Saturday, September 29, 2007

Sudoku Lesson VI - Solving Squares

O.k., is the suspense concerning coupling pairs from Lesson IV killing you yet? Here's why coupling pairs are so important. Let's add a new tool to your box -- solving a square. In this operation, we cycle through the numbers inside of a square, i.e., without projection. As we check possibilities, we can skip over boxes having the coupling pairs, and we can eliminate the coupled pair numbers from our test to see what numbers are left that fit.

Take, for example, the puzzle below. I've cycled through twice, and marked all the boxes:

Note in the middle top square that we have the numbers 2 and 9 marked for boxes (5,1) and (5,2). Despite the marking of a 5 in box (5,2), the 2 and the 9 are a coupling pair. That means that the 5 cannot go in (5,2), and therefore must go in (5,3):

In the top middle square, we can put a 4 only in (6,3), and thus 8 goes in (4,3), because 2 and 9 are already slated to go in the other two boxes (5,1) and (5,2) in the top middle square:

Thus, using the coupling pair, we've largely completed the top middle square!