Sudoku Candidates: how to use them to solve any grid

Introduction to Sudoku Game

The Sudoku game has become a very popular pastime worldwide. Its origin, however, dates back a long time ago.

Modern Sudoku was introduced in 1979 by Howard Garns, an American architect and puzzle creator. However, the game only became truly famous in the 1980s when it was published in the Japanese magazine Nikoli under the name “Sudoku,” an abbreviation of “Suji wa dokushin ni kagiru,” which means “the numbers must be single.”

Basic Rules of the Game

The rules of Sudoku are simple but require logic and attention:

The standard grid consists of 9×9 cells, divided into nine 3×3 subgrids. The objective is to fill the grid by inserting numbers from 1 to 9 so that each row, column, and subgrid contains all the numbers from 1 to 9 without repetitions. Some numbers are already pre-inserted in the grid as clues. These initial numbers can vary to create different levels of difficulty.

These simple rules make Sudoku accessible to everyone, but the challenge lies in finding the correct solution for each grid.

Importance of Candidates in the Sudoku Solving Process

Key Point: Before examining the strategies for solving Sudoku, it is important to understand what candidates are.

The Sudoku candidates are the numbers that could go in an empty cell while adhering to the rules of the game. In other words, they are all the possible choices for a position in the grid. This concept is fundamental because it helps to narrow down the options and guide the solving process.

How Sudoku Candidates Are Useful

Identifying Opportunities: Look at each empty box and write down all the numbers that could fit there without breaking the rules.
Reducing Options: Use strategies like elimination logic (which we will explain later) to remove some choices, thereby reducing the candidates.
Finding Solutions: When only one possible number remains for a box, we can confidently place it there.

For example, imagine an empty box with candidates 1, 3, and 7. If by looking at the nearby rows, columns, and quadrants we discover that 1 and 3 cannot go there, then we know it must be a 7. This method allows us to proceed in an orderly manner through the grid.

When we use the candidates well, solving Sudoku becomes easier and more logical.

1. Using the Elimination Logic in Solving Sudoku

The elimination logic is one of the most effective Sudoku solving strategies. It involves analyzing the possible options for each cell and eliminating the numbers that cannot be placed, until the only possible candidate is found.

How the Deletion Logic Works

Identify the Possibilities: For each empty cell, list all the numbers from 1 to 9 that could fill it, based on the numbers already present in the corresponding row, column, and sector (3×3).
Eliminate Impossible Numbers: Examine each row, column, and sector to see which numbers have already been used. Eliminate these numbers from the candidate list for the cell in question.
Isolate the Unique Candidate: If only one possible number remains for a cell, this is the candidate to insert.

Practical Example

Imagine a Sudoku grid where the cell (5,5) is empty. Let’s assume that in the same row (row 5) the numbers 1, 2, 3, 7, and 9 are already present; in the same column (column 5) there are the numbers 4 and 6; in the sector (3×3) the numbers 5 and 8 are present.

Initial Possibilities: [1, 2, 3, 4, 5, 6, 7, 8, 9]
Remove Numbers from Row: [4, 5, 6, 8]
Remove Numbers from Column: [5, 8]
Remove Numbers from Sector: []

After eliminating all impossible possibilities:

The only remaining number is the number “8”.

Entering this number in the cell (5,5), proceed with the same method for the other empty cells until the grid is complete.

This technique drastically reduces the number of possibilities to consider and makes the process of solving Sudoku puzzles much more manageable.

2. Positioning of Numbers through Digit Analysis

A crucial aspect of solving Sudoku is knowing how to use the information provided by the numbers already placed in the grid. This technique, known as sudoku number placement, requires careful observation and detailed analysis.

Steps for Analyzing Current Figures:

Row and Column Identification:

Observe the rows and columns that already contain various numbers. These can provide valuable clues on where to place the missing numbers.

For example, if row 5 already contains the numbers 1, 2, and 3, you can exclude these numbers from the empty cells in the same row.

Block Examination (3×3):

Each Sudoku grid is divided into 3x3 blocks. Check the numbers present in each block to determine which digits are missing.

If the numbers 4, 5, and 6 are missing in the block at the top left, you can focus on the empty boxes of that block to place these numbers.

Intersection of Information:

Use the intersection of information from rows, columns, and blocks to further narrow down the possibilities.

If column 2 does not contain the number 7 and row 4 does not either, but both intersect a block with an empty cell, that cell will likely need to contain the number 7.

Practical Example:

Let’s consider a grid where column A has the numbers 1, 2, and 5, while row 1 has the numbers 3 and 4. If there is an empty cell at the intersection of column A and row 1, we can deduce that this cell cannot contain the numbers 1, 2, 3, 4, or 5. Therefore, only other possible digits remain to be considered for that specific point.

This analysis technique not only simplifies the problem-solving process but also increases the effectiveness in finding the correct solutions.

3. Advanced Strategies for Tackling Complex Sudoku Challenges

Identify and Leverage the Boxes with the Highest Number of Candidates

When facing higher levels of difficulty in Sudoku, one of the fundamental techniques is to identify the cells that contain the highest number of candidates. These cells often represent the key points of the grid from which to start solving complex puzzles.

How to proceed: Observe the grid: Identify the cells that have multiple possible candidates.
Cross-analysis: Compare these cells with the surrounding rows, columns, and blocks to see if some candidates can be eliminated.

A practical example could be a box with candidates [2, 4, 7]. If 2 and 4 are present in other parts of the block or row/column, the number 7 might be the right choice.

In-Depth on Strategies ‘XYZ’ and ‘ABC’

To solve particularly complex situations, there are advanced strategies known as ‘xyz’ and ‘abc’. These techniques are based on specific patterns of candidate positioning that allow for further reduction of options.

XYZ-Wing Strategy: This technique uses three cells where candidates share a common relationship. If one cell has candidates (X,Y), another (Y,Z), and the third (X,Z), one of the elements can be eliminated from the grid. ABC Strategy: It employs a similar approach but at a more complex level, considering multiple relationships among different candidates across more rows, columns, or blocks.

These advanced strategies require practice and attention to detail, but once mastered, they can transform even the most difficult puzzles into solvable challenges.

Final Recommendations

In the Sudoku game, it is important not to limit yourself to a single solving technique. Experiment with different strategies and find the one that suits you best. Each grid may require a different approach, so being flexible and adaptable is essential.

Some useful tips include:

Try different combinations: Don’t be afraid to explore new or less familiar methods. Sometimes, a new perspective can lead to the solution.
Stay calm: Sudoku is not just a mental challenge; it’s also a way to relax. If you feel stuck, take a break and return to the puzzle with a fresh mind.

“Sudoku is not just about solving a puzzle, but also enjoying the process.”

Additionally, remember that every mistake is an opportunity to improve. Analyze where you went wrong and learn from your mistakes to enhance your skills over time.

The main goal is to have fun while solving. Whether you’re looking for quick solutions to improve your time or simply want to relax with a challenging activity, Sudoku offers something for everyone.

Stay positive and keep practicing. Consistent practice will make you increasingly skilled at finding the perfect solutions for every grid.

Conclusions

In this guide, we have explored the essential strategies for successfully solving the Sudoku game. From the use of Sudoku candidates to elimination logic and number placement, you now have the tools necessary to tackle any grid. Whether you are a beginner or an experienced player, we hope these tips will be helpful in improving your Sudoku skills.

Before we conclude, we want to challenge you to put into practice what you have learned:

Grab a pencil and a sheet of paper, or open your favorite Sudoku app. Solve at least three puzzles using the strategies we’ve discussed.

You will see how much faster and more effective you will be at finding Sudoku solutions. Have fun and happy solving!