This post continues the finishing coloring cluster expansion in Castillo’s Only Extreme 3, via not-both testing of AIC slinks. After extending the blue/green cluster in the North bank via AIC slink, we continue with a second AIC slink adjoining the cluster, shown below.
If 1r5c5 and 2r5c8 both true, we could declare green false, blue candidates true, and be almost home. If not, the burgundy slink is also a coloring link, and blue/green expands.
The both-true combination forces two 3’s into c6.
The cluster expansion traps 67r5c4, but more importantly, it enables a third AIC slink to apply for a coloring license.
In the olive AIC slink 2288, if both terminals 2r5c4 and 8r4c7 are true, blue is confirmed, but along with that, all three 8’s are removed from the South box. So 8r4c7 is green, and coloring makes a leap.
Traps along c8 and r5 are first, then the 8 removal in r5c6 creates a naked triple. In the North box, only the 5 sees all of its peers in the triple. The 6 and 7 candidates do not, because the triple is defined in the c6 column, not the N box.
After a brief marking,
The blue confirmation finishes Manuel Castillo’s Only Extreme 3.
Certainly a puzzle requiring three not-both extensions of the coloring network (and two posts) deserves the extreme grade.
I will review the Only Extreme collection by preselecting these 10: 3, 46, 89, . . ., 385 in case you want to get there first.
Before that, however, let’s look at Only Hard Sudoku, Manuel’s earlier collection of basic Sudoku, that came out in 2014. Next week, we’ll have the review table, and Only Hard 128, an unusual case of a box marking collapse triggered by hidden pair not accompanied by a naked triple. Can you do the Sysudoku basic without letting the hidden pair slip by?
Next Monday, I’m doing an introduction to Sudoku for the Fairlawn Ohio Senior Club. I’ll report what I did and how it went, in case you might consider doing that.