Solve Sudoku Puzzles with Sure-fire System

I'm a hopeless Sudoku-puzzle addict. As such, I have formulated a sure-fire system to successfully solve a standard Sudoku puzzle every single time, regardless of its degree of difficulty. We will begin with basics and then examine subsets. Subsets comprise the key to Sudoku success!

The standard Sudoku puzzle has eighty-one squares divided into nine boxes of nine squares. It begins with a few given numbers scattered throughout the squares. Our job is to fill in the rest of the numbers so that every box, column, and row each contains numbers 1 through 9.

The basic start to a Sudoku puzzle is to solve the squares that have an instant solution. This means looking for duplicate numbers. We begin with the top row of boxes and progress down to the third. Then we examine the columns.

Check out Fig. 1. In the second row of boxes, two of them each hold a 2. The third box does not. Because the third box is in the third column and the column's top and bottom boxes each hold a 2, there is only one square in which we can put the missing 2. And that is in the last column, fifth square down. As we follow this process in an orderly manner, we end up working on the whole puzzle simultaneously.

After filling in the quick-to-solve numbers, we try to solve columns, rows, and boxes with the fewest blank squares. However, when a column, for example, has many blank squares but it intersects with a row that has several numbers that it needs, we can solve all--or nearly all--of that column's squares. But it's usually best to start with the boxes, column, and rows that have the most given numbers and thus the fewest blank squares. In Fig. 1, for example, the center box (and, incidentally, center row) needs just three numbers (3,4,5). No other numbers can possibly solve those three squares. Thus, in this case, the numbers 3,4,5 comprise a subset. However, we will return to subsets later.