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

  • Bryce Sandlund
  • Kerrick Staley
  • Michael Dixon
  • Steve Butler
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8591)


Numerical Tic-Tac-Toe on the n×n board is a two player game where the numbers {1,2,…,n2} 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(n2 + 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.


Tic-Tac-Toe games symmetry backtracking pruning 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Bryce Sandlund
    • 1
  • Kerrick Staley
    • 2
  • Michael Dixon
    • 2
  • Steve Butler
    • 2
  1. 1.University of Wisconsin–MadisonMadisonUSA
  2. 2.Iowa State UniversityAmesUSA

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