Resolution of Sudokus Using Groebner Basis

Abstract

We study the resolution of sudokus and generalized sudokus using Groebner basis. Let x_1, ..., x_81 the 81 squares which form the sudoku, arranged from left to right and from top to bottom. Its solution will be (a_1, ...,a_81), where a_i is the number in the square associated to the variable x_i.$ Let $S$ be a sudoku with preassigned data {c_{i}}_{iin L}, for Lsubset {1, ..., 81}. All the necessary information to solve the sudoku is contained in the algebraic set mathbb V (I+<{x_{i}-c_{i}}_{iin L}>). We shall use Groebner basis to find a solution and give a SAGE code for that purpose.