RSS FeedsWhat’s the minimum number of filled squares that defines a unique Sudoku (9×9) game?
Let’s say we want to create the hardest set of sudoku games in the world.
How many numbers, the minimum the better, must the game be filled to define a unique Sudoku game (for 9×9)?
It does vary from one solution-grid to another, so far as I know.
There are some conditions that can be stated. The "given" numbers must include at least one instance of each of eight different numbers. (Proof: if two different numbers don’t appear among the "givens," then all their positions could be interchanged to produce a second valid solution.)
There must also be at least one "given" on two out of the three rows in each horizontal rank of 3×3 blocks, and on two out of the three columns in each vertical stack of blocks. (Proof: if two rows in the same rank or two columns in the same stack of blocks are blank, their contents could be interchanged to produce a second valid solution.)
July 4th, 2009
It does vary from one solution-grid to another, so far as I know.
There are some conditions that can be stated. The "given" numbers must include at least one instance of each of eight different numbers. (Proof: if two different numbers don’t appear among the "givens," then all their positions could be interchanged to produce a second valid solution.)
There must also be at least one "given" on two out of the three rows in each horizontal rank of 3×3 blocks, and on two out of the three columns in each vertical stack of blocks. (Proof: if two rows in the same rank or two columns in the same stack of blocks are blank, their contents could be interchanged to produce a second valid solution.)
References :
Wikipedia has an article on the mathematics of sudoku:
http://en.wikipedia.org/wiki/Mathematics_of_Sudoku
It contains a section on "minimum number of givens" that supports my assertion that the number varies, but gives interesting detail: the minimum number of givens for ANY puzzle to guarantee a unique solution is reported as 17.