"When you have eliminated the impossible, whatever remains, however improbable, must be the truth."
Sir Arthur Conan Doyle, creator of Sherlock Holmes.

Sherlock Holmes would love Sudoku puzzles. They're puzzles that rely on deductive reasoning - of eliminating the impossible to determine the truth - in this case the successful placement of numbers within a Sudoku grid.

Sudoku is based on determining what can't be in order to find the solution. It is a puzzle of elimination - eliminating possibilities until only one solution remains.

This is a Desktop Sudoku puzzle before any solving has taken place:

The puzzle consists of a 9 x 9 grid comprised of 81 cells. There are 9 rows and 9 columns. And, you'll notice that there are 9 3 x 3 boxes defined by the darkened lines.

The object? Simple. Fill in all 81 cells with numbers 1 through 9 without any repeaters in a row, a column or a box.

Each puzzle begins with some numbers already in place. These are used to help eliminate possible numbers, called candidates, that could be entered into a given cell.

Notice the 2 in the upper left-hand corner is highlighted. That means that no other 2 can appear in that column, row or that upper-left box. So you can cross 2 off as a candidate for any open cells in that column, row or in that particular box. Within that box, you can also eliminate 8, 4 or 6 as well as from the rows and columns in which they appear.

As you gradually eliminate candidates (because they already appear in a row, column or box) you eventually narrow down the correct number for each of the 81 cells.

That's it. That's how simple Sudoku puzzles are. Always remember: follow the Sudoku axioms and you'll always be working toward a solution.

Some Sudoku experts suggest that you can start solving anywhere on the grid. However, it makes more sense to start in a row, column or box that has lots of given numbers. This shortens the candidate list from the start.

It's nearly impossible to keep all viable candidates for a cell in your mind. Too many candidates, too many variables. Using a pencil, and very small numbers, enter possible candidates for each cell.

With Desktop Sudoku, you just switch to pencil mode to enter candidates for each open cell. It's so much neater and cleaner than to pencil in candidates on paper only to erase them.

The pencil option is ideal for entering candidates for open cells. Then, once you've deduced the correct number for the cell, switch to pen mode to make your selection "permanent."

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The Seduction of Sudoku Deduction

Look at top row in the example above. It already has 7 given numbers: 2, 3, 4 ,5, 6, 7, and 8. The only numbers missing from that row are 1 and 9. Take a moment to look at that top row. Using Desktop Sudoku's pencil option, you can easily enter candidates.

In the box between the 2 and 6, there are two candidate - 1 and 9, the only numbers missing from that row. So we enter 1 and 9 lightly in pencil or use the pencil feature on Desktop Sudoku.

Move to the other empty cell between the 8 and the 5. The only number that works in that cell is 1 because 9 already appears in that column. So we know that cell is number 1 and, by the process of elimination, we know that the remaining cell must be a 9. Good, you solved your first row of a Sudoku puzzle.

This illustration shows the top row completed with our additions of the missing numbers 1 and 9 using the pen mode.

We then try to build on that success, and if that's not possible, move to another section of the puzzle that contains many numbers entered into cells. In this example, the box in the upper right is only missing two candidates.

Singles are candidates about which you can be certain. They're usually the last cell filled in a row, column or box. However, you will also discover hidden singles. How?

If you penciled in all candidates for empty cells within a block and only one cell has the candidate 3, then you know, for certain, that cell contains the 3.

You can be certain that singles and hidden singles are the correct number for those cells.

Another important solving tip: once you've placed a number in a cell, remove it as a candidate from its row, its column and its box. In this way, you gradually eliminate candidates, working your way down to a single - a sure thing in a cell.

There are other formulas for solving Sudoku puzzles - strategies with names like X-wing and swordfish, but these are a bit more advanced for those just starting out, so stick with the process of elimination - your deductive reasoning skills - at the outset. Then, as you're ready to take on more difficult challenges, the world wide web is loaded with blogs, forums and tip guides that'll keep those challenges coming as your problem-solving skills improve with each Sudoku puzzle you complete.