There are 3 men sitting in a row facing the same way. Their names are A,B, AND, C. a hat has been placed on their heads without them seeing their own or anyone else's. A can see B and C, B can see only C, C sees none. The game goes as follows: (it can have 1,2,3 quest.)
A is asked if he knows the color of the hat on his head. If he says "yes" the game is over. What's his hat color and why?
If A says "No", then B is asked if he knows the color of his hat and if he says "yes" the game is over. whats his hat color and why?
If B says "no" then C says "yes". What is the color of his hat and why?
Let's analyze the scenarios step by step:
1. A is asked if he knows the color of the hat on his head. If he says "yes," the game is over. What's his hat color and why?
- Since A can see B and C, he can determine the color of his hat based on the colors he sees on B and C.
- If A sees that both B and C are wearing hats of different colors, he would know that his hat must be the remaining color.
- However, if A sees that both B and C are wearing hats of the same color, he would not be able to determine his own hat color.
- Therefore, if A says "No," it means that B and C must be wearing hats of the same color. A's hat color could be either color.
2. If A says "No," then B is asked if he knows the color of his hat. If he says "yes," the game is over. What's his hat color and why?
- B can only see C's hat and cannot determine the color of his own hat based on that information alone.
- However, B heard A's answer and knows that A and C must be wearing hats of the same color.
- If A said "No," it means that B's hat color must be the same as C's hat color.
- Therefore, if B says "No," it indicates that both C and himself are wearing the same colored hats.
3. If B says "no," then C says "yes." What is the color of C's hat and why?
- Based on B's answer, C knows that both B and himself are wearing hats of the same color.
- Since C cannot see anyone else's hat, he cannot determine the color of his hat.
- However, since B said "No" and C knows that B cannot determine his own hat color, C can conclude that he must be wearing the opposite colored hat as A, who has not said "Yes" yet.
- Therefore, if C says "Yes," it means that his hat color is different from A's hat color.
To summarize:
- If A says "No," B and C are wearing hats of the same color.
- If B says "No," C and B are wearing hats of the same color.
- If C says "Yes," C's hat color is different from A's hat color.
To solve this puzzle, we need to analyze the information given and think logically step by step.
Let's break down the different scenarios:
1. A is asked if he knows the color of the hat on his head. If he says "Yes," the game is over. What's his hat color and why?
Since A can see B and C but cannot deduce his own hat's color, we can conclude that both B and C must be wearing hats of the same color. If A sees two hats of the same color, it means that his own hat must be of the opposite color. Therefore, if A says "Yes," his hat color is the opposite of B and C's hat color.
2. A says "No," then B is asked if he knows the color of his hat. If he says "Yes," the game is over. What's his hat color and why?
Since A said "No," it means that A's hat color is the same as either B or C. If both B and C had the same color hats, B would see that C's hat is of the same color and be able to deduce his own hat's color. However, since B does not know the color of his hat, it means that A's hat color is different from C's hat color. Therefore, if B says "Yes," his hat color is the opposite of C's hat color.
3. If B says "No," then C says "Yes." What is the color of C's hat and why?
If B says "No," it means that A's hat color is different from C's hat color. Therefore, C can determine the color of his own hat based on A and B's answers. Since A said "No," C can see that his own hat must be the opposite of A's hat color. Thus, if C says "Yes," his hat color is the opposite of A's hat color.
In summary:
1. If A says "Yes," his hat color is the opposite of B and C's hat color.
2. If B says "Yes," his hat color is the opposite of C's hat color.
3. If C says "Yes," his hat color is the opposite of A's hat color.
Please note that this puzzle assumes that the men in the row are all logical and honest.