How to Eliminate Numbers in Sudoku: Key Strategies for Solving

To successfully solve a sudoku puzzle you need to be able to get the right numbers into the right cells. A crucial part of this process is eliminating or ruling out the numbers that it is unlikely to be. Find out more about how to effectively eliminate numbers in our guide below.

1. Identifying Candidates for Each Cell By Using the Process of Elimination

The trick to identifying possible candidates for each cell is to eliminate the numbers that cannot be placed there. One of the simplest ways to do this is to examine each row, column and block (3x3 squares) to see what digits are already present.

The reason for this is because of the rules of sudoku, if numbers are already present they cannot then be repeated in the same row, column or square which means you can eliminate them from your potential. Making it easier to deduce which numbers should be placed in each cell.

3. Applying Basic Sudoku Techniques

One of the most basic sudoku techniques that involved elimination is to look for single candidates. Single candidates otherwise known as naked singles happen when there is only one possible figure that can be entered into a cell.

For a naked single to occur every other possible digit between 1 and 9 must get ruled out because they are located elsewhere in the grid, be it in the same row, column or square.

4. Leveraging Pencil Marks

Using pencil marks can be incredibly helpful when playing sudoku because they allow you to keep track of the potential answers, thereby making the process of elimination easier and more efficient. This is especially crucial when playing more advanced games as it means you won't have to hold multiple figure possibilities in your mind for every open cell.

Most people think you can only use pencil marks when playing sudoku in real life on paper. But this isn't the case because many online sudoku games also can use pencil marks so you can keep track of the possible answer options.

What is pencil marking?

When using pencil marking in sudoku the idea is to write the potential figures that a cell could hold in a small size in the top left-hand corner. By doing this you will not get them confused with the answer when you write it in which should be larger and in the middle of the square.

In sudoku, the convention is to write any figure that could be placed in the square in pencil in the top left-hand corner. If you know that a figure cannot be placed in this square because it is featured elsewhere in the row, column or grid, you can leave it off.

5. Using Advanced Solving Strategies

While there are simple elimination methods that can be used in sudoku, as the games start to get more challenging it also makes sense to use some more advanced strategies of elimination as well. You can read about some of the most used advanced sudoku elimination strategies below.

X-Wing

Named for the shape it makes on the grid, just like a Star Wars X-wing this strategy ignores squares and is all about rows and columns. The trick is to look for four instances of the same number in the grid, and then draw a box around them with the numbers in the corner.

You're looking for four of the same (possible) number. If you drew a box around them (keeping the numbers in the corner), it would contain only vertical and horizontal lines with two of the potential numbers in the top corners and two in the bottom corners. What he means is that you can be sure that at least two of these potential figure placements are correct and therefore you can eliminate that figure from anywhere else in the rows and columns intersecting with those numbers. In this way, you eliminate many possibilities and make solving the puzzle easier.

Swordfish

Just like the X-wing the swordfish sudoku strategy is named that way because when executed it can end up looking like a swordfish. The swordfish can be a trickier technique of elimination though because it involves three pairs of figures that appear three times in the grid with the number also being present in the same three columns.

To find a swordfish you need to look for a (potential) number that occurs twice in one row, three separate times in a grid, that also appears in the same three columns. Once you have this you can draw a line through each row and column on which that potential number sits. You can remove any of the same potential numbers from those lines or columns where a single line runs through, but not both lines.

6. Recognizing Hidden and Naked Pairs

How to Find Naked Pairs

A naked pair is an elimination technique when you can find two cells that have the same two possible figures. They are known as naked because there are only two possible figures in each. If there were more they could be a hidden pair which we'll look at below.

Naked pairs can be found in rows, squares or columns in sudoku. They can also be very helpful in the process of elimination. This is because finding a naked pair means that one of the two numbers must go in one of those two squares. In turn, this allows you to eliminate any of the same potential numbers from the row, column or square in question. Hopefully, this will leave some cells with only single possibilities which means you have your number and you can fill them in!

How To Find Hidden Pairs

Hidden pairs is another elimination technique that can be incredibly useful when solving a sudoku puzzle. Hidden pairs are a bit harder to spot than naked pairs because they consist of having the same two potential numbers in a row, column or square. However, they are not naked (or on their own) but hidden among other potential numbers as well.

The Logic of Hidden Pairs

Hidden pairs allow you to eliminate potential figures from the grid, making it easier to solve. How a hidden pair does this is that once you have found one you can eliminate any other potential candidate from that cell. This can then trigger further moves when you can use other techniques such as hidden singles to continue filling in the grid.

7. Cross-Referencing Rows, Columns, and Boxes

If you want to be able to solve your sudoku effectively then cross-referencing is an essential skill. Cross-referencing means that you need to be able to analyze the relationship between different areas of the board.

For example, you could cross reference the relationship between a row and a column, a column and a particular cell, or a row and a square. It is this cross-referencing technique that allows you to find cells which can only possibly contain one figure or naked single as they are also known. Once you have found these cells you can use that information to eliminate any potential figures of the same number from the area in which they are working.

8. Tips for Efficient Number Elimination

Tip 1: Don't stay in the same place when scanning for too long

Scanning is a vital skill when it comes to number elimination because it will help you to recognise possibilities and easily remove numbers. However, you can scan an area of the grid for too long, delaying your progress.

Indeed, if you are spending too long on one particular area of the grid, it's likely that figures need to be placed elsewhere before you will be able to solve it. That is why you must learn to keep moving your focus around the grid, locating easier areas of elimination first and going back to the harder ones later.

Tip 2: Get good at scanning sections of the grid

Trying to focus on eliminating numbers from the entire grid at once can be confusing and overwhelming. Instead, it's much more effective to focus on specific sections like a single square, column or row at one time.

More advanced players can also take note of how two areas interact because the areas of the board where this happens will only have a few possibilities to consider, making elimination easier.

Tip 3: Use the facet that sudoku is a cascading game to your advantage.

A cascading game gets easier as you play. For example, when you begin in sudoku you will have the most possible cells to fill with figures, and the most possible figures to eliminate. However, as you go along and fill cells the permutations of figures that could go into the remaining cells becomes less.

To that end it's important to remember that everytime you add a new figure to a cell it could eliminate a possibility or unlock another cell completely, allowing you to further progress.

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