Abbreviated Arrays

Now while I usually just track whether or not I've looked at a symbol with dot or a square or an x, I sometimes find it useful to use a shorthand version of the array.  Think of a tic-tac-toe frame.

_|_|_
_|_|_
  |  |     (It doesn't look quite right, but you get the idea.)

A quick crosshatch like that can be used to represent the squares in a sudoku puzzle.  I put them over the columns to indicate the arrays 1 to 9, and then fill in the spaces in the crosshatch depending on whether or not that square has a known for the array or a pair.  I usually use dots for knowns and circles for pairs, but sometimes I use x's for knowns.  This time I'm going to use Ks, because I want to save the X for a different purpose.  So for an array with five givens I might start with something like this.

K|K|  
  |K|K
  |   |K    

That's a given in TL, TC, MC, MR, and BR.

Now, with no other information whatsoever from the puzzle, we can see that we will be able to make a deduction in TR, and find pairs in ML and BC.

Can you see why?