IDEAS home Printed from https://ideas.repec.org/a/inm/orited/v19yi1p48-55.html
   My bibliography  Save this article

Puzzle—Solving the n -Fractions Puzzle as a Constraint Programming Problem

Author

Listed:
  • Arnaud Malapert

    (Université Côte d’Azur, CNRS, I3S, France)

  • Julien Provillard

    (Université Côte d’Azur, CNRS, I3S, France)

Abstract

The aim in solving puzzles is to find the solution using several clues and restrictions. In this paper, we solve a numerical puzzle, the n -fractions puzzle, by constraint programming. The n-fractions puzzle is problem 41 of the CSPLib, a library of test problems for constraint solvers. Models referenced in the CSPLib return invalid solutions as soon as the number n of fractions exceeds five. To solve the n -fractions puzzle, we first provide an upper bound for the unsatisfiability inspired by constraint filtering techniques. Then we propose two new constraint programming models that exploit the integer factorization of the fractions’ denominators and their lowest common multiple. The proposed models can solve up to the 19-fractions puzzle within a few minutes and without returning invalid solutions. Some restrictions of the models that eliminate invalid solutions still allow them to solve larger n -fractions puzzles, even if the solving times increase. At the end, only six n-fractions puzzles remain open.

Suggested Citation

  • Arnaud Malapert & Julien Provillard, 2018. "Puzzle—Solving the n -Fractions Puzzle as a Constraint Programming Problem," INFORMS Transactions on Education, INFORMS, vol. 19(1), pages 48-55, September.
    • Handle: RePEc:inm:orited:v:19:y::i:1:p:48-55
    DOI: 10.1287/ited.2017.0193
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/ited.2017.0193
    Download Restriction: no
    File URL: https://libkey.io/10.1287/ited.2017.0193?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:orited:v:19:y::i:1:p:48-55. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.