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How Sudoku Works


Solving a Sudoku: Simple Logic
Michael Mepham's "Book of Sudoku 3" rates this puzzle as "gentle."
Michael Mepham's "Book of Sudoku 3" rates this puzzle as "gentle."

There is no right place to start a sudoku puzzle. You can shut your eyes and put your finger on the puzzle and start there, and that's as correct a place as any. Probably the most logical place to start, though, is at a row, column or box that has a lot of numbers in it. Let's take a look at the puzzle from the previous page:

Columns 4 and 6 each have six numbers filled in. Let's start the puzzle at column 4, which already has its 1, 3, 4, 5, 8 and 9.

In order to have one and only one of each digit from 1 to 9, we're going to have to provide column 4 with its 2, its 6 and its 7. But we can't just put them anywhere -- each number has a specific location in the puzzle's answer. So where does each number go? To find out, we need to look at the rows and boxes that interact with column 4. Take a look at the empty square at row 3, column 4 (3,4), and the row and box that interact with it:

To fill the empty square at row 3, column 4, we're going to have to look at column 4, row 3 and box 2.
To fill the empty square at row 3, column 4, we're going to have to look at column 4, row 3 and box 2.

The "simple logic" approach to sudoku requires only visual analysis and goes something like this: Can the 2 go in the empty square? It can't, because box 2 already has a 2, and it can only have one of each number. Can the 7 go there? Row 3 already has its 7, so we can't put a 7 there, either. That leaves us with the 6. Neither row 3 nor box 2 already has a 6, so we know the 6 is correct for that cell. We've solved our first number!

Now let's solve the rest of column 4, which still needs its 2 and its 7. The empty square at 5,4 interacts with row 5 and box 5, and the empty square at 7,4 interacts with row 7 and box 8.

Since box 5 already has its 7, we can't put a 7 in the 5,4 square. So right there we know the 2 goes at 5,4, and the 7 must go at 7,4:

We've now solved all of column 4, and we used only simple logic to do it. Since this is an easy puzzle, we could probably solve a good portion of it this way. But it's not always so clear-cut. There are strategies we can use when the solution is not so obvious, and it all starts with some little pencil marks.