by **Pyrrhon** » Mon May 15, 2006 7:41 pm

If I look at your examples and counterexamples I would see APE seems in the most general form to be the following:

Aligned Pairs Rule: Two buddies cannot duplicate the contents of any two-candidate cell they both see.

In this form it stills work in sudoku variants. Consider for example the cages in killer sudoku.

This rule could be generalized to a Aligned Set Rule, where we have a set where each cell sees each other.

XYZ-wing in the form which is independent to the sudoku variant is:

If three cells a, b, c, with a and b are buddies and b and c are buddies, with candidates xy, xyz and xz respectively, then x can be removed from the candidates of all cells (different from a,b,c) contained which can see a, b, and also c.