Resolution of Sudokus Using Groebner Basis

Abstract

We study the resolution of sudokus and generalized sudokus using Groebner basis. Let x1, . . . , x81 the 81 squares which form the sudoku, arranged from left to right and from top to bottom. Its solution will be (a1, . . . , a81), where ai is the number in the square associated to the variable xi . Let S be a sudoku with preassigned data {ci }i∈L , for L ⊂ {1, . . . ,81}. All the necessary information to solve the sudoku is contained in the algebraic set V(I+< {xi − ci }i∈L >). We shall use Groebner basis to find a solution and give a SAGE code for that purpose.