Happy 4th! Last post, on Maestro 49 of Fall 2009 we mixed coloring and AIC to good effect, and discovered the joys of the slink/wink color shortcut in AIC chains. We continue now with two clusters.
The second, red/orange cluster creates green/orange conflicts in r2, and we know red or blue or both to be true. Thus red and blue in the same number form a toxic set.
One removal comes from an XY wing, courtesy of the updated bv map. An AIC makes two 7-candidates toxic to a third in c9. A subchain shortened into a slink is shown in the thinner red curve. The removal extends the blue/green cluster.
The extended cluster generates two color traps, and the extension shows
NOT(red AND blue)=> green OR orange). This is enough to conclude that green is red and orange is blue, a true merge of clusters, because
(red OR blue) AND (orange OR green) => (red AND green) OR (blue AND orange).
Also c2np38=>NW9=>(N8=>(NE4=>NEr1np58), C2=>S9).
A final blow is the AIC removal , starting the collapse with SE8m=>NE5 SE5=>S3=>(N7, N4, green) .
There may be other AIC routes to the solution. Finding them all is just not humanly practical. But it is not necessary either. You only need to know how to explore links around the AIC hinges and bv. Removals are seldom anticipated. You find chains first, and then look for links to toxic set partners elsewhere along the chain.
Next, we see exactly how an ALS, an almost locked set, becomes a node in an alternate inference chain.
Systematic Sudoku 