Well, my point was not that you can solve the whole row, but that you need method two to reduce it to:

(12), (12), (357), (467), (346), (457), (3567), (345689), (3689)

And then method three to reduce it to:

(12), (12), (357), (467), (346), (457), (3567), (89), (89)

And that neither of these methods on their own would get you this far.

But, I think I'm wrong.

Take a look at this:

http://www.sudokusolver.co.uk/solvemethods.htmlI think most of his logic is covered by ours, though in very different language. Even his method D is covered by our method 2, but he raises the very interesting example of four cells each containing a subset of four numbers, but only containing three each. Up til now I had assumed that at least one of the cells would have to contain the complete grouping, even if the others only contained a subset, so now I'm back to square one as far as thinking of a programmable algorythm for this!

It also allows my example to be solvable only using method 2:

(12), (12), (357), (467), (346), (457), (3567), (345689), (3689)

Cells 3-7 only contain the numbers (34567), so therefore no other cells can contain them:

(12), (12), (357), (467), (346), (457), (3567), (89), (89)

So perhaps method 2 and 3 are synonymous after all. Can you give me an example where method 3 works but method 2 doesn't?

Milo