Guess the color of the hat puzzle, Guess the color of the hat

The woman who put down her hand reasoned like this:

She thought, "If my hat is white, what will the other two women think?" They will think:

There was already a woman whose hat was white, and if my hat was also white, then it would not be possible for all 3 people to raise their hands, so my hat was red', so someone can immediately judge and put down their hand, but no one puts it down, which means that my hat is not white, but red! And so it was reasoned!

This is a typical example of logical reasoning, which is reasoned by using the method of empathy! What are the two upstairs talking about, this is a logical reasoning question, not a ...... make a sharp turnAnd also plagiarism ......

I think the key should be to raise their hands immediately, after the cloth is removed, the hats they see should be in order, and they all immediately raised their hands, indicating that all three are red hats, because as long as one of them is red, they can raise their hands, and the moment they take off the cloth, no matter who they see first, they are all red, so they immediately raise their handsThat's it, super easy.

The logic of this question is actually flawed, so let's solve the problem according to the author's idea: because 3 people raise their hands at the same time, it means that there are at least 2 red hats. Next, if the hat is 2 red and 1 white, then the 2 people wearing red hats can immediately guess their color.

However, until "after a while", no one could guess the color of their hats, which means that all three of them were wearing red hats. So in fact, after "a while", anyone can guess the color of their hat, so back to the topic, the king is looking for smart women, that is to say, there are still "not smart" women, in case there are 2 women who are not smart enough, even if they see the white hat, they don't know how to guess it, then the woman who lets go is smart but is smart and mistaken. So the rigorous question should be: . . .

Screening to the back of the 3 most intelligent women... After a while, all three women put their hands down and guessed the color of their hats, how did they deduce it?

The question says: "The color of the hat is red or white" and because all three of them raise their hands at the same time, there can only be two red hats and one white hat, because this will satisfy the condition that all three people can see the red hats and hold them at the same time.

After the three of them take the cloth, one of them will see the two red hats and raise his hand, and the other two will see one red and one white and raise their hands.

At this point....One of them would see one red and one white and think, "If my hat was white, then there wouldn't be three people raising their hands."

So she made sure her hat was red.

D can see B's hat, and C can see B's hat. Because if D first says the color of his hat, it proves that the color of the BC hat is the same. If you don't say it, you know that C and B's hats are not the same color, and B's hat is yellow, and obviously C's hat is red.

When C gives the answer, B naturally knows the color of his hat, and this is how it is solved.

Let A tell them that they will know.

The 4 hats are A red, B yellow, C red and D yellow.

I can't say it, I can write a, well. Hehe.

It's white.

Because of it. The colors of the hats of the first two people can be: red, white; red, red; white, red; White, white.

And then. If it is the first three cases, the third person will not know what color his hat is, and if it is the fourth, it will do, so the fourth one is excluded.

Then, if it is the first two cases, the first person is red, then the second person has two possibilities.

Since the second person is sure that he knows the color, there is only the third case. White.

If C sees two black hats, then he can be sure that he must be wearing a red hat on his head, because there are only two black hats But since C cannot judge, it can be inferred that what he sees must be two red hats or one red and one black If B sees a black hat, then on the basis of the above reasoning it can be determined that he is wearing a red hat, but he says that he does not know the color of the hat on his head; Therefore, it is logical for A to conclude (even if he is colorblind, even if he is truly blind) that he must be wearing a red hat

C saw that A and B were both red, so he didn't know whether he was black or red.

B sees that A is red, and he does not know whether he is black or red.

And A can guess that he is red.

There were three people wearing black hats. Suppose n people wear black, when n = 1, the person wearing black can affirm that he is black when he sees that everyone else is white. So the first time you turn off the lights, there should be a sound.

N>1 can be determined. For everyone who wears black, he can see N-1 black hats, from which he assumes that he is white. But after waiting for n-1 times and no one has beaten him, everyone who wears black will know that he is also black.

So the nth time the lights are turned off, n people beat themselves.

Let's first set up that the three people are: A, B, C, A's eyes see: white, white, 1) guess that you are: black. He analyzes the psychology of B:

b1) see: white, black, if b = black, c must guess immediately.

c = white, (please note the word immediately).

b2) Seeing that C is not responding, it can also be immediately derived.

b = white, 2) A saw b, c, and did not react, so, pondered for a while.

Guess yourself as: White.

Similarly, a, b, c

They are all in the same situation and the same thinking, so they said in unison that they were wearing a white hat on their heads.