How to solve Sudoku Puzzles
No matter what level of puzzle you are attempting to solve you need to master the techniques and strategies that will allow you to find and place correct numbers in empty cells.
You should be aware there is no right or wrong way to solve a sudoku puzzle. Each player develop her own way. You will develop your own unique style.
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To the left is an unsolved Sudoku puzzle. It consists of a 9 x 9 grid that has been subdivided into 9 smaller grids of 3 x 3 squares. Each puzzle has a logical and a unique solution. To solve the puzzle, each row, column, and box must contain each of the numbers 1 to 9. Throughout this guide the entire puzzle will be referred to the “grid”, a small 3 x 3 grid as a “region”, and the square that contains the number as the “cell”. Rows and columns are referred to with row number first, followed by the column number – 4,5 is row 4, column 5 – 2,8 is row 2, column 8. Boxes are numbered 1 – 9 in reading order: 123 456 789. |
Starting the Game
To solve Sudoku puzzles you will need to use logic. You need to ask yourself questions like “if a 1 is in this cell, will it go in this column?” or “if a 9 is already in this row, can a 9 go in this cell?” To make a start, look at each of the regions in the grid below and see which cells are empty, at the same time checking that cell’s column and row for a missing number.
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In this example, look at region 9. There is no 8 in the region, but there is an 8 in column 7 and in column 8. The only place for an 8 is in column 9, and in this box the only cell available is in row 9. So put an 8 in that cell. Once you have done this you have solved your first number. Continuing to think about 8, there is no 8 in region 1, but you can see an 8 in rows 1 and 2. So, in region 1, an 8 can only go in row 3, but there are 2 cells available. Make a note of this by penciling in a small 8 in both cells. Later, when you have found the position of the 8 in regions 4 or 7, you will be able to disprove one of your 8’s in region 1. |
The more methodical that you are about solving your first Sudoku puzzles the better you will become at understanding the logic behind how you solve them. Take time when glancing through regions so that you don’t scan through and miss an obvious number that you can place in a cell. Missing one number can set you back on how fast you solve the puzzle.
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You have been looking at region 9. As you can see, there is a 2 in regions 7 and 8, but none in region 9. The 2’s in row 8 and row 9 mean the only place for a 2 in region 9 appears to be in row 7, and as there is already a 2 in column 8, there is only one cell left in that region for a 2 to go. You can enter the 2 for region 9 at 7,7. Once you enter the number 2 in region 8 you will be ready to eliminate other numbers from other regions. |
As stated earlier, the more time you take in learning which strategy works best for certain puzzles the faster you will catch on to the logic behind the puzzle.
Sudoku is all about filling in cells one by one by the process of elimination.
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There is a similar situation with the 4’s in regions 4 and 5, but here the outcome is not so definite. Together with the 4 in column 7 these 4’s eliminate all the available squares in region 6 apart from two. Pencil a small 4 in these two cells. |
Later on, one or other of your pencil marks will be proved or disproved.
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Having proved the 2 in region 9 earlier, check to see if this helps you to solve anything else. For example, the 2 in region 3 shows where the 2 should go in region 6; it can only go in column 9, where there are two available squares. As you have not yet proved the position of the 4, one of the cells may be either a 4 or a 2. It’s time for you to solve a number on your own. Take a look at region 8 and see where the number 7 should go. Continue to solve the more obvious numbers. |
There will come a point when you will need to change your strategy. There are, however, three steps you should always follow when approaching a new puzzle:
Step One – analyse your sudoku grid and decide your first move. Whether you decide to go for the number with the highest frequency first, or the region with most given numbers, is up to you.
Step two – After scanning your grid you want to proceed with one of the two sudoku solving strategies.
Initially you want to find the lone number. This is the easy part. When you are not able to prove any more numbers, you move on to the next step.
Step three – In short, step three is to go back to step one and scan your grid again. You have placed some numbers in their cells so you need to do another analysis and decide your next move. If you have not prepared yourself for a more structured approach to solving your puzzle, this may be the time to find a pencil and get ready for some subscript marking.
Secret Tip
If you are stuck and can not find more numbers, it may be your brain is playing a trick on you. Your brain is trained to read. Your scanning pattern will in most cases look like your reading pattern. That is – english readers typically scan from top left corner of the grid down along the left side. You do some horizontal scans from left to right as you move down the grid. Your scanning pattern looks like F or E.
If this is the case – you are missing half the grid and may be half the solutions.
Train your brain to look for solutions from all directions. Horizontal – from left to right and right to left. Vertical – from top to bottom and bottom to top.
