stand or fall together in the few remaining patterns. It’s like X-ray vision.

So next time, no April fooling, we will start the cluster trials to solve the Easter Monster. It may be less than exciting as we grind along, until we get close to the solution. No doubt there are many long trials of “almost” solutions. That’s the monster calling card, so we can’t complain.

I’m starting the trials with more orphans and fewer patterns for the monster to fall back on. So let’s say red to gray, then blue to yellow with the winning red/orange merge. Want to jump early? I’ll back you up.

## About Sudent

I'm John Welch, a retired engineering professor, father of 3 wonderful daughters and granddad to 7 fabulous grandchildren. Sudoku analysis and illustration is a great hobby and a healthy mental challenge.
This entry was posted in Extreme Solving, Monster and tagged , , , . Bookmark the permalink.