关于史坦因豪斯棋盘问题的一个证明(英文)

A PROOF OF STEINHAUS CHESSBOARD PROBLEM

推广并证明了由著名波兰数学家史坦因豪斯提出的棋盘问题 :在国际象棋棋盘 (8× 8)的某些格子里埋着地雷 ,使得开始时 ,不管把皇后放在哪个格子里 ,皇后总不能从棋盘的左边走到棋盘的右边 ,在这种条件下 ,车 (castle)

The authors extend Hugo D Steinhaus chessboard problem with a detailed proof. The problem says: Some mines are buried in some checks on a chessboard, such that no matter where we put the queen, she can not move from the left side of the chessboard to the right side, under such an assumption, a castle can move from the top side of the chessboard to the bottom side only along those checks where there are mines. We show that it is true for the case of any m×n chessboard.