For the second Sudoku, we have the following 10 equations: m+n=a. g+n+f=g+c⟹n+f=c. g+d=n….Sudoku 2.

There are more than a few techniques to solve a Sudoku puzzle, but per Conceptis Puzzles, the easiest way to a Sudoku solution is to, “Scan rows and columns within each triple-box area, eliminating numbers or squares and finding situations where only a single number can fit into a single square.” If you’re looking to …

We conclude that the rule-based algorithm is by far the most efficient al- gorithm when it comes to solving Sudoku puzzles. It is also shown that some correlation in difficulty rating exists between the backtrack and rule-based algorithms.

Google’s Goggles app for Android will now solve your Sudoku puzzle in less than 30 seconds. Sure, it’s a pointless application of the tech, but it looks really cool scanning the numbers and solving the puzzle and that’s the whole point. …

For example, in the first and fourth columns beginning from the left of the 9×9 grid, we can form the following equations: m+n=a, g+n+f=g+c. In the second and last rows beginning from the top of the 9×9 grid, the following equations can be formed: b+g+f=a+g, e+n+m=a+b+d.

The Algorithm One algorithm to solve Sudoku puzzles is the backtracking algorithm. Essentially, you keep trying numbers in empty spots until there aren’t any that are possible, then you backtrack and try different numbers in the previous slots.

The strategies are the following:

1. Search for cells with a unique solution possible.
2. Search for rows with a unique cell for an specific digit.
3. Search for columns with a unique cell for an specific digit.
4. Search for “squares” with a unique cell for an specific digit.

A Hidden Single is a single candidate remaining for a specific digit in a row, column or box. In Sudoku variants, additional constraints can also produce Hidden Singles. An alternative term is Pinned Digit.

Overall, though linear algebra cannot be used to solve all sudoku puzzles it can be a very useful tool in solving them and it could be implemented to drastically reduce the number of possibilities and help with solving a Sudoku puzzle.

Sudoku with rectangular regions

Here are two Sudoku hints that will help you solve a row or column where two cells are empty. Look at the graphic at the left. You will notice that in column 1 we are missing two numbers. They are circled in red. Counting from 1 to 9 you find that a 2 and a 4 are missing. But where do they go? To solve this column, look at row 8.

If you look at the right – center region carefully, you will see that there is a 4 in cell (R6,C7). Since you cannot have two 4s in the same region, cell (R5,C8) must be a 3. If cell (R5,C8) is a 3, cell (R5,C2) must be a 4. There you have done it! You learned two new Sudoku hints that will help you solve two missing cells in a row or column.

While solving the sudoku puzzle you can only use each number one time in the square, column, and row. Columns and rows are not limited by the thicker boundaries of the square (also sometimes called a region.) They run from the top of the puzzle to the bottom of the puzzle (as pictured in blue above). The same is true of rows.

With crosshatching, you start by focusing on one 3×3 square and filling it in with the numbers needed. It’s a way to give you a starting point for your game that doesn’t involve looking at the entire grid. Crosshatching can be especially useful for brand new Sudoku players who are overwhelmed with an entire grid to fill.