Block / Block Interactions

Advanced methods and approaches for solving Sudoku puzzles

Block / Block Interactions

Postby keith » Wed Apr 12, 2006 10:35 pm

I was looking at the SadMan site and noticed this item, which I had missed before:
Block / Block Interactions
Firstly, If a number appears as candidates for only two cells in two different blocks, but both cells are in the same column or row, it is possible to remove that number as a candidate for other cells in that column or row.

I can understand the examples, but I don't understand how to find the pattern.

Do others have a different name? Where can I find a fuller explanation?

Thank you,

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Postby Ruud » Wed Apr 12, 2006 11:10 pm

Hi Keith,

The block-block technique is usually combined with the rowcol-block technique. (block = box)

Other terms used are locked candidates, pointing pairs, line-box interactions (my favorite)

With line-box interactions, you look for a row or column with all candidates in a single box. You can then remove the remaining candidates in that box. You can also look for a box with all candidates in a single row or column (a pointing pair). Then you can eliminate the remaining candidates on that row or column.

block-block is basically the same technique, but it looks at 2 boxes in a chute (3x9 region) with candidates for only 2 rows or columns in that chute. When you find it, eliminate the remaining candidates in those 2 rows/columns (in the 3rd box)

Now think of this: When you find 2 boxes with candidates in only 2 rows/columns, the 3rd row/column must have all candidates in the 3rd box: a line-box interaction. These techniques, like many other patterns, are complementary.

I hope this explanation did help.

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Postby Carcul » Thu Apr 13, 2006 11:14 am

Hi Keith.

In my "personal terminology" I call that technique "X-Wing between boxes", or "Generalized X-Wing". Please consult this link (and check the section entitled "Generalized X-Wing") for what I consider a good explanation. Also check this link (which is written in French) and look particularly at the sections entitled "X-Wing" and "Swordfish".

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Postby keith » Thu Apr 13, 2006 3:29 pm

Ruud and Carcul,

Thank you. That helps a lot.

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