The 3 × 3 × … × 3 Points Problem solution

Marco Ripà
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 25, 2019, Number 2, Pages 68-75
DOI: 10.7546/nntdm.2019.25.2.68-75
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Authors and affiliations

Marco Ripà

sPIqr Society, World Intelligence Network
Rome, Italy

Abstract

We offer the first proof of Ripà’s 3 × 3 × 3 × 3 Dots Problem, providing a general solution of the 3k case (3k points arranged in a 3 × 3 × … × 3 grid), for any k ∈ ℕ − {0}. We give also new bounds for the n × n × n problem, improving many of the previous results.

Keywords

  • Graph theory
  • Topology
  • Combinatorics
  • Four-dimensional
  • Nine dots
  • Creative thinking
  • Segment
  • Connectivity
  • Outside the box
  • Upper bound
  • Lower bound
  • Point
  • Game

2010 Mathematics Subject Classification

  • 91A43
  • 05C40

References

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  2. Loyd, S. (1914). Cyclopedia of Puzzles. The Lamb Publishing Company, p. 301.
  3. Lung, C. T., & Dominowski, R. L. (1985). Effects of strategy instructions and practice on nine-dot problem solving. Journal of Experimental Psychology: Learning, Memory, and Cognition, 11 (4), 804–811.
  4. Ripà, M. (2016). The n × n × n Dots Problem optimal solution. Notes on Number Theory and Discrete Mathematics, 22 (2), 36–43.
  5. Ripà, M. (2014). The Rectangular Spiral or the n1 × n2 × … × nk Points Problem. Notes on Number Theory and Discrete Mathematics, 20 (1), 59–71.
  6. Ripà, M., & Bencini, V. (2018). n × n × n Dots Puzzle: An Improved “Outside The Box” Upper Bound, viXra, 25 Jul. 2018, Available online: http://vixra.org/pdf/1807.0384v2.pdf.
  7. Sloane, N. J. A. (2013). A225227. The Online Encyclopedia of Integer Sequences, Inc. 2 May. 2013. Web. 25 Aug. 2015, Available online: http://oeis.org/A225227.
  8. Sloane, N. J. A. (2015). A261547. The Online Encyclopedia of Integer Sequences Inc. 24 Aug. 2015. Web. 22 Sep. 2015, Available online: http://oeis.org/A261547.

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Cite this paper

APA

Ripà, M. (2019). The 3 × 3 × … × 3 Points Problem solution. Notes on Number Theory and Discrete Mathematics, 25(2), 68-75, doi: 10.7546/nntdm.2019.25.2.68-75.

Chicago

Ripà, M. “The 3 × 3 × … × 3 Points Problem solution.” Notes on Number Theory and Discrete Mathematics 25, no. 2 (2019): 68-75, doi: 10.7546/nntdm.2019.25.2.68-75.

MLA

Ripà, M. “The 3 × 3 × … × 3 Points Problem solution.” Notes on Number Theory and Discrete Mathematics 25.2 (2019): 68-75. Print, doi: 10.7546/nntdm.2019.25.2.68-75.

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