![]() Ī puzzle can be expressed as a graph coloring problem. The general problem of solving Sudoku puzzles on n 2× n 2 grids of n× n blocks is known to be NP-complete. Solving Sudokus from the viewpoint of a player has been explored in Denis Berthier's book "The Hidden Logic of Sudoku" (2007) which considers strategies such as "hidden xy-chains". See Glossary of Sudoku for other terminology. A minimal puzzle is a proper puzzle from which no clue can be removed without introducing additional solutions. A puzzle is a partially completed grid, and the initial values are givens or clues. A band is a part of the grid that encapsulates 3 rows and 3 boxes, and a stack is a part of the grid that encapsulates 3 columns and 3 boxes. Other variants include those with irregularly-shaped regions or with additional constraints ( hypercube). ![]() A rectangular Sudoku uses rectangular regions of row-column dimension R× C. ![]() Unless noted, discussion in this article assumes classic Sudoku, i.e. There are many Sudoku variants, partially characterized by size ( N), and the shape of their regions. same arrangement where all instances of one digit is switched with another digit).
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