Common Techniques for Solving Sudoku

by • 6/24/2023, 12:00:00 AM

There are several different techniques and strategies that can be used to solve Sudoku puzzles. Here are some common ones:

Candidate Elimination

For each empty cell in the Sudoku grid, analyze the numbers in the same row, column, and block to eliminate numbers that are already present. The remaining numbers become the possible candidates for the cell.

A basic and simple strategy that can be used in the early stages of the puzzle to eliminate invalid candidates and narrow down the possibilities.

Can be time-consuming and inefficient in more complex puzzles where more advanced strategies are required.

Single Candidate

In a particular row, column, or block, if there is only one number that is a possible candidate for a specific cell, that number must be placed there.

An effective strategy for finding and placing a number when there is only one possible location for it.

Limited to individual cells and cannot solve more advanced puzzles on its own.

Naked Pairs/Triplets/Quads

If two or more cells within a row, column, or block contain the same set of two, three, or four possible candidates, all other occurrences of these candidates within the same row, column, or block can be eliminated.

Eliminates possible candidates by identifying common sets of numbers in related rows, columns, and blocks.

Requires two or more cells to contain exactly the same possible candidates, which can be rare.

Hidden Singles

If a row, column, or block has only one remaining spot for a specific number, that number must be placed there.

A quick method for finding and placing numbers where there is only one possible spot remaining for a specific number.

Requires careful examination of each row, column, and block to find lone possible candidates.

X-Wing

If there are two rows and two columns where only four specific cells contain possible candidates for a particular number, that number can be eliminated from all other cells in those rows and columns.

Eliminates possible candidates by identifying patterns involving two rows and two columns where a particular number can be placed.

Requires the presence of the pattern involving two rows and two columns, which can be uncommon.

Swordfish

An extension of the X-Wing technique, where there are three rows and three columns where only nine specific cells contain possible candidates for a particular number. This can eliminate that number from other cells within those rows and columns.

Restricts possible candidates by identifying patterns involving three rows and three columns where a particular number can be placed.

Harder to find than X-Wing, as it requires three rows and three columns to share the same pattern.

Jellyfish

An extension of the Swordfish technique, where there are four rows and four columns where only sixteen specific cells contain possible candidates for a particular number. This can eliminate that number from other cells within those rows and columns.

Identifies patterns involving four rows and four columns where a particular number can be placed, further reducing possibilities.

Rare to find patterns involving four rows and four columns.

Backtracking

When no logical deductions can be made, backtracking can be used. It involves making a guess for an empty cell and attempting to solve the rest of the puzzle. If it leads to an incorrect solution, backtrack and try another guess. Continue until the puzzle is solved.

These techniques can be used in combination to solve Sudoku puzzles of varying difficulty levels. By applying logic and strategies, the grid can be gradually filled in until it is correctly completed.

Used when other logical deductions are no longer applicable and allows for making guesses to progress.

Can be time-consuming and requires testing different guesses to find the correct solution. If a guess leads to an incorrect solution, you must backtrack and try another guess.

In Summary

When no logical deductions can be made, backtracking can be used. It involves making a guess for an empty cell and attempting to solve the rest of the puzzle. If it leads to an incorrect solution, backtrack and try another guess.

These are just some of the common techniques used to solve Sudoku puzzles. The difficulty level of a specific puzzle may require the use of more advanced strategies or combinations of multiple techniques. It is also possible to use computer programs or apps that can automatically solve Sudoku by applying various algorithms and strategies.

Remember that different techniques work better in different situations and difficulty levels. By combining multiple techniques, you can increase the chances of solving a challenging Sudoku puzzle.