How to Solve Sudoku

Today, Mytour will walk you through the basic steps of solving sudoku. At first glance, sudoku may seem tricky because it’s filled with numbers, but in fact, this puzzle game doesn’t rely on mathematical foundations. Even if you're not a math expert, you can still solve sudoku. Additionally, the numbers can be replaced by letters or symbols, and the results will be the same; it all revolves around the ability to recognize patterns. Let’s begin by understanding the basic rules of sudoku, then move on to learn both elementary and advanced techniques.

Understand the layout. A typical sudoku puzzle consists of a grid made up of 9 large squares. Each large square contains 9 smaller boxes, some of which will already have numbers filled in from 1 to 9. The fewer pre-filled boxes there are, the harder the sudoku puzzle will be.

• The large squares are often bordered with bold lines, while the smaller boxes have thinner borders. Sometimes, the large squares are colored like a chessboard pattern.

Arrange the rows and columns. A fundamental rule in this game is that every row and column must contain all the numbers from 1 to 9. This means you cannot repeat any number in the same row or column.

Pay attention to the numbers inside the large squares. Similarly, each of the 9 large squares must contain all the numbers from 1 to 9. This means that each number can only appear once in the 9 small cells of each large square.

• For example, if a large square already contains the number '2', you cannot place another '2' in any of the small cells within that square.

Use a pencil instead of a pen. Beginners often make mistakes, and using a pen could quickly make the sudoku grid messy. Instead, use a pencil so you can erase and correct your mistakes. Also, consider writing lightly to make erasing easier.

Look for the single empty cell in a large square. Check each large square to see if there is a single empty cell that hasn't been filled in yet. If there is, this is a great starting point. Simply identify the missing number (from 1 to 9) for that square.

• For instance, if a large square contains the numbers 1-3 and 5-9, the only number missing will definitely be '4'.

Check for rows and columns with fewer empty cells. Look through each row and column to see if any row or column has only one empty cell. If so, determine the missing number from 1 to 9 and fill in the cell in that row or column.

• If a column already contains the numbers 1-7 and 9, you can immediately place the missing number, '8'.

Scan rows or columns to fill in large squares. Consider a row consisting of three large squares and look for a number that repeats in two of the different squares. Follow the rows containing that number. The third large square must have that number but not in the two rows you already checked. This number will go in the remaining row. Sometimes that row already has two numbers filled in, making it easy to place the missing number in the remaining empty cell.

• If the number '8' has been repeated in two squares, continue to check the third square. Follow the rows containing '8' and eliminate them, as the '8' in the third square won’t appear in those rows.

Work backwards. Once you’ve mastered checking rows or columns, try working in the opposite direction. Take the previous example but with a slight change. When you examine the third square, you’ll see that this row only has one number given and two empty cells.

• In this case, examine the columns of the two empty cells. Check if the number you need to place appears in either of those columns. If it does, eliminate the empty cell in that column and place the number in the remaining empty cell.

Work with number groups. When you notice that several instances of a particular number are already present in the grid, follow the suggestion and try to place that number in the appropriate cells. For instance, if there are many '5's in the grid, use the scanning technique to fill in as many '5's as possible.

Look at the large 3-square sets. Another approach is to analyze a row or column containing 3 large squares. Choose a number and see where you can place it across these 3 squares.

• For example, the number "6". Find the rows and columns where the number 6 is already placed, then begin to check within the 3 squares you're considering. Based on the existing numbers in the squares, try to place as many 6s as possible.

Make pencil notes for your assumptions. As the difficulty increases, you'll find that you can't always solve sudoku using the techniques mentioned earlier. In such cases, you'll need to add assumptions for each empty cell. If you identify any number as a possibility, jot it down in the corner of the small square using a pencil. You might end up writing down as many as 3 or 4 possible numbers in each cell while solving the puzzle.

• When solving, if you come across a cell that can only contain one possible number, you can fill it in with ink.

Regularly recheck your progress. When you fill in more numbers, revisit the empty cells you've left behind. The new numbers may give you clues to fill in those blank cells.

• Apply techniques when rechecking the empty cells.

• For each cell you fill in, don't forget to recheck it logically; a small mistake can completely mess up the entire sudoku grid.