Step-by-Step Solutions
When solving sudoku, there's no right or wrong place to begin, nor is there a preferred way to arrive at the solution. There is, however, only one final solution to the puzzle.

For an in-depth video tutorial teaching you the most advanced Sudoku Secrets Take a look at the Sudoku Video

What are your strategies for solving sudoku?



This is an unsolved sudoku, with the black numbers already provided. Using it, let's discuss some key strategies for solving the puzzle (courtesy of Wayne Gould's Web site, Sudoku.com).

Scanning

Concentrating on the center section, notice that the right and left boxes have 6s, while the center box needs a 6. We can figure out where the missing 6 goes by scanning the middle section's rows. The top row has a 6. The center row has a 6. The bottom row does not. Therefore, the center box's missing 6 goes between its 9 and 1.

















Similarly, by scanning the columns in the middle section for 6s, including the one we just added, we can figure out where the top box's 6 goes: below the 3.

Hatching

When single-scanning doesn't provide enough information, try double-scanning or hatching. In the sample, look at the bottom-left box. It needs a 6. Scan the section's rows for 6s. Then scan the columns. By combining the two, we know that the missing 6 goes to the left of the 4.












Hatching can also reveal the location of the missing 6 in the bottom-right box: to the left of the 2.

Counting Rows and Columns

Remember: Each row and column needs one of each number 1 to 9. In the center vertical section, look at the left column. By counting, we deduce it's missing two numbers: 7 and 8. The center box already has a 7, so therefore the column's missing 7 must go in the bottom box, in the square above the 2.

With the 7 placed, the row is missing only one number: 8. There's nowhere else for it to go but in the center box, below the 4.

Counting Boxes

As the grid fills up, it becomes possible to deduce a box's missing numbers, often by combining process of elimination and scanning. In this example, the center box is missing two numbers: 3 and 5. Scanning the middle row, we see a 3 in the right-hand box. Therefore, the middle box's 3 can't go in the middle square. The only other option is the middle square between the 4 and 7. With the 3 assigned, one blank square remains, and only 5 can go there.

Helper Numbers

Scanning and counting are often enough to complete most of a puzzle. When only a handful of stubborn squares remain blank, it helps to write down within a square its possible numbers. (Some puzzlers use this method from the get-go, but the squares do get crowded with notations.) By writing down these helper numbers, you can help your brain see the patterns of logic emerge.

This example shows helper numbers for the top-left box. To arrive at a square's numbers, scan its row, box, and column for each number from 1 to 9, and write down only those numbers that are possible answers. Take the top-left square, for example: It can't be 1 (its row has one); can't be 2 (column has one); could be 3 (write this down); can't be 4 (row has one); can't be 5 (column has one); can't be 6 (row has one); can't be 7 (column has one); can't be 8 (box has one); could be 9 (write this down).

With the upper-right box's helper numbers added, we can see there is the only possible number for the middle-left square: 1 is the answer. And now that 1 is known, we can see that the middle square has only one possible number: 7.

A full markup like this is often unnecessary. Start by limiting your markups to exclusionary pairs: those numbers that have only two possibilities in a larger square. In the current example, the solver would have only marked the 1, 5, 7 & 9. By doing this, you will quickly identify if two squares have an exclusive relationship (can only be one of 2 numbers) and begin limiting other number choices.

A simpler and quicker technique is to use a simple dot to represent the numbers. A dot in the top left is a 1, top middle is a 2 and so on, like a phone keypad. Your grid will remain much less cluttered this way.

Sample Solution

This is the finished grid for this example puzzle.



















See also:

• Advanced Solving Strategies
  
• Sources for Puzzles

• Sudoku 101
• Stumped and Stumpers
  
• The History of Sudoku