Three people enter a room and have a green or blue hat placed on their heads. They cannot see their own hat but can see the other hats.
The colour of each hat is purely random. They could all be green, blue, or any combination of green and blue.
They need to guess their own hat colour by writing it on a piece of paper, or they can write 'pass'.
They cannot communicate with each other in any way once the game starts. But they can have a strategy meeting before the game.
If at least one of them guesses correctly they win $10,000 each, but if anyone guesses incorrectly they all get nothing.
What is the best strategy?

I am taken from a mine and shut up in a wooden case, from which I am never released, and yet I am used by almost every person. What am I?

I am the black child of a white father, a wingless bird, flying even to the clouds of heaven. I give birth to tears of mourning in pupils that meet me, even though there is no cause for grief, and at once on my birth, I am dissolved into air. What am I?

There is a straight highway. Four different villages lie on that highway. The distance between them is different. The third village is 60km away from the first village; the fourth is 40 km away from the second; the third is 10 km near to the fourth that it is to the second.

Can you calculate the distance between the fourth and the first village ?

Alpha is Beta's sister.

Gamma is a Beta mother.

Delta is Gamma's father.

Tango is Delta's mother.

Then,

How is Alpha related to Delta?

This is a most unusual paragraph. How quickly can you find out what is so unusual about it? It looks so ordinary, you'd think nothing was wrong with it. Actually, nothing IS wrong with it. But it is not as ordinary as you might think. If you think about it for a bit, you will find out why it is truly so unusual. So what is it? What is so unordinary about this paragraph?

There is a circular car race track of 10km. There are two cars, Car A and Car B. And they are at the exact opposite end to each other. At Time T(0), Both cars move toward each other at a constant speed of 100 m/seconds. As we know both cars are at the same speed they will always be the exact opposite to each other.
Note, at the center, there is a bug which starts flying towards Car A at time T(0). When the bug reaches car B, it turns back and starts moving towards the car A. The speed of bug is 1m/second. After 5 hours all three stop moving.
What is the total distance covered by the bug?

Why are all black people so quick ?

John was working on a Chemical Mixture whose weight comprise 90% liquid and 10% solid. The total weight of the mixture is 20 pounds. After a while, John noticed that some of the liquid evaporated and now the liquid comprises just 50% of the weight.

What is the weight of the chemical mixture now?

A wife and her husband were driving in their car on the highway. All of a sudden, they ran out of gas. So the husband said to the wife, 'Now, you stay here. I will go down the highway to the nearest gas station, and it will be about 1 hour. Just listen to the radio and read some books, and remember to lock all the windows and doors. I will leave the keys with you.' So, off the husband went, and the wife first locked ALL the windows and doors. Next, she turned on the radio, and this is what she heard on the news report:
'THERE IS A MURDERER ON THE LOOSE. HE WAS LAST SEEN ON THE HIGHWAY, WEARING ALL BLACK, ABOUT 5 FOOT 11 INCHES. PLEASE, BE AWARE AND CONTACT THE POLICE IMMEDIATELY.' The wife got very scared. She turned off the radio and double-checked the locked doors. Then she saw the murderer, only a couple of feet away from the car. An hour later, the husband returned to his car. Inside the car, his wife was DEAD, she had been murdered. All the windows were still locked, and the doors. No windows were broken, and the car was in PERFECT condition. No scratches or anything, it was the same way as when he left it. How did the murderer kill the wife?