How to Solve Sudoku Puzzles

This section explains some of the basic strategies that are used to solve sudoku puzzles. If you want to discover these strategies on your own, feel free to jump right to the puzzles. You can always return here if you need more guidance, or want to compare these strategies to the ones you discover.

Slice and Dice

This is a good strategy to use at the very start of solving a puzzle. Once you get the hang of this technique, it will make filling in numbers seem like grabbing low hanging fruit.

Figure 1-1: Slicing

To begin, notice that in Figure 1-1 rows 2 and 3 already have 9s in them. This means that no more 9s can be placed anywhere in rows 2 and 3. Now notice that the upper-left 3×3 box does not have a 9 in it yet. Of course, there must be a 9 somewhere in this box. And the 9 must go in row 1 because rows 2 and 3 have been ruled out. The only possibility is the blank square at row 1, column 3 where we correctly enter a 9 Congratulations, you have just sliced a row and found your first number!

Figure 1-2: Slicing and Dicing

In the next example in Figure 1-2, notice that columns 1 and 3 already have 4s in them. Now notice that the upper-left 3×3 box does not have a 4 in it yet. Using similar logic as in the previous example, we know that a 4 must go in this box in column 2. Uh-oh! There are two possible places in column 2: row 1 or row 3. This is where dicing comes into play. We see that row 1 already has a 4 in it, which leaves row 3 as the only possibility. A 4 is correctly placed in row 3, column 2 of the grid. You just sliced and diced a column! This basic strategy can be applied to all columns and rows within 3×3 boxes. With a little practice, you will easily notice where a puzzle can be sliced and diced.

Scanning Squares

Figure 1-3: Scanning Squares

Frequently there will be just one possible number for a square. For example in Figure 1-3, look at the square at row 1, column 1. If we run through all of the numbers 1 to 9 we can see that only a 6 is possible, so a 6 should be placed in row 1, column 1. All numbers except 6 are ruled out because they are already found in the same row, or column, or 3×3 box. When scanning, look for blank squares that have a lot of numbers in their row, column, and 3×3 box. Or sometimes it is necessary to methodically scan all blank squares just to find one elusive entry.

Scanning Rows, Columns, and 3×3 Boxes

Let's start with rows. Of course, every row must have all of the numbers 1 through 9. So pick a row and ask: where in this row can a 1 go? (We are assuming a 1 is not already found in the row.) If there is only one possible square in the row, then we can enter a 1 into that square. If we find two or more squares for a 1, then we can skip it and move on. We continue by looking for a unique square in the row for a 2, for a 3, and so on up to 9. After awhile, you will be able to do this surprisingly fast.

Figures 1-4: Scanning Rows

Try this strategy with the first row in Figure 1-4. You should find that a 7 can be entered into column 2. This strategy can be applied to all rows, columns, and 3×3 boxes. You might start with just the areas of the grid that are nearly filled-in; or it might be necessary to go methodically through all rows, columns, and 3×3 boxes.

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