By popular demand, (well Big T is popular

), I present three new brainteasers:
1Four intrepid explorers are captured by bandits in the desert. They are knocked out, and when they come to, they find that they are all buried in the sand up to the tops of their necks, so they cannot turn their heads. They are buried in a line, one behind the other, so they can each see the backs of the heads of those in front of them, except for the one in front, who is behind a wall, so he can't see any of the others and they can't see him.
They are each wearing a brimless hat.
The leader of the bandits then says to them, "Two of you are wearing red hats, and the other two are wearing green hats. If any one of you can correctly guess what colour hat they're wearing, then all of you can go free. But if you guess wrongly then we'll leave you all here to die. Only one of you is allowed to speak.
After a few minutes, one of them guesses - correctly - and they are all freed.
Which one of the four spoke, and how did he know what colour hat he was wearing?
2You're following a road through the jungle, and come to a fork in the road. You know that the one road leads to where you want to go, and the other road leads to certain disaster. There is a tribesman standing at the fork. You know that there are two tribes living in the jungle, the members of the one who always tell the truth, and the other whose members always lie. You don't know which of the two tribes he belongs to.
You ask him one question, and his answer leaves you in no doubt as to which road to take.
What's your question?
3Two distinguished maths professors meet at a pub after not seeing each other since they were students. They sit down to eat in the pub garden,and start talking about their lives.
"Do you have any kids?", asks the one.
"Three boys", comes the reply.
"How old are they?"
"Well, the product of their ages is 36", was the answer (they used to enjoy quizzing each other)
The other thought about this for a few moments, then said, "You'll have to give me a bit more than that"
"Well, the sum of their ages is the same as the number of cars in the parking lot"
He pondered this a bit longer, then said, "I'm afraid I need another clue".
"Ok then, my eldest son wears glasses".
He then gave him the answer immediately.
How old were they?