Puzzle - What's the answer?

With the information provided we can reconstruct the correct riddle and the correct answer.

First of all the men were not standing in a line facing the same way, because the answer states that they could see each other. It would be silly to ask the front man and the middle man anything if the front man cannot see any of the other men, and the middle man can only see the front man. They just have too little information to know anything.

However, if they all can see each other, then it becomes an interesting riddle. But the answer given is not correct either that the first two men both saw a blue and a red hat (how did that follow from the facts?). Here is the correct reasoning.

Since he did not see two blue hats, the first man did not know the color of his hat. In effect he said that there is at least one red hat in front of him. This information can be used by the second man, who can look at the third man. Since the second man did not know the color of his hat, he must have seen a red hat. But it is irrelevant what the color of the first man's hat is. (I will give a configuration that contradicts the given solution). So, now that the third man knows that the second man saw him wearing a red hat, he knows that he is wearing a red hat.

The configuration could be as follows:
Man 1: red
Man 2: blue
Man 3: red

The first man sees a blue and a red hat.
The second man sees two red hats.
There are more possible configurations.

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A variant of the riddle is the one where they are standing in a line, facing in the same direction.

But then you start asking the last man (who sees both other men).
He will give you the correct answer, whether he knows his color or not.
Then you ask the middle man. He will answer you also correctly.
The question is what the front man is going to say, the one that can not see either of the other men. Does he know the color of is hat?

Answer: Yes, the front man knows what the color of his hat is.
If the last man said that he knows, it means that he saw two blue hats. So in this case, the front man knows immediately what the color of his hat is. If the last man does not know the color of his hat, it means that he sees at least one red hat in front of him.

Now, the middle man can know the color of his hat, if he sees a blue hat, because then he himself must wear a red hat. If he does not know the color of his hat, then it means he sees a red hat.

In all cases, the front man knows the color of his hat when he is asked.

Enjoy.