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

Abstract

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. © 2014 Springer International Publishing Switzerland.