Global Solution for Sudoku

The following sections are included:

• Preface
• Contents

A grid with 9 × 9 cells is divided into nine blocks with 3 × 3 cells. We will call this grid as a Sudoku diagram. In the following, the symbol “Ra” means the ath row in the diagram, the symbol “Cb” means the bth column in the diagram, and the symbol “Bd” means the dth block in the diagram. The cell shared by Ra and Cb is denoted by $\overline{ab}$…

In the previous chapter we solved a very easy problem of Sudoku by the usual local solution. In the solving process even for this easy problem, the player has to observe the distribution of the fixed cells in the Sudoku diagram, to analyze logically, to make inferences, and to determine the correct order of filling the digits. In this chapter we present another method to solve problems of Sudoku, called the global solution, which is so much better than the local solution, especially for hard problems of Sudoku. The main purpose of the present book is to explain the rules in the global solution and to show its high performance through examples. The reader, who is familiar with the local solution, may solve a hard problem of Sudoku first by the local solution, and then by the global solution when meeting trouble…

The following sections are included:

• Problem of Sudoku 1 obtained online
• Problem of Sudoku 2 obtained online
• Problem 3 from World Sudoku Championship
• Problem 4 from World Sudoku Championship
• Problem 5 from World Sudoku Championship
• Problem 6 from World Sudoku Championship
• Problem of Sudoku 7 with n = 17
• Problem of Sudoku 8 with n = 17

The following sections are included:

• Advanced Techniques
• Problem of Sudoku 1 with n = 25
• Problem of Sudoku 2 with n = 26
• Problem of Sudoku 3 with n = 17
• Problem of Sudoku 4 with n = 25
• Problem 5 from World Sudoku Championship
• Problem 6 from World Sudoku Championship
• Problem of Sudoku 7 with n = 24
• Problem of Sudoku 8 with n = 23
• Problem of Sudoku 9 with n = 23

A Sudoku puzzle which has to be solved by trial and error (guessing) is called a hard problem of Sudoku. After some deleting steps, the full diagram of a hard problem of Sudoku becomes a suspected full diagram which is not the answer of Sudoku, but cannot be simplified by the 6 rules of global method. For a suspected full diagram, we have to choose one cell with a few allowed digits and conjecture one allowed digit of the cell such that the cell becomes a fixed cell. The obtained full diagram with the conjectured fixed cell is called a tried full diagram. After a few conjectures, only one series of tried full diagrams can be solved to the answer of Sudoku and the remaining of the tried full diagrams must lead to confliction, if the problem is proper. The confliction means that the basic requirement of the Sudoku game is violated, say a digit appears more than once in a unit. The difficulty level of a hard problem of Sudoku depends on the number of conjectures…

The following section is included:

• Index