Solving Sudoku?

Question

Hi, I recently read up on this article of how to solve Sudoku here: http://www.ddj.com/windows/184406436

But I dont understand the 'Pile exclusion' and 'Chain exclusion' methods used?

Can someone explain it to me in relation to the 'figure one' ?

http://www.ddj.com/showArticle.jhtml?documentID=ddj0602i&pgno=2

thankyou!

Answer 1

Pile exclusion:

If two numbers are permissible in ONLY two cells of a row or column or square, then all other numbers that are permissible in those cells may be excluded, since one cell MUST be one of the numbers and the other MUST be the other number. (You need another test to find out which.)

The same argument can be extended to 3 or 4 numbers.

Chain exclusion is a little more complicated, but works the same way. Consider the numbers 1,2,3.

There are only 3 possible pairs of these numbers:  {1,2}, {1,3}, and {2,3}.  In any 3 cells showing this pairwise combination you can exclude any other permissible number.

Note that neither method is applicable if one of the digits appears in another cell.

I was looking for examples of this in your "figure 1", but found I had made an error, and there's not enough time left on your question.  The wording also takes a lot of space.