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Solving a hard Sudoku puzzle turns on a system of constraints. A constraint is a mathematical concept which forces an object to fish or fowl but not both. For Sudoku this means in some cases that a number can be in one place but not another. You are on your way to solving the puzzle when the constraints tell you that the number MUST be one value and that it CANNOT be any other value. The constraints for a Sudoku puzzle are inherent in the description of the puzzle. All rows must contain the sequence 1 through 9 in any order once and only once. All columns must contain the sequence 1 through 9 in any order once and only once. And finally, each of the 9 matrices that constitute the puzzle can contain the numbers 1 through 9 in any order once and only once. If you need more clues read all about it here: How to Solve a Difficult Sudoku Problem
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