What most people don’t know is that sudoku is not a mathematical game. It requires absolutely no arithmetic skills, but it does require logical reasoning. As you learn to arrange the numbers correctly, your logical thinking skills improve. But don’t you sometimes wish you could try out a slightly different variation compared to the standard one? Introducing diagonal Sudoku.
Do not worry because as sudoku becomes more popular each day, more variations arise to make the game more unique and fascinating. And one of the earliest variations that exist is a puzzle without a lot of changes to the rules of standard sudoku. It’s called diagonal sudoku. Even though a diagonal sudoku puzzle may seem tougher, the extra constraint can make it easier to figure out the numbers. Keep reading for everything you need to know about diagonal sudoku, from the basic rules to the best ways to solve them!
Is there a diagonal rule in sudoku?
One of the reasons so many people love diagonal sudoku is because of the simplicity of its rules:
- Each column has to contain the numbers 1 through 9 exactly once each without repeating
- Each row has to contain the numbers 1 through 9 exactly once each without repeating
- Each 3×3 region has to contain the numbers 1 through 9 exactly once each without repeating
- The two 9-cell diagonals must contain all the numbers 1 through 9 exactly once each without repeating.
Yes, the rules are simple but solving them is a different topic. The additional constraint of the fourth rule means that you potentially have more information to work with when trying to figure out which digit goes into one of the cells along either of the long diagonals. Diagonal sudoku puzzles usually have lines drawn through the diagonals to remind you of this rule. Now, let’s proceed with solving diagonal sudoku.
First, solve the puzzle like a regular sudoku using the rules #1 through #3 as mentioned above. Use the tips and techniques you have learned in solving standard sudoku and try solving it as much as you can.
(Puzzle after using the standard rules of standard sudoku)
If you are stuck and you’ve exhausted all your techniques in solving the puzzle using the rules of standard sudoku like in the picture above, it is now time for you to use the additional constraint set by the diagonal rule.
Look at those that are highlighted in green. In region 3 of the puzzle, the only missing numbers are 2, 3, and 9. Looking at the diagonal, you can see that 2 and 9 are already given. Therefore, by using the fourth rule that says the numbers 1-9 will appear exactly once in the diagonal line, 3 is the missing number in Row 1 Column 9 (R1C9) cell.
Now focus on numbers and lines highlighted in blue. In region 6, number 8 is only possible in R7C2. Why? Because if you look at that diagonal line, there is already number 8, therefore 8 cannot be placed in R8C2. It is also not applicable in R8C3 because 8 is already given in row 3. So, weare only left with 8 to be placed in R7C2.
Another clue using the diagonal rule, look at the numbers and lines highlighted in pink. Focusing on the diagonal line slanted up to the right (/), we know that numbers 1-9 will appear exactly once in that diagonal line. Then let’s examine number 5. Number 5 cannot be in R7C2 because 5 is already present in that region. It is also not applicable in R6C4 because 5 is already given in row 6 and also not in R5C5 because 5 is already given in row 5. Which only leaves us number 5 to be placed in R4C6.
Try using the combined rules of the standard sudoku and the diagonal rule as explained above to finish this puzzle. I assure you that you can easily solve this diagonal sudoku puzzle in no time. Good luck!