There are currently many versions of the five hats on the Internet. The following two versions are used for analysis.
Version one:
question
There are 3 red hats and 2 white hats. Now give 3 of them to 3 people in a column, each wearing one, and each can only see the hats of the person in front of him, but not the hats of himself and the person behind him. At the same time, the 3 people do not know the color of the remaining 2 hats (but they all know that their 3 hats are taken from the 3 red hats and the 2 white hats).
First ask the person standing at the back of the 3 people: "Do you know what color your hat is?" The person at the back replies: "I don't know."
Then he asked the man in the middle if he knew the color of his hat. Although the person in the middle heard the answer from the person behind, he still replied that he did not know the color of the hat he was wearing.
After listening to the answers from the two of them, the person at the front answered the color of his hat without waiting to ask.
Do you know why the man at the front knows the color of his hat? What color is his hat?
logical analysis
This is a typical logic question. The exclusion method is used in the question. The specific analysis is as follows:
3 people line up in a column, named A, B, and C from front to back. The logical reasoning steps are as follows:
a. C, who is standing at the back, can see the colors of the hats of A and B, but after seeing the hats of A and B, he says he does not know, indicating that A and B are not all wearing white hats, at least one of them is red.
b. In the middle, B can see the color of A's hat, but after seeing it, B says he doesn't know, indicating that A must be wearing red, and B himself may be either red or white, so he doesn't know who he is what colour. If A is wearing white, then B can only be red, because if it is white, C can't say he doesn't know, and B can only be red, then B can't say he doesn't know after seeing it, so the exclusion method can also be determined The armor is red.
c. The front A has passed the above conclusion and knows after exclusion that he is wearing a red hat.
Version two:
question
A teacher showed three bright students a look at five prepared hats: three white and two black. Then ask them to close their eyes, put a hat on each, hide the rest of the hat, and then ask the three students to open their eyes and say the color of their hat, they see each other, hesitate for a while, almost At the same time, the answer was given. How do they judge the color of their hats? What color hats do they wear?
logical analysis
All three of them wore white hats on their heads.
Reasoning process: (the key to reasoning: hesitating for a while, feeling embarrassed)
The three students are identified as A, B, and C. Student A reasoned like this: If I am wearing a black hat, then B sees the black hat on my head, and he also assumes that he is wearing a black hat. If both assumptions are correct, then C sees two black hats, and C should immediately say that he has a white hat on his head. But C hesitated, which means that what C saw was not two black hats. In this case, if the hypothesis that I have a black hat on my head is true, then B sees C's hesitation and knows that he is not a black hat on his head. So B should immediately say that he has a white hat on his head. But B also hesitated. This shows that my head is not a black hat, it should be a white hat.
The other two reasoned the same.