A grid (or matrix) of 9x9 numbers divided in 3x3 sub-matrix (or blocks)
In each column, row and block of the matrix, all the integers one to nine must occur one and only one time
What is a Sudoku puzzles games
A Sudoku grid where only some numbers are initially given
The target of the puzzle game is to find all the missing numbers and to rebuild the original Sudoku grid
A valid Sudoku puzzle has a unique solution
Features of isBooth Sudoku puzzle games
When you click a number in the grid, all the boxes with the same number, inserted or noted, are highlighted
Two playing modes - pen and pencil - can be selected with the rightmost button on the virtual keyboard
In pen playing mode, you insert numbers in the Sudoku grid - Errors are hilighted
In pencil playing mode, you can make annotation of possible numbers for each cell - clicking on a number already noted, erase that number from the annotations
What material you need to play Sudoku
You can play our Sudoku puzzles online with a smartphone, a laptop, a desktop or a console as the XBOX or the Playstation
You need a modern browser supporting HTML5 (recent Firefox, Chrome or Safari, IE10+, Android 4.4+)
You can play with a touch screen or with a mouse, but not with a keyboard
The total possible valid complete Sudoku are 6,670,903,752,021,072,936,960 (6.67x10^21)
Given a Sudoku, changing two numbers between them, exchanging two horizontal (vertical) bands, exchanging two rows (columns) within the same horizontal (vertical) band, or even transposing the matrix gives back a new valid Sudoku
These means that for each Sudoku, it is possible to generate another 9! x 6^4 x 2 equivalent Sudoku - 940,584,960 members in each class - leaving only 7,092,292,600,576 essentially different Sudoku (classes of equivalence)
Each Sudoku can be stored as a string of 81 numbers for programming purposes and the essential Sudoku can thus be ordered alphabetically
In each equivalent class of Sudoku, choose the first one in alphabetic order as canonical representative of the class
It is not hard to build a brute force program which generate complete Sudoku grids
Then the utility shall take out numbers from the grid to produce a Sudoku puzzle game
The difficulty is to proove that the resulting Sudoku puzzle has a unique solution: better taking out the numbers from the complete grid one by one and check at each iteration if the solution is unique
a minimum grid is reached when it is impossible to take out any number without the solution loosing its uniqueness
The minimum required of initial given numbers for the solution to be unique is known to be 17
However most Sudoku complete grid do NOT contain any subset of 17 numbers allowing to make a valid puzzle: most grid need a minimum of initial given numbers in the range 20-25 to produce a puzzle with a unique solution
Hint: to test for uniqueness, build a routine to solve Sudoku puzzle, then test if the routine output the same result, when you try to solve the Sudoku puzzle after transposing the grid and after each of the four rotations: if the result is always the same, the probability that the puzzle has a unique solution are very high