Six teenagers ABCDEF are sitting around a regular hexagon, and another teenager G is sitting in the middle with a towel (so G can't see anything). Each of them is wearing a hat, including four white hats and three black hats.

It was blocked by g, and everyone around six people couldn't see clearly what color hat the person directly opposite was wearing. People can't tell what color hat he is wearing.

Turn left | turn right

Now let ABCDEF six people guess what color hats they are wearing.

At first, six people who didn't guess, are in meditation. At this time, G sitting in the middle said, "I'm wearing a white hat."

Excuse me: how does G reason?

first step

AD two people can't see each other.

Assuming that AD is all white hats, AD can see two white hats and three black hats among the five people in BCEFG. In this case, because there are three black hats, AD can immediately guess that there is a white hat on his head. So it is impossible for AD to have a white hat on his head.

Assuming that all AD's are black hats, AD can see four white hats and 1 black hats among the five people in BCEFG. In this case, because there are four white hats, AD can immediately guess that there is a black hat on his head. So it is impossible for AD to have a black hat on his head.

So, the six people sitting around didn't guess, indicating that AD should have a white hat and a black hat on his head, and no one knows who is white or black.

Second step

The six people sitting around didn't guess, indicating that AD was wearing a white hat and a black hat. BE, like AD, should wear a white hat and a black hat on his head. Similarly, cf. So G knows that everyone can't guess. G knows that six people around him are wearing three white hats and three black hats, so G knows that his head should be a white hat.