A Sudoku puzzle is a nine-by-nine grid of cells, and this grid is divided into nine smaller three-by-three regions. The rules are simple: each cell gets one numeral—1, 2, 3, 4, 5, 6, 7, 8, or 9—and no numeral may be repeated in any row, column, or three-by-three region. This means that all nine numerals will be represented in every row, in every column, and in every region. So, let's get started!

You may want to print a larger image of the puzzle we'll use in this example, so you can follow along.

Look at the region on the bottom right. Because each region must contain one of each numeral 1-9, we know that the bottom right region must have a 5 in one of its five empty cells. There cannot be a 5 in the two bottom cells, because there is already a 5 in that row. And there cannot be a 5 in either of the two upper cells, as there is already a 5 in their row.

This leaves us with only one option for placing a 5 in the bottom right region: the middle cell, between the 7 and the 3. Let's write in a 5 there.

Looking in the same bottom right region, let's consider how we might place a 2. Now that there are only four blank cells, we see that three of them cannot hold a 2, because of the 2 that's already in the far right column combined with the 2 in the third row from the bottom.

Notice that we could not have reached this conclusion without having first put the 5 in the cell above it.

Let's turn our attention to the center region. Because two of the rows that go through the region already have 7's, and two of the columns that go through it also have 7's, there is only one possible place for us to write a 7.

By now you have the idea of the most common technique for making progress on a Sudoku puzzle: look in a region, and try to exclude all the empty cells but one for a particular numeral. Those excluded cells are in rows or columns that already contain that numeral.

Let's move on to some other techniques.

Rather than looking at a region, let's look at a column—the one second from the right. After having written a 5 and a 2 in the bottom of this column, there are only three blank cells left. Because the row already contains 1, 2, 3, 5, 7, and 8, the three numerals left are 4, 6, are 9. We can't yet place the 4 or the 6, so let's consider the 9.

We can't put a 9 in either of the cells in the top right region, because that region already contains a 9. This leaves us with only one option, so let's put a 9 there.

Now there are only two options left for the second column from the right: 4 and 6. Luckily, there are clues on the board that help us conclude how to complete this column.

Let's look at the cell on the very top, second from the left. We know that this cell must have a value that is either 1, 2, 3, 4, 5, 6, 7, 8 or 9. However, it can't be a 1, 2, or 3—those values are already taken in that cell's row. It can't be a 5, 7, or 9—those are already in the cell's column. It can't be a a 6 or 8—each is already in the cell's region. This leaves only one value possible, 4, so let's fill it in.

Well, by now you get the basic idea.

If you'd like to continue solving this puzzle, you can print out a larger image of the puzzle we've been working on. If you get stuck, you can check out the progressive solution keys for hints on how to proceed.

You can also continue to discoverSudoku.com's explanation of advanced techniques (coming soon).