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Numerical Tic-Tac-Toe on the 4×4 Board

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Computing and Combinatorics (COCOON 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8591))

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Abstract

Numerical Tic-Tac-Toe on the n×n board is a two player game where the numbers {1,2,…,n 2} are divided between the two players (usually as odds and evens) and then players alternately play by placing one of their numbers on the board. The first player to complete a line of n numbers (played by either player) that add up to n(n 2 + 1)/2 is the winner. The original 3×3 game was created and analyzed by Ron Graham nearly fifty years ago and it has been shown that the first player has a winning strategy. In this paper we consider the 4×4 game and determine that in fact the second player has a winning strategy.

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References

  1. Graham, R.: Personal communication

    Google Scholar 

  2. Hansen, B.: Personal communication

    Google Scholar 

  3. can den Herik, H.J., Uiterwijk, J.W.H.M., van Rijswijck, J.: Games solved: Now and in the future. Artificial Intelligence 134, 277–311 (2002)

    Article  MATH  Google Scholar 

  4. Markowsky, G.: Numerical tic-tac-toe–I. J. of Recreational Math. 22, 114–123 (1990)

    MATH  Google Scholar 

  5. Markowsky, G.: Numerical tic-tac-toe–II. J. of Recreational Math. 22, 192–200 (1990)

    MATH  Google Scholar 

  6. Munroe, R.: xkcd: Tic-Tac-Toe, http://xkcd.com/832/

  7. Orr, S., Cooper, C.: A compact strategy for numerical tic-tac-toe. J. of Recreational Math. 27, 161–171 (1995)

    Google Scholar 

  8. Schaeffer, J., Burch, N., Björnsson, Y., Kishimoto, A., Müller, M., Lake, R., Lu, P., Sutphen, S.: Checkers is solved. Science 317, 1518–1522 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  9. Thompson, K.: Retrograde analysis of certain endgames. ICCA Journal 9, 131–139 (1986)

    Google Scholar 

  10. Allis, L.V., van der Meulen, M., van den Herik, H.J.: Proof-number search. Artificial Intelligence 66(1), 91–124 (1994)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. University of Wisconsin–Madison, Madison, WI, 53706, USA

    Bryce Sandlund

  2. Iowa State University, Ames, IA, 50011, USA

    Kerrick Staley, Michael Dixon & Steve Butler

Authors
  1. Bryce Sandlund
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  2. Kerrick Staley
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  3. Michael Dixon
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  4. Steve Butler
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Georgia State University, 34 Peachtree Street, Suite 1410, 30303, Atlanta, GA, USA

    Zhipeng Cai

  2. Department of Computer Science, Georgia State University, 34 Peachtree Street, Suite 1443, 30303, Atlanta, GA, USA

    Alex Zelikovsky

  3. Department of Computer Science, Georgia State University, 34 Peachtree Street, Suite 1449, 30303, Atlanta, GA, USA

    Anu Bourgeois

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© 2014 Springer International Publishing Switzerland

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Sandlund, B., Staley, K., Dixon, M., Butler, S. (2014). Numerical Tic-Tac-Toe on the 4×4 Board. In: Cai, Z., Zelikovsky, A., Bourgeois, A. (eds) Computing and Combinatorics. COCOON 2014. Lecture Notes in Computer Science, vol 8591. Springer, Cham. https://doi.org/10.1007/978-3-319-08783-2_46

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  • DOI: https://doi.org/10.1007/978-3-319-08783-2_46

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08782-5

  • Online ISBN: 978-3-319-08783-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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