Techniques for solving Sudokus

The best tips and tricks for solving sudokus

Here you will find several techniques that we have been compiling that we hope will help you solve sudokus better and faster.

Techniques 1: First Tips

Let's start by reviewing the basic rules of the game:

In this first lesson we will expose some useful tips when solving sudokus.

1. Use a pencil. It is much more comfortable to make a sudoku in pencil than on a computer screen. In addition, the pencil allows you to erase it in a simple way.
2. Practice gradually. Usually many newspapers and magazines do not catalogue sudokus because of difficulties so, for a neophyte, it can be really complicated to finish a complex sudoku. At PrintSudoku.com we catalogue sudokus so that you can practice with sudokus according to your level. The higher the level the more difficult it will be (usually) to put the numbers and, in the case of the very difficult ones, sometimes you will have to try plays.
3. To test plays there is nothing better than typing the candidate numbers in the upper left corner of the cell. If you write small or in a margin, as you discard numbers, strike them out.
4. Take it easy, sudoku is a relaxed game. Some sudokus can be resolved in a matter of minutes but others may take hours or maybe days.
5. Well-designed sudokus have a unique solution, use this feature to your advantage.
6. Never feel until you have finished carefully examining all the possible moves.
7. Follow an order in the placement of the numbers, a good tactic is to start with the numbers that appear more frequently ending in the less frequent; in case of ties decide the order and follow the whole game.
8. Check that every step you take is valid, a failure at first can be disastrous.
9. If you don't find a possible solution, ask for help, or try sudoku at another time. Many times the solution appears when you least expect it, and not always when you are in front of the sudoku. .

Techniques 2: Basic Method

The easiest way to discover a number is when there is only one number left in a row, column or quadrant. In this case the missing number goes into the only empty box.

As you can see, the first row is located all the numbers but the 7, so in the empty cell you can only go this number. In the first column something similar happens with 5, just like in the sixth quadrant with 1.

Techniques 3: Crossing by row and column

Another way to discover numbers is to cross by row and column. This consists of focusing attention on a square and checking which numbers can go in that position, eliminating those that are in the same row or column.

In the following image we can verify that in the indicated box only the 7 can go, because the numbers 1,8, 3, 6 and 9 are in the same column and the numbers 2, 4 and 5 in the same row.

An improvement of this technique is achieved by also controlling the numbers that are in the same quadrant. In the following example we can see that using the cross between rows and columns we would have the candidates numbers 5, 7 and 8 to place them in the marked box. Since the numbers 5 and 8 are already placed in their positions within the quadrant, we can discard them, so the number 7 is the one that occupies the indicated position.

Swordfish

The Swordfish technique is used in Sudoku when a specific number appears as possible in exactly three rows and three columns. For example, if the number 5 can only appear in columns 2, 5 and 8 of three different rows, a Swordfish pattern is formed. Here, if the 5 cannot be in any other cell in those rows outside of columns 2, 5 and 8, then the 5s can be eliminated as possibilities in those columns from other rows.

This method is especially useful for unlocking stuck situations in an advanced game. In a practical case, if you notice that in rows 1, 4 and 7, the number 5 can only go in the same three columns, you have identified a Fish Sword. You can now safely remove the number 5 from columns 2, 5 and 8 in all other rows, which often clears multiple cells and makes it easier to solve the rest of the Sudoku.

XYZ-Wing

XYZ-Wing focuses on finding three cells that form a connection, where two have two possible numbers and the third (pivot) shares a number with each of the other two. For example, suppose three cells where one has options 1 and 2, another 1 and 3, and the pivot 1, 2, 3. This configuration allows the number 1 to be removed from other cells that are seen by all three, since the 1 must occupy one of them, thus clarifying the options in those areas.

In practice, if you encounter this configuration in a Sudoku game, it opens up an opportunity to significantly reduce the possibilities. Notice how the cells interact and how the presence of the shared number in the pivot cell constrains the location of that number in related cells. By applying the XYZ-Wing technique, you can strategically eliminate choices, making it easier to solve the more complex parts of the puzzle.

Double link (Dual linking)

The Dual Linking technique is applied when two numbers can only go in two cells of a row, column or block, and these cells do not contain other numbers. Solving for one of the numbers automatically solves for the position of the other. This technique is effective in eliminating choices in areas where numbers are strongly interconnected, helping to simplify the board and move towards solving Sudoku.

Imagine a sudoku where in a specific row, only cells A2 and A8 can contain the numbers 3 and 7. We do not yet know which of these cells contains 3 or 7, but we do know that no other cell in that row can contain these numbers. If elsewhere on the board we solve that A2 must contain 3, we automatically know that A8 must contain 7. This direct link between the two cells allows us to move forward in solving the Sudoku, eliminating those choices in the rest of the row.

Chain box (Box line reduction)

The Box Line Reduction technique is an advanced strategy in Sudoku that is employed when the possible locations of a number in a row or column are entirely within a single region or box. By identifying this configuration, you can eliminate that number from the possible locations in other cells of the same box that are not in the specific row or column. This is because, since the number must appear in the row or column in that box, it cannot be in another position within the same box.

For example, if in a top box of a Sudoku, the numbers 4 can only appear in cells that are also part of row 2, then you can eliminate 4 as a possibility in the other cells of that box that are not part of row 2. This action helps narrow down the choices and can be key to advancing the game, especially in situations where the board is very congested and solutions are not immediately obvious. Using this technique improves efficiency when solving Sudoku by clarifying the possibilities and making it easier to identify numbers that can be placed elsewhere on the board.