How to Solve a 9 by 9

Sudoku is a logic puzzle game that has become a worldwide sensation. It is a great way to challenge your mind and improve your problem-solving skills. A standard Sudoku puzzle consists of a 9×9 grid that is divided into nine 3×3 sub-grids. The goal of the game is to fill each row, column, and sub-grid with the numbers 1 through 9, without repeating any of them. In this article, we will explore different strategies to solve a 9 by 9 Sudoku puzzle.

Introduction to Sudoku

Sudoku is a logic puzzle game that has become popular all over the world. It was invented in the late 1970s by an American puzzle designer named Howard Garns, and it became popular in Japan in the 1980s. Since then, Sudoku has become a global phenomenon, and it is now enjoyed by millions of people worldwide.

The game is played on a 9×9 grid that is divided into nine 3×3 sub-grids. The puzzle is presented with some of the cells already filled in with numbers. The player’s task is to fill in the remaining cells with the numbers 1 through 9, without repeating any of them in any row, column, or sub-grid.

Sudoku is a game of logic and deduction, and there is no need to guess or use trial and error to solve the puzzle. With the right strategies and techniques, anyone can solve a Sudoku puzzle.

Basic Strategies

The first step in solving a Sudoku puzzle is to look for the cells that are already filled in. These cells provide clues and constraints that can help you fill in the rest of the puzzle. Here are some basic strategies to help you get started:

1. Check for duplicates: Look at each row, column, and sub-grid to make sure that there are no duplicate numbers. If you find a duplicate, you can eliminate the possibility of that number appearing in any of the other cells in that row, column, or sub-grid.
2. Look for single candidates: Look for cells that only have one possible number. If a cell can only be filled with a particular number, then that number must be the correct answer.
3. Use cross-hatching: Look at each row and column to determine which numbers are missing. Then, look at the sub-grid to determine which numbers are missing in that section. By cross-hatching, you can eliminate possibilities and narrow down the candidates for each cell.
4. Use the process of elimination: Use the information you have gathered so far to eliminate possibilities for each cell. If a particular number cannot appear in a certain row, column, or sub-grid, you can eliminate that number from the candidate list for the cell.

Advanced Strategies

Once you have exhausted the basic strategies, you may need to use more advanced techniques to solve the puzzle. Here are some advanced strategies that can help you solve a 9 by 9 Sudoku puzzle:

1. Naked pairs: Look for two cells in the same row, column, or sub-grid that have the same two candidate numbers. These two numbers can only appear in these two cells, so you can eliminate them from the candidate lists of all other cells in that row, column, or sub-grid.
2. Hidden pairs: Look for two candidate numbers that only appear in two cells in the same row, column, or sub-grid. These two numbers can only appear in those two cells, so you can eliminate all other candidates from those two cells.
3. X-wing: Look for two rows or columns that have the same two candidate numbers in the same positions. If the two rows or columns form an X shape, then you can eliminate those two numbers from all other cells in those two rows or columns.
4. Swordfish: Look for three rows or columns that have the same three candidate numbers in the same positions. If those three rows or columns form a shape that looks like a swordfish, then you can eliminate those three numbers from all other cells in those three rows or columns.

5. Coloring: Pick a candidate number and assign it a color. Look for cells that can only be one of two candidate numbers, and color them accordingly. If you find two cells that are colored with the same color, but they are in different sub-grids, then you know that the candidate number that they share cannot appear in any other cells that are also colored with that color.
6. XY-wing: Look for three cells that form a pattern where two cells have the same two candidate numbers, and the third cell has one of those two candidate numbers plus a third candidate number. If the two cells with the same two candidate numbers are in different rows and columns, then you can eliminate the third candidate number from all other cells that share a row or column with both of the two cells.
7. XYZ-wing: Look for three cells that form a pattern where two cells have the same two candidate numbers, and the third cell has one of those two candidate numbers plus a third candidate number. If the two cells with the same two candidate numbers are in different sub-grids, then you can eliminate the third candidate number from all other cells that share a sub-grid with both of the two cells.
8. X-chain: Look for cells that have two candidate numbers. If there is a chain of cells that alternate between those two candidate numbers, then you can eliminate those two numbers from all other cells in that chain.
9. XY-chain: Look for cells that have two candidate numbers. If there is a chain of cells that alternate between those two candidate numbers, and the chain ends in a cell that has a third candidate number, then you can eliminate that third candidate number from all other cells in the chain.
10. Bowman’s Bingo: Look for a row, column, or sub-grid that has n cells with n candidate numbers. If those n candidate numbers are unique to those n cells, then you can eliminate all other candidate numbers from those n cells.

Frequently Asked Questions

1. Is it possible to solve a 9 by 9 Sudoku puzzle without using any advanced strategies?

Yes, it is possible to solve a 9 by 9 Sudoku puzzle using only basic strategies. However, some puzzles may require the use of advanced strategies to solve.

2. How long does it take to solve a 9 by 9 Sudoku puzzle?

The time it takes to solve a 9 by 9 Sudoku puzzle depends on the difficulty of the puzzle and the skill level of the solver. Some puzzles can be solved in a matter of minutes, while others may take hours or even days to solve.

3. What is the hardest Sudoku puzzle ever?

The hardest Sudoku puzzle ever created is believed to be the “AI Escargot” puzzle, which was designed by Finnish mathematician Arto Inkala. It has been rated as the most difficult Sudoku puzzle by many Sudoku experts.

4. Is it possible to create a Sudoku puzzle with more than 9×9 grid?

Yes, it is possible to create Sudoku puzzles with larger grids, although they are less common. Some Sudoku puzzles have been created with grids as large as 25×25.

5. Can Sudoku be solved using a computer program?

Yes, Sudoku can be solved using computer programs that use algorithms to find the solution. However, many Sudoku enthusiasts prefer to solve puzzles by hand as a way to challenge their problem-solving skills.

6. What is the origin of the name “Sudoku”?

The name “Sudoku” comes from a Japanese phrase that means “single number.” The puzzle game was popularized in Japan in the 1980s and was given the name “Sudoku” by a Japanese puzzle company.

7. Are there any benefits to playing Sudoku?

Yes, playing Sudoku can have several benefits for the brain, including improving memory, concentration, and problem-solving skills. It can also help reduce stress and improve mood.

8. Can Sudoku be used as an educational tool?

Yes, Sudoku can be used as an educational tool to teach logic and problem-solving skills. It can also be used to teach math concepts such as number patterns and relationships.

9. Can Sudoku be played on mobile devices?

Yes, there are many mobile apps that allow you to play Sudoku on your phone or tablet. Some apps even offer daily puzzles and allow you to compete against other players.

10. Is it possible to create your own Sudoku puzzles?

Yes, anyone can create their own Sudoku puzzles using a variety of tools and software. There are also online resources that provide templates and guidelines for creating Sudoku puzzles.