Wednesday, October 03, 2007

Sudoku Lesson VII - Solving Rows and Columns

Let's continue with the puzzle from Lesson VI. Much like solving squares, solving rows and columns can take advantage of coupling pairs to skip over them and find numbers that remain.

I like to take the following approach when solving rows and columns:

  1. Try to find a solution for the blank boxes first. Often, a result of the cycle is that there are some boxes left blank. Many times, these boxes might only have one number that fits. If so, write it in, then eliminate dots for that number in that box's row and column, and put in dots in other squares that have not yet been marked. If you eliminate a dot, be sure to check the square for a corresponding dot, and write the number in there too, then wash, rinse and repeat before going back to the rest of the row/column that you were checking.

  2. For example, let's attack column 4. Note that 1 can only go in (4,5). We put that in, and then mark the left and right middle squares for 1:

    All that is left is to put a 9 in box (4,7), and column 4 is done, check mark it, then erase the 9 dot in (8,7), put a 9 in (8,8), and put a 9 in lower left square at (1,9), thus solving the 2 in (3,9).

  3. Next, check all of the one-dot boxes. If the dot indicates the only number that fits, write it in and eliminate any other dots for that number in that box's square. Then follow the process for 1. above.

  4. Next, check all of the two-dot boxes. Remember the rule for coupling pairs from Lesson VI.
If you happen to mark all the boxes in a row or a column, put a check mark beside the row or column to indicate that you've completely marked the row/column. This helps prevent wasting time, and will help you later when you bifurcate. For example, I'm going to mark rows 3 and 9: