Homework Help--MATH?

Question

I have a word problem that my friends sister has for homework. We can not figure it oout. Here it is: Three women enter a room with five hats. Two white and three black. No one can se what hat they pick up. They put the hat on their head. They walk out of the room single file, facing straight ahead. They can not see the hats,except for the one(s) in front of them. The last women says,"I can not tell what color my hat is?" The middle women says the same thing. But the first women, who can see no hats, knows what color she is wearing.
Questions:
What color is the hat?
How can she tell?


Thank You so much. She is in 8th grade and will thank you so much. Who ever gets it right will get 10pts.

I will post the answer on here Friday when she gets the paper back with the correct answer!!

Answer 1

The hat is black.

Suppose that both of the women in front had white hats. Then, the woman in back, seeing this, would know that she could not possibly have a white hat, because both of them are being worn by the other women. But she did not know this, therefore we infer that at least one of the first two women is wearing a black hat.

Now suppose that the woman in fron had a white hat. By the previous paragraph, the woman in the middle could deduce that either she or the woman in front is wearing a black hat, and since the first woman is not wearing a black hat, it must be her. But she could not deduce this, therefore the woman in front must be wearing a black hat. She knew this, because she is capable of the reasoning in the preceding two paragraphs.

Note that contrary to the first answer, we really don't know what color the other two women's hats are.

Answer 2

The first woman must be wearing a black hat. If the woman in back saw two white hats, she would know she as wearing a black hat. So she sees either 2 black hats, or one black and one white. If the middle woman saw the first woman wearing a white hat, she would have known that hers was not white based on the third women's statement (because if both women's hats were white, the third women would know her hat was black). Therefore, the first woman knows, based on what the other women can see, that her hat must be black.

Answer 3

If the last woman saw two white hats she would know that she had a black hat. So she either saw two black hats or one white and one black, which meant she could be wearing either. Based on the (lack of) knowledge of the last woman, if the middle woman saw a white hat she would know that she had a black hat on. If she only saw a black hat, then she wouldn't know if her hat was black or white, which means the lead woman had on a black hat.

j

Answer 4

The first woman never changed her hat in the dark room, knowing she had a black hat on the way in, she recalled the white hat.

Answer 5

last sees a black and white or two blacks. if middle saw a white hat then she would know that her own hat was black so the first would have to be wearing black.

Aaaaaaaaaaaaaahhh!!!! I don't know, your frying my brain!

Answer 6

black

Third woman sees a white hat and a black hat

second woman sees a black hat on the first woman and knows that her hat is either color with a 50% chance of black or white

The first woman looks in a mirror and sees a black one on her own head.

Hell, I don't know.

Answer 7

She has a white hat and the ofthers have black and they don't know what color it is because their probably color blind. Hope i helped.

Answer 8

Black, white is like no color

Answer 9

o ya 8th grade gets a lot of questions like that
basiclly u can answer anything if you can explain it however they chose black as the stock was highest

Answer 10

omg i am going crazy trying to figure this out, when you get the answer can you tell me?? and ill get my dad on herer later i bet he can get it