I was wondering if there is a way to solve these puzzles with matricies and/or diophantine equations: http://www.sudoku.com/ If you define the basis as nine orthogonal vectors, and input the given initial values to the corresponding places in a 9X9 matrix, and also brake it up into 9 3X3 matricies, and also use the fact that the cross product of all values in each 3X3 matrix (amongst themselves) = 0, and also the cross products in the set of values in each column and row of the 9X9 matrix = 0. could you find a way to solve the puzzle for uniquie values using linear algebra? You could also approach it with a set of diophantine equations. In the 9X9 matrix, the set of values in each row and column must add up to 45, and also the values in each 3X3 matrix must add to 45. I just can't put these ideas together in a way that lets me solve the problem... the reason why I put it in this section is because I think there is some combinatorical apporach too. Maybe I should've put it in a different section.