Master framework, and blockades

I've worked up a master framework for our continuing sudoku adventures that I hope will work.  It has the thinking track labelled around the edge, so that as you actually do the thinking you can override the labels.

	1	2	3	4	5	6	7	8	9
TL										Tt
TC										Tm
TR										Tb
ML										Mt
MC										Mm
MR										Mb
BL										Bt
BC										Bm
BR										Bb
	Ll	Lc	Lr	Cl	Cc	Cr	Rl	Rc	Rr

I don't know why the left hand border line doesn't show nice and thick -- it's fine in the word document.  But computers are annoying and strange.


























The reason I had to come up with it was so I could show why blockades are a kind of data when it comes to our assessment of which factors make for fast answers.

	1	2	3	4	5	6	7	8	9
TL								X		Tt
TC		1						X		Tm
TR								X		Tb
ML										Mt
MC		1					X	X	X	Mm
MR										Mb
BL							X	X	X	Bt
BC		1								Bm
BR										Bb
	Ll	Lc	Lr	Cl	Cc	Cr	Rl	Rc	Rr

Imagine a situation where you have a single known in the zone and a blockade in one of the squares.   We'll use a 1 for our symbol and X's for the blockade, standing for knowns of different arrays.

There are three possible configurations.

In the Top Zone, we have the blockade perpendicular to the effects of the known 1.

It doesn't matter which column the blockade is in, or which space the known 1 is in in the other square.  If that's all the data we have, we haven't learned anything.

In the Middle Zone we'll put the blockade parallel to the known 1, and in the same row.  Again, we've learned nothing.

But in the Bottom Zone, we'll put the blockade parallel to the known 1 and in a different row.  Now, we do know something!  In this particular example we now know that the 1 in BR will have to be in the bottom segment of that square (BRb).  We also know that in BC, the 1 will have to be in the top segment (BCt).  We don't have a pair in either place yet, but we don't need much more data to get one.  Either an additional known from a different array in the segment, or an additional known 1 in the intersecting zone will do.


And of course, the same principle works with columns, just tipped on one side.