eleven wrote : Of course the proof is (can be made) general for any pair loop over these cells (just replace the numbers by variables).

Agreed (despite which I'd probably check the non-pair loop should I ever come across one of those animals)

base/cover is a more general approach, as i have seen and i dont doubt its benefits. I just dont know much about it and have no practice at all, how to find the sets. For the special case of SK loops, they are easy to spot with my method.

Part of the trick is locating non-overlapping sets (btw I was editing my previous post to put in this very point when your last post arrived).

For loops non-overlapping sets are crucial, just as overlapping sets are hopeless for loops (the overlap means that the number of truths is not fixed at the outset, since it all depends on what happens in the overlaps, equivalent to "almost" logic).

In this grid we have the rectangle of cells r2c28 / r8c28 assigned with givens 9538. This is a very strong hint that the-therefore-non-overlapping r2r8c2c8 rows and columns are of great interest with respect to the remaining candidates (ie excluding those givens) particularly so (in fact this may be a necessary condition) as those givens include no repeats.

=> consider 12467 in r28c28

but 4 already appears in r2 and c8, so reducing its potential.

=>consider 1267 in r28c28.