The tenth man standing at the end said, "Although I have seen each of your hats, I still don't know what color my hat is." What about you? "
The ninth man said, "I don't know."
The eighth man said, "I don't know."
Seventh, sixth ... until the second man said on the other hand that he didn't know the color of the hat on his head. Unexpectedly, the first man said, "I know the color of my hat."
Excuse me: What color hat is the first person wearing? Why does he know?
There are three red hats, four black hats and five white hats. Let 10 people stand in a row from short to high, each wearing a hat. Everyone can't see the color of his hat, but he can only see the color of the hat of the person standing in front. So the last person can see the color of the hats on the heads of the first nine people, while the first person can't see anyone's hats. Now, start with the last person and ask him if he knows the color of the hat he is wearing. If he says no, keep asking the person in front. Suppose the person in front must know that he is wearing a black hat. Why?
3. A professor who teaches logic has three students, all of whom are very clever! One day, the professor gave them a question. The professor put a note on everyone's forehead and told them that everyone had written a positive integer on the note, and the sum of some two numbers was equal to the third! Everyone can see the other two numbers, but not his own.
The professor asked the first student: Can you guess your own number? Answer: No;
Ask the second one, no;
Third, no;
Ask the first one again, no;
Second, no;
The third one: I guessed it right. 144!
The professor smiled with satisfaction. Can you guess the numbers of the other two? Please tell me the reason!
4. After five pirates robbed 100 gold coins, they discussed how to distribute them fairly. They agreed on the distribution principle is:
(1) Draw lots to determine each person's distribution sequence number (1, 2, 3, 4, 5);
(2) Pirates who draw lots. 1 Propose a distribution plan, and then five people will vote. If the plan is agreed by more than half of the people, it will be distributed according to his plan, otherwise 1 will be thrown into the sea to feed sharks;
(3) If 1 is thrown into the sea, No.2 puts forward the allocation plan, and then four people are left to vote. If and only if more than half of the people agree, they will be allocated according to his proposal, otherwise they will be thrown into the sea;
4 and so on.
Assuming that every pirate is extremely intelligent and rational, they can make strict logical reasoning and rationally judge their own gains and losses, that is, they can get the most gold coins on the premise of saving their lives. At the same time, assuming that the results of each round of voting can be implemented smoothly, what distribution scheme should the pirates who have drawn 1 put forward to avoid being thrown into the sea and get more gold coins?
You and four other people (***5 people) are very smart people. From a total of 5 white hats, 2 red hats and 2 black hats, put 1 hat on everyone at random. Everyone can see the colors of the other four hats, but not their own. At the same time, everyone was asked to infer the color of his hat from the color of other people's hats. You see that the other four people's hats are all white, and everyone is silent for a while. So you guessed the color of your hat (maybe, you are a little smarter than the other four).
May I ask what you guessed? Tell me about your reasoning process.