Here men were invited to lunch one day. The host places them in a line on three chairs. The men are positioned in such as way that Man #3 can see both Man #1 and Man #2 , Man #2 can see only Man # 1 , and Man #1 can see none of the other men. The host then show each man 5 hats , 2 of which are black and 3 of which are white . After this he blindfolds the men, places one hat on each of there heads , and removes the blindfolds again. The host asks if any of the men can determine the color of his hat within one minute. None of the men can see his own hat. After 59 seconds , Man #1shouts out the color of his hat ! He is correct.
What is the color of Man #1 hat, and how does he know ?
Man #1's hat is black. He knows this because of the information provided about the positions and visibility of the other men in the line.
Let's go through the reasoning step by step:
1. Man #3 can see both Man #1 and Man #2. If both of their hats were white, Man #3 would know that his own hat must be black because there are only 2 black hats in total.
2. However, Man #3 remains silent. This implies that he cannot see two white hats in front of him (since if he did, he would know his own hat color is black). Therefore, Man #3 must see at least one black hat in front of him.
3. Man #2 can only see Man #1. If Man #1's hat were black, Man #2 would see that and quickly realize his own hat color is white. However, Man #2 remains silent.
4. This means that Man #2 does not see Man #1 wearing a black hat. Therefore, Man #1's hat cannot be black and white, otherwise, Man #2 would know his own hat color is white.
5. Since Man #2 remains silent, it means he sees a white hat on Man #1. Now, Man #1 knows that his own hat must be the remaining black hat since there are only 2 black hats in total.
Therefore, Man #1 correctly deduces that his hat is black and confidently announces it after 59 seconds.
The color of Man #1's hat is black, and he knows this by observing the hats of the other men and making an inference based on the information he has.
Here's the explanation of how Man #1 can determine the color of his hat:
1. Man #1 cannot see the hats of the other men, so he must rely on their reactions and deductions from their positions.
2. Man #3 is able to see both Man #1 and Man #2's hats. If Man #3 sees two white hats, he would conclude that his own hat must be black, as there are only two black hats available. However, since Man #1 confidently states the color of his hat, we can deduce that Man #3 must see at least one black hat.
3. Man #2, who can only see Man #1's hat, should be able to figure out the color of his own hat based on Man #3's reaction. If Man #2 sees that Man #3's hat is white, he would conclude that his own hat must be black, as there are only two black hats available. However, since Man #1 also confidently states the color of his hat, we can deduce that Man #2 sees a black hat on Man #3.
4. Since Man #2 sees a black hat on Man #3 and Man #1 states the color of his own hat with confidence, Man #1 realizes that he, himself, must be wearing a black hat. He could deduce this because if his own hat were white, then both Man #2 and Man #3 would see two white hats and conclude that their own hats are black.
Therefore, Man #1 shouts out that he is wearing a black hat.