Sudoku is just a puzzle, but the backtracking technique for solving it is used in many important application domains. To solve a Sudoku without backtracking, you could generate every possible solution, then evaluate all of them and collect the legal ones. But there are 9^81 ways to fill in a Sudoku grid. 9^81 is ~= 2*10^77. If you could evaluate a billion grids per second, it would take 2*10^68 seconds. The universe is less than 10^18 seconds old. For this homework, you will learn the power of backtracking by writing a Sudoku solver that finds answers in just a few seconds.