To Logically Solve Sudoku
Would you like better ways to solve Sudoku? Try these Sudoku hints. It is best to approach solving a Sudoku puzzle in a systematic way. Applying logical reasoning rather than guessing will assure you a solution with greater satisfaction.
Guessing will most often lead you down the wrong road. You may get half way through a puzzle before you realize that a mistake was made somewhere.
Usually you will end up with two identical numbers in a row, column, or region. This breaks the Sudoku rules rendering an unsolvable puzzle. Let's skip the guessing and learn to solve Sudoku by reason and logic.
Sudoku Hints For Beginners
Look for the obvious.
Is there a row, column, or region that has one cell unsolved? If there is you can quickly find the solution.
Count from 1 to 9 locating each number in that row, column, or region. The missing number is the solution for that empty cell. What is the missing number in the graphic at the left?
Where do you start?
Most people I suspect just pick a spot at random to start. It is better to have a systematic approach to solving Sudoku. I like to start by first looking for a number that has the most "givens". The more the merrier.
Use the scanning method
Since we know that every row, column, and region can only have one instance of each number, you can logically use the scanning method I illustrated in my article "How To Play Sudoku"
to find other cells that contain the same number. I won't repeat that technique here. It is essential to learn this technique because every Sudoku puzzle requires it's use.
After you have solved (if possible) for the number(s) that had the most "givens", cycle through all the numbers 1 through 9, solving for each number as many as you can using the scanning method.
Repeat again and again until you can no longer find a solution for any cell.
Sudoku Hints For Slightly Harder Puzzles
Look for the only possible choice.
In the example at the left, I have identified the only possible positions for the number 7.
The existing sevens prevent the number 7 from being in any other empty cells except for the ones circled in red.
Sometimes you will encounter the situation where there is only one place a number can possibly go. This is a classic example.
At first glance one might think that it isn't possible to place a 7 in the top three regions. After all each region has two places a 7 can go.
Upon closer scrutiny, you will see that cell (R2,C5) is the only place a 7 can go in row 2 even though there are other empty cells in that row.
This is just another way to find a cell's solution using a little logic.
Hints To Solve Solve Sudoku With Two Cells Missing.
Here are two Sudoku hints that will help you solve a row or column where two cells are empty.
Look at the graphic at the left. You will notice that in column 1 we are missing two numbers. They are circled in red.
Counting from 1 to 9 you find that a 2 and a 4 are missing. But where do they go? To solve this column, look at row 8.
You will notice that there is a 4 in (R8,C5). Since there can only be one 4 in row 8, the cell (R8,C1) must be a 2. Therefore the other empty cell (R2,C1) must be a 4.
Now let's look at row 5. Again you have two empty cells circled in red. Counting from 1 to 9 you will find that a 3 and a 4 are missing.
This time you don't have a 3 or a 4 in column 2 or column 7 to help you solve the two empty cells in row 5. So how can you solve it?
It's simple. If you look at the right - center region carefully, you will see that there is a 4 in cell (R6,C7). Since you cannot have two 4s in the same region, cell (R5,C8) must be a 3.
If cell (R5,C8) is a 3, cell (R5,C2) must be a 4. There you have done it! You learned two new Sudoku hints that will help you solve two missing cells in a row or column.
More Sudoku Hints
Sometimes you will be in a situation where this Sudoku hint will work.
If you look at the graphic at the left, let's try to find a 3 in the middle stack of three grids.
I have circled in red the only possible positions a 3 can go in the middle stack. Check it out using the scanning method.
When you look at column five you will notice that a 3 must go in that column in the middle region. There is no other place available in the middle region.
Since a 3 must go in column 5 in the middle region, it can not go in cells (R8,C5) or (R9,C5) of column 5. Therefore you can conclude that the only possible place a 3 can go is in cell (R8,C4) in the lower middle region.
You probably won't use this hint often, but it is a nice one to add to your Sudoku solving tool chest.
Sudoku Hints For Harder Puzzles
Sudoku Hints To Solve For Multiple Missing Numbers
Here is another neat trick to help you solve cells when there are multiple cells missing.
This probably wouldn't happen often, but when it does you will want to know this hint.
In the upper left region of the graphic at the left there are four cells vacant circled in red.
You will notice that three of those cells make up column 3.
Counting from 1 to 9, you find that 1, 3, 5 and 7 are missing in the upper left region. Again counting from 1 to 9 you will find that 1, 3 and 5 are the numbers missing from column 3.
Since 1, 3 and 5 must go into column 3 somewhere, you can deduce that the 7 must go into cell (R2,C1). Write it in.
Now let's try solving for the other three missing numbers 1, 3 and 5 from the upper left most region.
Analyzing row 1, you can see that there already is a 3 and a 5 in that row. This means that a 3 and 5 can not go into cell (R1,C3). The only possible remaining candidate is a 1. Write it in.
You are making great progress.
Now you have two numbers 3 and 5 that are missing from the upper left most region.
Examining row 2 you will notice a 5 in that row. Since the only two numbers left are 3 and 5, and a 5 is already in row 2, then you can conclude that cell (R2,C3) must be a 3. Write it in.
The only remaining cell (R3,C3) has to be a 5.
Great job! You just learned another great Sudoku hint. Now try solving the lower right region using the same technique.
Learn these great Sudoku tips!
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