Set Logic, and the Rule of Two

The Rule of Two is Do.

I'll expand on that quite a bit over time, but it essentially comes down to recognizing that when you're doing sudokus, a lot of the time you can't get down to a single answer.  Now, you can see from some of my links that a lot of people have figured out that marking for pairs is Very Useful, and I quite agree.  But when I'm using set logic I take it one step farther and mark for twoshares.

Remember challenge one?

Note that at the bottom of column Ll I've written in all of the symbols that can fall into that column (2,5,6,7).  The 2 can't go into the bottom square at all, so it has to fall into MLl.  MLtl is elimnated by the 2 in MCtr, so I placed the 2 for Ll into MLbl.  I still had (5,6,7) as possibles, and since there's a 6 in ML, I was able to place a twoshare of (5/7) into MLtl.  I could also place a pair of 6s into BLl(t/m), but I didn't think of it before I took the picture.

In row Mm, I had (1,2,3,6,7) left, and I can easily see, looking across the Middle Zone that the 2 is going to fall into MRmc.  I can also find a twoshare of (1/7) at MLmc.  

At this point I know that both the 6 and the 3 in Mm will have to fall into the segment MCm.   I could easily set the pair of 6s in that row, but glancing at the center zone I see that the most complete column is Cc.  I didn't write it in, but you can tell that the remaining symbols are (1,3,4,6,9) and by a lucky coincidence the 3s are eliminated from that column in the Top and Bottom squares.  Therefore the 3 in column Cc has to be in MCc.

If a 3 has to be in MCm and has to be in MCc, then it MUST be in MCmc.

This kind of crosshair maneuver doesn't happen often, but when it does, it's very satisfactory.

  

Here's something to try.  I have a puzzle I've just done, and I found that it using set logic on row Mt  did something nice right away.  Since I can't just copy it for you, I'm going use notation to describe it.

row by row 

TLtr5, TCtl9, TCtc2, TRtr8
TLml8, TLmr9, TCml1 
TMbc8, TMbr5, TRbr9

MLtl5, MLt48, MRtc6, MRtr3
MLml7, MRmr2
MLbl9, MLbc2, MRbl7, MRbr5

BLtl3, BCtl5, BCtc7, 
BCmr8, BRml5, BRmr6
BLbl2, BCbm9, BCbr6, BRbl8

The puzzle is number 179 from the Everything 30-minute Sudoku Book by Charles Timmerman, which has been knocking around my apartment since 2006.