Printable Sudoku Puzzles by Sudoku.com: The Ultimate Sudoku Site
Sudoku: A Fun and Challenging Number Puzzle Game
If you are looking for a way to exercise your brain and have fun at the same time, you might want to try Sudoku. Sudoku is a logic-based number puzzle game that has become one of the most popular pastimes in the world. In this article, you will learn more about what Sudoku is, how to play it, its history, its benefits, and its variations.
What is Sudoku and how to play it
Sudoku is a game that involves filling a grid with digits from 1 to 9. The grid usually consists of 9 rows, 9 columns, and 9 smaller squares called regions or boxes. Each row, column, and region must contain all the digits from 1 to 9 without repeating any of them. The puzzle setter provides some digits as clues or givens in some of the cells. The solver's task is to fill in the remaining empty cells using logic and deduction.
The main objective and basic rule of Sudoku
The main objective of Sudoku is to complete the grid with digits from 1 to 9 according to the following rule:
Each digit can appear only once in each row, column, and region.
This rule is simple but powerful. It allows you to eliminate some possibilities for each cell based on what digits are already present in its row, column, and region. For example, if a cell belongs to a row that already has a 5 in it, then you know that the cell cannot contain a 5. Similarly, if a cell belongs to a column that already has a 9 in it, then you know that the cell cannot contain a 9. And so on.
Sudoku rules and tips
Now that you know the basic rule of Sudoku, you might wonder how to apply it to solve Sudoku puzzles. There are many methods and techniques that can help you with that. Here are some of them:
How to use logic and elimination to solve Sudoku puzzles
The most fundamental strategy for solving Sudoku puzzles is to use logic and elimination. This means that you look at each cell and try to figure out what digits can or cannot go in it based on the basic rule of Sudoku. You can do this by scanning the row, column, and region of each cell and seeing what digits are already there. Then you can eliminate those digits from the possible candidates for that cell.
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For example, suppose you have an empty cell in the top left corner of the grid. You look at its row and see that it has a 1, a 2, a 4, a 6, an 8, and a 9 in it. You look at its column and see that it has a 3, a 5, a 7, an 8, and a 9 in it. You look at its region and see that it has a 1, a 2, a 4, and a 6 in it. By eliminating these digits, you can conclude that the only possible digit for that cell is a 7. So you can fill in the 7 in that cell.
How to use pencil marking and other techniques to keep track of possibilities
Sometimes, you may not be able to find a cell that has only one possible digit. In that case, you may want to use pencil marking or other techniques to keep track of the possibilities for each cell. Pencil marking means that you write down the possible digits for each cell in small numbers inside the cell. This way, you can see at a glance what options you have for each cell and update them as you progress.
For example, suppose you have an empty cell in the middle of the grid. You look at its row and see that it has a 1, a 3, a 5, and a 9 in it. You look at its column and see that it has a 2, a 4, a 6, and an 8 in it. You look at its region and see that it has a 1, a 2, a 4, and a 7 in it. By eliminating these digits, you can conclude that the possible digits for that cell are 3, 5, or 9. So you can write down these digits in small numbers inside the cell.
Other techniques that can help you keep track of possibilities include using colors, symbols, shapes, or notes to mark the cells. You can also use online tools or apps that have features for pencil marking and other aids.
How to use cross-hatching, hidden singles, pairs, triples, and other advanced strategies
As you get more familiar with Sudoku puzzles, you may encounter some situations where logic and elimination are not enough to solve them. You may need to use some more advanced strategies that involve looking for patterns and relationships among the cells. Here are some examples of these strategies:
Cross-hatching: This means that you look at a row, column, or region and see what digits are missing from it. Then you scan the other rows, columns, or regions that intersect with it and eliminate those digits from the cells that share them. For example, if you know that a row is missing a 5 and you see that the only cells in that row that can contain a 5 are in the same column or region as another cell that already has a 5 in it, then you can eliminate the 5 from those cells.
Hidden singles: This means that you look at a row, column, or region and see if there is only one cell that can contain a certain digit. This digit may not be obvious at first glance because it may be hidden among other possibilities. For example, if you have a row that has two cells with the possibilities of 1 or 2 and one cell with the possibilities of 1 or 3, then you can deduce that the cell with the possibilities of 1 or 3 must contain a 3 because the other two cells must contain a 1 or a 2.
Pairs: This means that you look at two cells in the same row, column, or region that have the same two possibilities. This implies that those two digits must go in those two cells and nowhere else in that row, column, or region. For example, if you have two cells in the same column that have the possibilities of 4 or 5 and no other cell in that column has either of those digits as a possibility, then you can eliminate those digits from all other cells in that column.
Triples: This means that you look at three cells in the same row, column, or region that have three possibilities among them. This implies that those three digits must go in those three cells and nowhere else in that row, column, or region. For example, if you have three cells in the same region that have the possibilities of 1, 2, or 3; 1, 2, or 4; and 1, 3, or 4; then you can deduce that those cells must contain a 1, a 2, and a 4 in some order and eliminate those digits from all other cells in that region.
There are many other advanced strategies that can help you solve Sudoku puzzles, such as X-wing, swordfish, coloring, forcing chains, etc. You can learn more about them from online tutorials, books, or videos.
Sudoku history and origin
Sudoku may seem like a modern invention, but it actually has a long and fascinating history that dates back to centuries ago. Here are some of the milestones in the evolution of Sudoku:
How Sudoku evolved from Latin squares and magic squares
The earliest ancestor of Sudoku is the Latin square, a mathematical concept that was first studied by the Swiss mathematician Leonhard Euler in the 18th century. A Latin square is a grid of n rows and n columns filled with n different symbols, such that each symbol appears exactly once in each row and column. For example, here is a Latin square of size 4:
A special type of Latin square is the magic square, which has the additional property that the sum of the symbols in each row, column, and diagonal is the same. For example, here is a magic square of size 3:
Magic squares have been known and used for various purposes since ancie