How many possible solutions are there for Sudoku?

6,670,903,752,021,072,936,960 possible
There are 6,670,903,752,021,072,936,960 possible solvable Sudoku grids that yield a unique result (that’s 6 sextillion, 670 quintillion, 903 quadrillion, 752 trillion, 21 billion, 72 million, 936 thousand, 960 in case you were wondering). That’s way more than the number of stars in the universe.

Does Sudoku always have one solution?

The short answer is no. While people commonly think that Sudokus can only have one unique solution, any puzzle with seven or fewer starting clues must mathematically have multiple solutions. This is because in these Sudoku puzzles there cannot be a clue for every digit from 1 to 9 in the initial clue.

How many valid Sudoku puzzles with exactly one solution exist?

Starting from a fully filled Sudoku, you can make many Sudokus (sudoku with one solution). Please refer “Create Classic Sudoku: Make Your Own in Minutes ”) or free E-book from this website. Therefore, there are at least 6,670,903,752,021,072,936,960 Sudoku puzzles exist (puzzles with one solution).

How many different possible 9×9 Sudoku grids are there?

The number of Sudoku grids on a 9×9 board is 6,670,903,752,021,072,936,960. This number is given in Felgenhauer and Jarvis’ article Enumerating possible Sudoku grids.

Is there more than one solution?

A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line).

What is the sum of all the numbers in any mini grid of a completed sudoku puzzle?

There are 9 rows, 9 columns and 9 squares. The sum of 1 to 9 is 45. 45×9= 405. Each set of 9 cells add up to 45 and there are 9 sets and so the sum is 45*9 = 405.

How do you check for multiple solutions in sudoku?

A sudoku can have multiple or unique solution based on the clues and their positions in the grid. If a sudoku has less than 17 clues then it will definately have mutliple solutions. But if it has 17 or more clues it can have unique or multiple solutions based on the clues positions.

Are all Sudoku solutions unique?

Most Sudoku puzzles published have only one solution. If there is more than one solution, it is probably a mistake. That said, puzzles with incomplete clues can have multiple solutions. In the extreme case, a puzzle with no clues has 6,670,903,752,021,072,936,960 solutions according to Wikipedia.

Can a Sudoku puzzle have more than one solution?

Most Sudoku puzzles published have only one solution. If there is more than one solution, it is probably a mistake. That said, puzzles with incomplete clues can have multiple solutions.

How many grids are there in the world of Sudoku?

The main results are that for the classical Sudoku the number of filled grids is 6,670,903,752,021,072,936,960 (6.67 × 1021), which reduces to 5,472,730,538 essentially different groups under the validity preserving transformations. There are 26 types of symmetry, but they can only be found in about 0.005\% of all filled grids.

What is the difference between arithmetic and Sudoku?

Sudoku is not really about arithmetic at all, the numbers in each cell are just symbols. You could replace the symbol for a “7” with anything (as long as you did it throughout) and it would be just as valid a puzzle requiring exactly the same logical techniques.

How to construct Sudokus and related numbers?

As in the case of Latin squares the (addition- or) multiplication tables ( Cayley tables) of finite groups can be used to construct Sudokus and related tables of numbers. Namely, one has to take subgroups and quotient groups into account: