I’m surprised to hear so quickly from someone who knew this Intersection Rule - yesterday I found someone else who used it, too. On the other hand it’s very reassuring to know there are lots of us sensible people out there. I’ve always thought (and still do) that there are two kinds of people - those who guess at sudoku and don’t think to solve it methodically, and those who solve sudoku methodically and absolutely abhor guesswork. I cannot fathom the mindset of the guessers, and I suspect I’ve spent too much time with them to realise there were so many of us methodologists.

Whether there should *always* be a logical way of solving them is something else. I can’t imagine how a definitive (ie mathematical) proof of that would look. But if I’m really, really, really, bored one time then I might create a program to show (just by generating and solving loads of them) either that the two rules together aren’t sufficient, or to give a very strong indication that they are.

I’d like to think I have better things to do with time, though.

I came late to the intersection rule (good name, by the way) myself but with that and the rule of N combined I’ve yet to meet one that I couldn’t solve (albeit sometimes quite slowly). Having said that, I’ve not encountered one of these “diabolical” puzzles of which you speak. I have heard it said that there should *always* be a logical way of solving them, so you shouldn’t ever have to rely on guesswork, but regardless of this they are clearly they are the work of beelzebub.