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A New Development of the Classical Single Ladder Problem via Converting the Ladder to a Staircase

Author

Listed:
  • Ralph Høibakk

    (Department of Computer Science and Computational Engineering, UiT The Arctic University of Norway, 8514 Narvik, Norway)

  • Dag Lukkassen

    (Department of Computer Science and Computational Engineering, UiT The Arctic University of Norway, 8514 Narvik, Norway)

  • Annette Meidell

    (Department of Computer Science and Computational Engineering, UiT The Arctic University of Norway, 8514 Narvik, Norway)

  • Lars-Erik Persson

    (Department of Computer Science and Computational Engineering, UiT The Arctic University of Norway, 8514 Narvik, Norway
    Department of Mathematics and Computer Science, Karlstad University, 651 88 Karlstad, Sweden)

Abstract

Our purpose is to shed some new light on problems arising from a study of the classical Single Ladder Problem (SLP). The basic idea is to convert the SLP to a corresponding Single Staircase Problem. The main result (Theorem 1) shows that this idea works fine and new results can be obtained by just calculating rational solutions of an algebraic equation. Some examples of such concrete calculations are given and examples of new results are also given. In particular, we derive a number of integer SLPs with congruent ladders, where a set of rectangular boxes with integer sides constitutes a staircase along a common ladder. Finally, the case with a regular staircase along a given ladder is investigated and illustrated with concrete examples.

Suggested Citation

  • Ralph Høibakk & Dag Lukkassen & Annette Meidell & Lars-Erik Persson, 2021. "A New Development of the Classical Single Ladder Problem via Converting the Ladder to a Staircase," Mathematics, MDPI, vol. 9(4), pages 1-18, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:339-:d:495723
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