Angels and demons play games on an infinite chessboard. Every time the devil can dig out any grid on the chessboard, the angel can land by flying 1000 steps on the chessboard; If the angel falls on the dug grid, the angel loses.

Question: Can the devil trap the angel (dig a hole with a thickness of 1000 around the angel)?

This is another classic puzzle of Conway Daniel. People who often read this blog will find that Conway Daniel's appearance rate is extremely high. But this time, Conway really broke the brains of many mathematicians. As a very "normal" combination game, the problem of angels and demons has not been solved. At present, it has been concluded that if the angel can only walk step by step, the devil will surely win. However, as long as an angel can fly two steps at a time, it seems invincible. Of course, the devil's advantage is not small-he doesn't have to worry about "problems", and every extra hole dug is beneficial to him.

On the other hand, Conway himself still seems to believe that angels can win-he offered a reward of $65,438+$0,000 for the devil to win, but only $65,438+$0,000 for the angel to win.

1+ 1=2 is because angels and demons make rules. The angel asked the devil not to walk all the squares at once, and the devil asked the angel not to fly 2000 squares at once. Everything starts with making rules and becomes orderly. If the rules are too old, we should break them and make new rules. Then came subtraction, multiplication and Divison.