- Contents
- [pdf] The Mathematics Of Sudoku - Geometer Org
- How to Solve Sudoku Puzzles Quickly and Reliably
- Solve Sudoku Swordfish And Become A Pro
- Sudoku - Advanced Techniques

To solve a regular Sudoku puzzle, place a number into There are 8 different deductive techniques that SudokuSolver will point out for you when they are. The sudoku puzzle reached craze status in Japan in and the craze spread . no matter what level of puzzle you are attempting, there are a few strategies. Solving Sudoku puzzles is one of the most popular pastimes in the world. The current paper explains and compares three algorithms for solving Sudoku puzzles. It infallibly solves a Sudoku puzzle or deduces that a unique solution does not exist.

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Advanced Techniques. At this point, you have learned all the basic Sudoku concepts. And while understanding them is certainly no easy task, you have. In this paper, an exhaustive study has been made on different techniques for solving a Sudoku puzzle. Keywords: Sudoku puzzle, Cell, Minigrid, Elimination. Tips and Methods for Solving Sudoku Puzzles. FREE CUSTOM PDF BOOKLET ยท SEARCH A A sudoku puzzle comprises 9 rows, 9 columns and 9 block.

You'd like to translate the site? Send an email to A sudoku puzzle comprises 9 rows, 9 columns and 9 block. Each of them must contain all numbers from 1 to 9. The following concepts are there to help you understanding the methods to solve a sudoku. The cell is the base unit of sudoku wich must be assigned a number from 1 to 9. Each cell is part of three groups at a time: one row, one column and one block. The groups The row has nine cells disposed horizontally The column has nine cells disposed vertically The block has nine cells disposed in 3x3 squares, the puzzle comprises nine of these blocks.

You should be able to solve almost any Sudoku puzzle using these techniques. Techniques for removing numbers: Sole Candidate When a specific cell can only contain a single number, that number is a "sole candidate". This happens whenever all other numbers but the candidate number exists in either the current block, column or row. In this example, the red cell can only contain the number 5, as the other eight numbers have all been used in the related block, column and row.

Unique Candidate You know that each block, row and column on a Sudoku board must contain every number between 1 and 9. This example illustrates the number 4 as the unique candidate for the cell marked in red. The example shows that the number 7 can only be inserted in the red cells of the middle row. Thus you can remove 7 as a possible candidate from the rest of the row. In the middle and the middle-left blocks, the number 8 must be placed in one of the red cells.

This means, we can eliminate 8 from the upper and lower rows in the middle-right column.

Naked Subset The example shows that row number 1 and row number 5 both have a cell in the same column containing only the candidate numbers 4 and 7. These two numbers appear as candidates in all of the other open cells in that column too, but since they are the only two candidates in rows 1 and 5, these two numbers cannot appear anywhere else in the row, thus you can remove them. In the example, the two candidate pairs circled in red, are the sole candidates.

Since 4 and 7 must be placed in either of these two cells, all of the pairs circled in blue, can remove those numbers as candidates. In this puzzle, this means 1 becomes sole candidate in the second row; 2 becomes sole candidate in row 6; and thus, 6 is sole candidate for row number 4.

You can also use this technique if you have more than two candidates. For example, let us say the pairs circled in red were instead triple candidates of the numbers 1, 4, 7. This would mean those three numbers would have to be placed in either rows 1, 2 or 5.

We could remove these three numbers as candidates in any of the remaining cells in the column. Hidden subset This is similar to Naked subset, but it affects the cells holding the candidates. In this example, we see that the numbers 5, 6, 7 can only be placed in cells 5 or 6 in the first column marked in a red circle , and that the number 5 can only be inserted in cell number 8.

Since 6 and 7 must be placed in one of the cells with a red circle, it follows that the number 5 has to be placed in cell number 8, and thus we can remove any other candidates for this cell; in this case, 2 and 3.

X-Wing This method can work when you look at cells comprising a rectangle, such as the cells marked in red.

In this example, let's say that the red and blue cells all have the number 5 as candidate numbers. Now, imagine if the red cells are the only cells in column 2 and 8 in which you can put 5. In this case you obviously need to put a 5 in two of the red cells, and you also know they cannot both be in the same row.

Well, now, this means you can eliminate 5 as the candidate for all the blue cells. This is because in the top row, either the first or the second red cell must have a 5, and the same can be said about the lower row.

Swordfish Swordfish is a more complicated version of X-Wing. In most cases, the technique might seem like much work for very little pay, but some puzzles can only be solved with it.

So if you want to be a sudoku-solving master, read on! Example A In example A, we've plotted in some candidate cells for the number 3.

Now, assume that in column 2, 4, 7 and 9, the only cells that can contain the number 3 are the ones marked in red. You know that each column must contain a 3. Example B Look at example B. The Rules of Sudoku While solving Sudoku puzzles can be significant challenge, the rules for traditional solution finding are quite straight forward: Each row, column, and nonet can contain each number typically 1 to 9 exactly once. The sum of all numbers in any nonet, row, or column must match the small number printed in its corner.

For traditional Sudoku puzzles featuring the numbers 1 to 9, this sum is equal to In order to solve Sudoku puzzles reliably, you must be disciplined, focused, and patient. These two techniques are simple, straightforward, reliable, and sufficient in solving most standard Sudoku puzzles. It is important to understand that all Sudoku puzzles require an iterative approach. Except for in the case of the most simple puzzles, players will have to visit each nonet more than one time. Fortunately, each successive application of the solution techniques yields more completed cells.

Crosshatching To begin with we will want to use the Crosshatching technique. By looking across each row and down each column, we can determine if a number can or cannot go in a cell. We will be solving a Sudoku puzzle taken from Sudoku Latin Squares.

Getting Started Sudoku puzzles can be started anywhere, but we recommend you begin with nonet A and work alphabetically, left to right, top to bottom. We will follow this advice and focus on nonet A. As there are 5 numbers missing in this nonet 1, 5, 6, 7, and 8 , we will make 5 passes, attempting to place each of the five missing numbers in empty cells.

Crosshatching for 1 Nonet A In trying to place the number 1, we cross out all rows and columns that contain the number 1 and pass through the nonet we are focusing on. Crosshatching for 5 Nonet A In trying to place the number 5, we again, cross out all rows and colums with 5 and are left with 3 empty cells. An improvement, but this still prevents us from placing the number. This is very common in Sudoku. Some puzzles are straightforward, while others take a bit more time to successfully solve.

We can place our first number. As such, we know the number 2 must go in the final empty box. If we continue to apply the Crosshatching technique to nonets C through I, we complete our first Crosshatching pass with the following puzzle status. Penciling In Of course, we could continue to Crosshatch and possibly fill in more empty boxes.