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Solve Sudoku - How the logic puzzle works
The structure of the puzzle is quite simple. A 9 x 9 grid, which results in 81 individual boxes, must be filled in completely with numbers. The entire square is again divided into nine smaller sub-squares.
The goal is to fill each row, each column and each sub-square with the numbers from 1 to 9. The order does not matter. However, in no case may a digit appear twice in one of the mentioned areas.
The challenge is to find out which digits are missing by using some of the digits already entered on the sheet. The difficulty depends on how many digits have already been entered: the more, the easier the Sudoku puzzle.
Sudoku has two simple rules:
- Each column, row and block must contain all numbers from 1 to 9.
- Therefore, no column, row or block may contain two or more fields with the same number.
Use the numbers 1-9
Sudoku is played on a grid of 9 x 9 squares. Within the rows and columns there are 9 "squares" (consisting of 3 x 3 squares). Each row, column and square (9 squares each) must be filled in with the numbers 1-9 without repeating the numbers within the row, column or square. Does this sound complicated? As you can see from the picture below, each Sudoku grid has some squares already filled in; the more squares filled in, the easier the game - the more difficult Sudoku puzzles have very few squares already filled in.
As you can see, this square in the upper left (circled in blue) has already filled 7 of the 9 squares. The only numbers missing from the square are 5 and 6. By seeing which numbers are missing from each square, row, or column, we can use the process of elimination and deductive reasoning to decide which numbers belong in each empty square.
For example, in the upper left square, we know we need to add a 5 and a 6 to complete the square, but based on the adjacent rows and squares, we cannot clearly deduce which number should be added in which space. This means that we should ignore the upper left square for now and instead try to fill in blanks in some other areas of the grid.
Do not guess
Sudoku is a game of logic and reasoning, so you shouldn't have to guess. If you don't know what number to put in a particular box, scan the other areas of the grid until you have a chance to place a number. But you shouldn't try to "force" anything - Sudoku rewards patience, oversight, and recognizing patterns, not blind luck or guessing.
Use process of elimination
What do we mean by "process of elimination" to play Sudoku? Here's an example. In this Sudoku grid (see below), only a few numbers are missing from the leftmost vertical column (circled in blue): 1, 5, and 6.
One way to find out which numbers belong in each box is to use the "process of elimination" by checking which other numbers are already in each box - since there can be no duplication of numbers 1-9 in each box (or row or column).
In this case, we can quickly see that there is already a number 1 in the top left and middle left squares of the grid (with the number 1 circled in red). This means that in the leftmost column there is only one space left where a 1 could go - circled in green. This is how the process of elimination works in Sudoku - you figure out which blanks are available, which numbers are missing - and then deduce which numbers fit in each box based on the position of those numbers within the grid.
Sudoku rules are relatively straightforward - but the game is infinitely varied, with millions of possible number combinations and a variety of difficulty levels. But it's all based on the simple principles of using the numbers 1-9, filling in the blanks based upon deductive reasoning, and never repeating numbers in a box, row, or column.
Sudoku - this is how the number puzzle originated
The Asian name of the popular Sudoku puzzle suggests that the game originated in the Far East. However, this assumption is wrong. The first versions of Sudoku, the so-called magic squares, were published by French daily newspapers towards the end of the 19th century. In these square puzzles with 9x9 squares, the sum of all columns, rows and diagonals is equal. However, this original variant of Sudoku could also contain two-digit numbers compared to today's version.
Solve Sudoku: The 5 best strategies
Solve Sudoku puzzles with notes
Especially for beginners it can be helpful to make notes on the Sudoku field. However, it can also help you if you are already very advanced and the Sudokus are particularly difficult. The notes are about solving a Sudoku according to the exclusion method, which is also called negative grid.
- To do this, first draw a grid with nine numbers in each empty field, or write them in the field. A pencil is best suited for this. If you are using a Sudoku app, it usually has an option to do this.
- Then you start with the exclusion method, and cross out each number that already occurs in the respective nine field.
- So if there is a three in the same box, logically it can't be in the free field, so you can cross that number out of your grid.
- Then do the same with each number that occurs in the respective vertical and horizontal columns.
- When you have done this for each field, you will see that in some positions only one number is possible. You can then enter this number and delete it from other affected grids.
The method of skimming
Skimming is particularly suitable for solving easy puzzles and the beginnings of more complicated Sudoku puzzles.
- Take a box and check where the respective number could be placed.
- The easiest way to do this is to start with one and gradually work your way up to nine.
- Your goal now is to find the possible location of the one. You do this by first including the lines. If, for example, a one is missing in one box, check in which rows of the adjacent boxes the one can be found.
- If there is a one in the second and third line, you know that the one of the first box must be in the first line.
- Often this information is already enough, for example if only one free box remains in the first line. If several boxes are still open, you additionally draw in the respective lines according to the same principle.
- In this way, the surrounding fields tell you in which position a particular number fits.
The only possible candidate
More often than you think, in Sudokus it is already clear from the beginning that only one number is possible in a certain field. For these situations the method of the only possible candidate is suitable.
- In a field, a single candidate is possible only if all other numbers occur in the affected box, the affected row, and the affected column altogether.
- So with this principle, you select a box, and check every other box that interacts with it.
- The number that does not occur in the immediate vicinity is the only possible candidate.
- With this method you can quickly and easily solve your Sudoku.
If you have a 50/50 chance of two numbers in each of two boxes of a box, use the "Naked Pairs" strategy. This is a more sophisticated technique that is used especially for difficult Sudoku puzzles.
- At the end of the day, however, this method is not about solving these fields. Rather, you use this pair to solve another field.
- Because no matter what number is where, you know that both fields are blocked.
- So if a third field is still open, you know that the remaining number can only go into that field.
- But even if there are two other fields left, the method of "Naked Pairs" combined with a process of exclusion can bring the solution.
Find missing numbers
This technique is especially useful if you have some columns, rows or boxes where only a few numbers are missing. In this case, it makes the most sense to take them one by one.
- Select a row, for example, in which only three numbers are missing. Now check each box for the remaining numbers by checking the surrounding boxes, columns and rows for overlaps.
- In this situation you will usually find that for at least one number often only one position is possible, because it would be blocked in another box.
- This way you can quickly find the missing numbers and complete your Sudoku.