Solve Sudoku Without Guessing
In this article you will learn how to apply a simple Sudoku strategy that will help you solve Sudoku puzzles. Additional advanced strategies are described in articles at the bottom of this page as they are written.
Sudoku Strategy – One And Only Choice
In my article “How To Play Sudoku”, I touched upon the Sudoku strategy to look for a cell in every row, column, and region that can be solved by looking for the only possible choice.
In the example above, the cell circled in red can be solved quickly by looking for the missing number. Count from one to nine. You will notice the “8” is missing. That is the answer, so fill the cell in with an “8”.
Above we have another example where all the cells are filled in a region, except for the cell circled in red. Again, count from one to nine. What number is missing? The “7” is. Any child can solve for the missing cell when they know the Sudoku rules.
At the left we have a third example of a cell that can be solved using the one and only choice Sudoku strategy. This example is different. Can you find the only choice that will satisfy the cell circled in red?
At first glance you might think that there aren’t enough cells filled in to solve it. After all, every row, column, and region has several empty cells.
To solve the cell circled in red, say to yourself, “What number can or can not go here?”. Let’s try it.
Well a “1” can not go there because cell R5C1 of the same row has a “1” in it.
Well a “2” can not go there because cell R1C5 of the same column has a “2” in it.
Well a “3” can not go there because cell R5C9 of the same row has a “3” in it.
Well a “4” can not go there because cell R5C4 of the same region has a “4” in it.
Well a “5” can not go there because cell R2C5 of the same column has a “5” in it.
Well a “6” might go there since there isn’t any “6” in the same row, column, or region. Pencil it in. Continue checking.
Well a “7” can not go there because cell R9C5 of the same column has a “7” in it.
Well an “8” can not go there because cell R5C7 of the same row has an “8” in it.
Well a “9” can not go there because cell R4C6 of the same region has a “9” in it.
Well, sure enough! The cell circled in red (R5C5) has to be a “6” since there isn’t any other choice. You solved it!
You will be able to use this simple Sudoku strategy in every Sudoku puzzle, if not at first, then eventually. Some easy Sudoku puzzles may be solved using only this one technique. Usually however, you will need to add a few more strategies.
Sudoku Strategy – Scanning
I touched upon the Sudoku strategy called scanning in my article “How To Play Sudoku”. You will use this technique to help you solve every Sudoku puzzle from easy to fiendish.
In the example at the right, we have two 8s. If you scan each column that has an 8 as depicted by the two red arrows, you will find three cells where it is possible that an 8 could be placed. They are circled in red.
We know that an 8 can not go into either the top three cells of the middle column, or the bottom three cells because there is an 8 in both the top and bottom region.
Still we do not have enough information to place an eight in any of the three circled cells.
Now if we already have two of the three cells solved as shown in the graphic at the left, it is easy to solve for the center cell circled in red.
There is only one possible solution. The circled cell must be an 8. Write it in.
When you scan, it is helpful to be systematic in your approach to the puzzle. Scan for all numbers in sequence from 1 to 9 in all directions.
You now have two Sudoku strategies that you can use to solve Sudoku puzzles and games. However, not every puzzle can be solved using the one and only choice and the scanning method. You will eventually find a puzzle where you can not solve any more cells using these two methods. We need another Sudoku puzzle strategy.
The third Sudoku strategy you need is learning the art of candidate elimination.
Sudoku Strategy – Candidate Elimination
In order to effectively use the candidate elimination strategies, you will need to find all of the possible candidates for each blank cell in your Sudoku puzzle.
If you have a computer program like Sudoku Dragon, then you can select an option for the program to show all possible candidates. Simple. This saves a lot of time.
If you are using paper and pencil, I suggest using my free blank grid with candidates form. Use liquid paper for best results to remove candidates from consideration.
In my popular article titled “Can You Use Some Sudoku Tips”, I address some common techniques to safely eliminate candidates in cells from further consideration. These include naked and hidden singles, naked and hidden pairs, naked and hidden triples, and naked and hidden quads.
As you may have found, these are not enough to solve every Sudoku Puzzle. So, I want to introduce another Sudoku trick, locked candidates.
Sometimes you will find that a candidate within a 3×3 region is restricted to one row or column. When this occurs you can safely remove that candidate from the remaining cell(s) in that row or column that is outside of the region.
In the example above, we have the situation in the right region as highlighted in red, where we have a row of three cells. The numbers 3, 7, and 9 are restricted to the three cells in this region.
If you will notice, the number 7 also appears in the three cells circled in red.
Since, a 7 must be located in one of the three cells of the right region, it is safe to remove the 7 from each of the cells circled in red.
This example comes from my Hard 2 puzzle.
Another version of locked candidates occurs when you find a candidate within a 3×3 region that is restricted to one row or column. When this occurs you can safely remove that candidate from the remaining cell(s) in that row or column that is inside the region.
In the example at the right, we find that the right most column needs a 3. The only 3s are restricted to the top two vacant cells in the column.
Since we know that one of these two cells must contain a 3, then it is safe to remove any other 3s in that region. In this case, the 3 that is in the cell circled in red may be eliminated safely.
This example comes from hard 7 puzzle.
For more strategies to eliminate possible candidates, please see my advanced Sudoku strategy articles that will appear below.