A class containing a 1d array of 81 ints (0 is empty) is sufficient for the rule class. The rule class enforces the rules (no duplicate numbers in each row, column or 3x3 square). It also has an array of 81 bools so it knows which cells are fixed and which need to be solved. The public interface to this class has all the methods you need to manipulate the board:
int getCell(int x, int y);
bool setCell(int x, int y, int value);
bool clearCell(int x, int y);
int[] getRow(int x);
int[] getCol(int y);
int[] getSubBox(int x, int y);
void resetPuzzle();
void loadPuzzle(InputStream stream);
Then your solver uses the public interface to this class to solve the puzzle. The class structure of the solver I presume is the purpose of writing the 5 millionth Sudoku solver. If you are looking for hints, I'll edit this post later.
