How did she do it?

Question

You have a square table with four people (one on each side) sitting round it. In the centre of the table there is a large obstruction which prevents each person seeing the person directly in front of them. They are then told to raise their hand if they can see at least one woman either side of them.

In actual fact, all four people are women and so they all raise their hands. They are then told to deduce the sex of the person sitting opposite. After quite a while, one of them successfully works out that the person opposite her is also a woman.

Assuming that no cheating takes place, how could she logically come to this conclusion?

Answer 1

I don't think this relies on being able to see the person across raise his/her hand. I assume the barrier is tall enough to block the face and the raised hand.

Anyway, here's the thinking that is going on in the mind of one of the women:

"Let's assume the person across from me is a man. Then I would expect "him" to announce that "he" knows that I am a woman, because the two women "he" sees are both raising their hands."

But after a short time passes and no announcement is made, the woman realizes that person across from her is also a woman who seems to think there is no conclusion to be made.

So, she announces, correctly, that the person opposite is a woman.

Note: any of the 4 women could have come to the same conclusion, but I guess we assume one woman was able to figure out the "double logic" faster than the other three.

Answer 2

The only thing I can think of is that she looked at either (or both) of the women to each side of her, and saw them raise her (or their) hand(s) after looking at the opposite side from the one the first woman is sitting on. This way, she realizes that they weren't raising their hand because they saw her, but because there was another woman to the other side...that is, across from the first woman.

But I'm guessing that's not the right answer, simply because I often don't come up with the right answer (and it sounds too inarticulate anyways). =P

Answer 3

Because she can see the raised hand of the person opposite, then it obvious that the sex of the woman opposide is a woman, i think , i gotta go and rest now ok ha ha, tell me the answer someone!

Answer 4

because the person in paragraph 2 is desigused a guy, so if both people on both of his sides raise their hand she knows the person opposite of hr is a girl. because they are not raising their hand because of him because he is a 'guy', so the person across from him has to be a girl. i hope im right, by the way, im only 14

Answer 5

well if they all raise their hands then they know the other people are seeing women on the sides of them

Answer 6

it says "...They are then told to raise their hand if they can see at least one woman either side of them..." If they all raised their hands they must have been able to see each other

Answer 7

She happens to be dressed in disguise as a man so she knows that the person opposite her must be a woman.

Answer 8

haha very clever they were asked to raise ther hands if they could see the other women lol they all raised there hand there for they all know there is a female in front of them but only one women answered

i could be very wrong but thats what i think, please post answer soon as its killing me trying to think of it lmao

Answer 9

Because its rigged

Answer 10

kudos to bandf for figuring it out...i was stumped!