Solving 7,7,5-game and 8,8,5-game

Abstract

An mnk-game is a kind of k-in-a-row game played on an m x n chess board, where two players alternatively mark empty squares with their own colors and the first one to get k-consecutive marks wins. This paper solves 7,7,5-game and 8,8,5-game as draws. In the proof, we propose some methods based on pairing strategies and potential weights, and then use a program implementing these methods to solve 7,7,5-game in about one minute and 8,8,5-game in about three days.