I've been open about the technique I used to solve this puzzle (quoting myself: "trying one of two numbers in a 2 candidate cell until you meet error [meaning getting to a point where two instances of a number in a r, c or box is the outcome]. Error is good, because that means it's the other candidate. Merely meeting an impass [can't get any further], however doesn't prove it's right).
Max now informs me that this method is, by some, called trial and error, and therefore not includable within the spirit of this thread, which is to find logical reasoning that would enable us to deduct why one candidate should be chosen over the other (did I get it right, Max?).
I'll digress, however, and I've since found the method described in Wikipedia's sudoku entry in the paragraph on analylsing:
http://en.wikipedia.org/wiki/Sudoku#ConstructionHere's their way of saying this: "In the [if-then] approach, a [number in a] cell with only two candidate numbers is selected[. ... The other methods] above are repeated unless a duplication is found, in which case the alternative candidate is the solution. In logical terms, this is known as
reductio ad absurdum".
Still in Wikipedia, reductio ad absurdum is defined as a "reduction to the impossible", often used by Aristotle, is a type of logical argument where we assume a claim for the sake of argument, arrive at an absurd result, and then conclude the original assumption must have been wrong, since it gave us this absurd result. This is also known as
proof by contradiction. "
This type of logical argument is also used in mathematical logic, where there are some fancy if-then equations:
http://en.wikipedia.org/wiki/Reductio_ad_absurdum (then scroll down). I doubt you can use these to solve Sudoku's, though.
In my mind (and you don't have to agree), reduction to the impossible or proof by impossibility are perfectly all right logical alternatives. I'd even add that this is the principle at the base of all logical deductions, including all the basic scanning techniques. It's fine by me if someone wants to call this trial and error, I'll call it an if-then in mathematical terms, or if you prefer a new term, 'deduction in the second degree'.
I've just realized that, especially with this lenghty post, I've just proved Max's point that I'm no help in solving the puzzle with logic-ex-reductio-ad-absurdum. (Anyone wishing to discuss which criteria to include in a logical purist approach should start a new thread).
I'll therefore sign off from this thread now. I'll thank everyone for putting up with an beginner/amateur like me stomping around in a glass house and appologize if anyone was sent off on a wild goose-chase on account of my lack of sudoku-vocabulary and ignorance of protocole pertaining to this thread.
Cheers, Jac