There is an 8*8 chess board in which two diagnolly opposite corners have been cut off. You are given 31 dominos, and a single domino can cover exactly two squares. Can you use the 31 dominos to cover the entire board? Prove your answer.
不可能，棋盘的格子黑白相间，去掉的对角的颜色是一致的，而每个多米诺骨牌一次盖住1黑1白，因此31个牌盖住31黑和31白，而实际上是30黑32白或者32黑30白，因此不可能