The assault on Easter Monster continues with coloring induced by the SK loop, and a plan for cluster mergers by means of pattern analysis on the monster’s favorite numbers: 1, 2, 6 and 7.
Without bv, or productive ALS, I’m feeling weaponless.
Coloring the corner box slinks and free line grouped slinks gives me an idea that the pattern slices of 1,2,6 and 7 might merge these corner clusters to give me effective ones.
For example, if green and purple 2-candidates are proved to be in the same pattern slice, pink or purple, then purple is green. Or if they are proved to be in different slices, then green is yellow. Either way, the merge clears monster fog. Have I convinced you that it is a plan? OK, where do we start?
It’s got to be with 7, right? After I shade 7-panels blue, green, yellow and purple to show which patterns can include these colors, I draw freeforms from the left, for patterns starting on blue and ending on yellow. Then for patterns starting on green and ending on purple.
There are two blue- to-yellow patterns, and two green- to- purple, so the blue/yellow mapping is possible. I’ll hang on to that, and give you a week to test the 7-panel blue-to-purple mapping, in the same way.
Meanwhile, let’s freeform the blue/yellow mapping on the 2-panel, which is a much harder enumeration challenge.
The 2-patterns must step in the center box as they cross the grid. There are more patterns, and this is more reason to divide the freeform panel into blue-to-yellow and blue-to-purple panels. Going left to right again, here is the panel before green-to-purple patterns are added. I’ve shown two aborted freeforms in red. Do you see why hey stop at c5?
Patterns crossing r5c2 have only one destination candidate remaining in c8, and cannot use the r4c5 stepping stone. Thus among blue-to-yellow patterns, r5c2 is an orphan. So is r4c8, because it is yellow. Sad, but what matters is that these candidates are removed in a trial of the blue/yellow cluster merge.
Completing the blue-to-yellow 2-panel enumeration, we have five green-to purple patterns, and no more orphans. The cluster merge depends on two blue patterns that both include r4c5. In a blue-to-yellow trial therefore, 2r4c5 is blue.
Have we accomplished anything? Yes, we know that so far, a blue-yellow/green-purple cluster is possible, and which 2 and 7 patterns support it. If blue-to-purple is also possible, then we may have trials of both.
So what about a blue-to-purple, green-to-yellow merge? That would be just as good. We set up the grid in the exact same way, and draw the freeforms differently. You can try it before the next post.
In addition, you might set up the grid for testing the red/orange to maroon/grey merge. But as busy as you may be, keep an eye on the hairy beast in the corner over there.