Sudokus and Gröbner Bases: Not Only a Divertimento

  • Jesús Gago-Vargas
  • Isabel Hartillo-Hermoso
  • Jorge Martín-Morales
  • José María Ucha-Enríquez
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4194)


Sudoku is a logic-based placement puzzle. We recall how to translate this puzzle into a 9-colouring problem which is equivalent to a (big) algebraic system of polynomial equations. We study how far Gröbner bases techniques can be used to treat these systems produced by Sudokus. This general purpose tool can not be considered as a good solver, but we show that it can be useful to provide information on systems that are —in spite of their origin— hard to solve.


Polynomial Equation Algebraic System Polynomial System Hilbert Scheme Colouring Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jesús Gago-Vargas
    • 1
  • Isabel Hartillo-Hermoso
    • 2
  • Jorge Martín-Morales
    • 3
  • José María Ucha-Enríquez
    • 1
  1. 1.Dpto. de ÁlgebraUniv. de SevillaSevillaSpain
  2. 2.Dpto. de MatemáticasUniv. de CádizPuerto Real, CádizSpain
  3. 3.Depto. de MatemáticasUniv. de ZaragozaZaragozaSpain

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