COCOON 2014: Computing and Combinatorics pp 537-546

# 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)

## 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.

### Keywords

Tic-Tac-Toe games symmetry backtracking pruning

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© Springer International Publishing Switzerland 2014

## Authors and Affiliations

• Bryce Sandlund
• 1
• Kerrick Staley
• 2
• Michael Dixon
• 2
• Steve Butler
• 2