When Hua was a teenager, he especially loved math, but his math performance was not outstanding. 19 years old, an excellent article shocked the famous mathematician Xiong Qinglai at that time. From then on, under the guidance of Mr. Xiong Qinglai, he embarked on the road of studying mathematics. In his later years, for the sake of national economic construction, he applied pure mathematics to industrial and agricultural production and struggled for the construction of the motherland for life. Grandpa Hua carefully cultivated the younger generation. Let young mathematicians thrive and make them stand out. After work, they don't forget to write some popular science books for their friends for many years. Here is an interesting math game that Grandpa Hua once introduced to his classmates. A teacher wants to know which of his three students is smarter. He took the following measures: show them three white hats and two black hats in advance, then tell them to close their eyes, put on their hats and hide the remaining two. Tell them to open their eyes, look at other people's hats and say the color of their hats. The three students looked at each other, hesitated for a moment, and told them in unison that they were wearing white hats. Think about it. How do they know the color of their hats? "In order to solve the above problems, let's first consider the problem of' two people 1 black hat and two white hats'. Because,

In this way, the problem of "three people, two blacks and three whites" will be solved. If I wear a black hat, the two of them will become a question of "1 two people in black hat and two people in white hat", and they can answer it immediately, but they all hesitated for a while, which means that I wear a white hat, and all three of them have gone through the same thinking, so they all think it over. Students may clap their hands and say it is wonderful. Grandpa who came to China later complicated the original problem. How to solve the problem of "n people, n- 1 black hat and several (not less than n) white hats" can be solved in the same way. He also warned us that complex issues should be good at "retreating" and retreating enough.