What is the exact no of distinct sudoku puzzles that can be made?

# Combinations to Sudoku

**supriyas**#2

No clue,how we make sure that we have put enough entries such that there will exist a solution to sudoku puzzle or also how we make sure we have put entries in such a way thats its a valid sudoku.

The only approach I am getting in it is starting with top left corner ,we have 9 entries to fill then from bottom left leaving one entry I have 8 entries like,then similarly 8 entries then 7 entries from left to right in bottom,

But I am not considering anything about that sum in 3 by 3 should also be 9.

Am I on the right path?

I calculated the total unique solutions as 96845.

How I got there:

Start with a blank grid and put an X in Aa. 1 of 9.

Then put another X in Bd. 1 of 6.

Then put an X in Cg. 1 of 3.

So far for X, 9*6*3=162.

Now put an X in Db. There are already 3 places taken by Xs in the

upper third so it has 6 possible spots.

An X then in Ee. 4 choices here.

To finish the middle third put an X in Fh. One of only 2 possibilities.

So, for the middle third, 6*4*2.

Repeat this for the bottom third and the possibilities are 3*2*1.

For one number in a blank grid the total possibilities are: 9*6*3*6*4*2*3*2*1=46656

I proceeded to fill in the rest of the grid and counted the possiblie placements of succesive letters (yes, I used letters to avoid confusion.)

My totals are: A (X, as listed above)46656; B 23040; C 1260; D 17280; E 6400; F 384; G 1728; H 96; I 1.

This yeids a puny total of 96845 unique solutions for a 9x9 grid.

I am not a trained mathematician, and I smoke a lot of crack, so I could be wrong.

**sssrocks**#4

Bro 9!only is the no. of combinations to fill the first line which is far more than your answer.

No Supriyas u r not going in a write path A Sudoku puzzle is defined as a logic based number placement puzzle. The objective is to fill a 9×9 grid with digits in such a way that each column, each row, and each of the nine 3×3 grids that make up the larger 9×9 grid contains all of the digits from 1 to 9. Each Sudoku puzzle begins with some cells filled in. It is important to stress the fact that no number from 1 to 9 can be repeated in any row or column although, the can be repeated along the diagonals.

Each row, column, and nonet can contain each number typically 1 to 9 exactly once.

The sum of all numbers in any nonet, row, or column must match the small number printed in its corner. For traditional Sudoku puzzles featuring the numbers 1 to 9, this sum is equal to 45.