How to calculate sudoku combinations. The better way to know!!

To calculate the total number of combinations in sudoku. we can follow some easy step!!!!

    1. To Understand the Basics of Combinations:

       Sudoku have 9*9 grides and these grides are divided into sub-grides of 3*3. Each row, each column and                sub-grid must contains 1 to 9 numbers.

     2.   Apply the permutation for each row:  

       In the sudoku, each row has 9 elements so according to the law to permutation, there are total possibility of         combinations are 9! . so when we calculate it that is equals to 362880. This accounts for all the possible                 arrangements of the numbers 1 to 9 without repetition.

      3.  Permutations for the entire grid:

        There are total 9 grides. To know the total combinations we have to multiply 9!*9 and when we calculate it            this is equals to 6.67 x 10^21 combinations and this is actually very large number.

      4.  Note equivalent solutions.

       Sudoku puzzles can have multiple solutions that are basically the same because of the nature of the rules.             For example, swapping rows, columns, or numbers within a subgrid will not change the solution. Adjusting           for these equivalent solutions reduces the total number.

       5. Divide by equivalent solutions:

        we can not determine the total number of combinations very precisely. How ever it is estimated approx                6,670,903,752,021,072,936,960.Therefore, divide the total combinations by this estimate to get the number          of unique Sudoku grids.
       According to this given way, we can easily find out the total number of possible ways of  combinations.

Leave a Comment