What makes sudoku difficult

Hopefully it can keep one step ahead of even the most expert human player! Sudoku is not really about arithmetic at all, the numbers in each cell are just symbols. You could replace them with letters, fruit, different chess pieces, or even abstract shapes. There are two options for mirroring vertically or horizontally , each of which can be used or not, so that makes another multiple of 4. Ciphering is what really multiplies it up though!

There are 9! We use this in our daily puzzles, so that each player gets their own variant of the puzzle, but we know they are all equivalent for when they submit times.

Sudoku Difficulty Ratings. How do we rank the difficulty of Sudoku puzzles? But when it comes to classifying Sudoku levels based on their difficulty, there is an ongoing debate.

Several research studies analyzed this game from a mathematical point of view, suggesting that its algorithmic properties are the ones that generate the challenge. The number of revealed squares might indicate to you the difficulty or the challenge your Sudoku puzzle has. This means that the difficulty level of Sudoku puzzles can be described based on the number of tricks you need to discover to solve them:.

Of course, this depends on your skills and experience with mastering Sudoku puzzles. The difficulty of a Sudoku puzzle is related to the number of tricks such as x-wing, xy-wing, unique rectangles, and so on. This happens whenever all other numbers but the candidate number exists in either the current block, column or row. In this example, the red cell can only contain the number 5, as the other eight numbers have all been used in the related block, column and row.

Unique Candidate You know that each block, row and column on a Sudoku board must contain every number between 1 and 9. This example illustrates the number 4 as the unique candidate for the cell marked in red. The example shows that the number 7 can only be inserted in the red cells of the middle row. Thus you can remove 7 as a possible candidate from the rest of the row. In the middle and the middle-left blocks, the number 8 must be placed in one of the red cells.

This means, we can eliminate 8 from the upper and lower rows in the middle-right column. Naked Subset The example shows that row number 1 and row number 5 both have a cell in the same column containing only the candidate numbers 4 and 7. These two numbers appear as candidates in all of the other open cells in that column too, but since they are the only two candidates in rows 1 and 5, these two numbers cannot appear anywhere else in the row, thus you can remove them.

In the example, the two candidate pairs circled in red, are the sole candidates. Since 4 and 7 must be placed in either of these two cells, all of the pairs circled in blue, can remove those numbers as candidates. In this puzzle, this means 1 becomes sole candidate in the second row; 2 becomes sole candidate in row 6; and thus, 6 is sole candidate for row number 4.

You can also use this technique if you have more than two candidates. For example, let us say the pairs circled in red were instead triple candidates of the numbers 1, 4, 7. This would mean those three numbers would have to be placed in either rows 1, 2 or 5.

We could remove these three numbers as candidates in any of the remaining cells in the column. Hidden subset This is similar to Naked subset, but it affects the cells holding the candidates.

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