A Sudoku puzzle can have more than one solution, but in this case the kind of logical reasoning we described while discussing solving strategies may fall short. It turns out that for a Sudoku of rank n, at least n2-1 distinct symbols must be used for the puzzle to have a unique solution.
Can Sudoku have more than 9 numbers?
The game of Sudoku consists of a grid of nine rows and nine columns subdivided into nine 3×3 subgrids. It has two basic rules: Each column, each row, and each box (3×3 subgrid) must have the numbers 1 to 9. No column, row or box can have two squares with the same number.
How many solutions can a Sudoku have?
There are exactly 6, 670, 903, 752, 021, 072, 936, 960 possible solutions to Sudoku (about 10^21) . That’s far more than can be checked in a reasonable period of time.
How many digits are there in a Sudoku puzzle?
Sudoku is a number puzzle consisting of a 9 x 9 grid in which some cells contain clues in the form of digits from 1 to 9. The solver’s jobs is to fill in the remaining cells so that each row, column and 3×3 box in the grid contains all nine digits. There’s another unwritten rule: the puzzle must have only one solution.
How is a number guaranteed to fit in a cell in Sudoku?
You know that each block, row and column on a Sudoku board must contain every number between 1 and 9. Therefore, if a number, say 4, can only be put in a single cell within a block/column/row, then that number is guaranteed to fit there. This example illustrates the number 4 as the unique candidate for the cell marked in red.
What happens when the rank of a Sudoku increases?
As the rank of a Sudoku increases from n to n+1, the extra computational time needed to find a solution increases quite fast. This places the game of solving rank-n Sudoku puzzles in a class of problems that computer scientists have named NP-complete. An NP-complete problem satisfies the following two properties:
Which is the largest number of empty rows in Sudoku?
The largest total number of empty groups (rows, columns, and boxes) in a Sudoku is believed to be nine. One example is a Sudoku with 3 empty rows, 3 empty columns, and 3 empty boxes (third image). [77] [78]
