论文标题
序列4
Tic-Tac-Toe on an Affine Plane of order 4
论文作者
论文摘要
TIC-TAC-TOE的游戏是众所周知的。特别是，在其经典版本中，它以任何玩家都无法表现而闻名。虽然从经典上讲，它是在网格上播放的，但自然要考虑玩游戏对富裕结构（例如有限飞机）的效果。以前已经研究了在有限仿射和投影飞机上玩TIC-TAC-TOE的游戏。虽然第二个球员通常可以迫使抽签，但对于小订单来说，第一个球员有可能获胜。在这方面，计算机证明了TIC-TAC在Order 4的仿射平面上播放的是首次胜利。在本说明中，我们使用拉丁正方形和横向设计理论中的技术来为人类可验证的，明确的证明这一事实。
The game of tic-tac-toe is well known. In particular, in its classic version it is famous for being unwinnable by either player. While classically it is played on a grid, it is natural to consider the effect of playing the game on richer structures, such as finite planes. Playing the game of tic-tac-toe on finite affine and projective planes has been studied previously. While the second player can usually force a draw, for small orders it is possible for the first player to win. In this regard, a computer proof that tic-tac-toe played on the affine plane of order 4 is a first player win has been claimed. In this note we use techniques from the theory of latin squares and transversal designs to give a human verifiable, explicit proof of this fact.
