I look at you, you look at me I raise my right, you raise your left. What am I?

You are given 16 witch hats. The hats are divided in four different colours – red, blue, green and yellow. Every colour has been assigned to four hats. Now each of the hat will be glued with a label of an arithmetic sign – ‘+’, ‘-‘, ‘x’ or ‘/’. But you can label one sign only once on one colour. In such an arrangement, the hats can be uniquely defined by its colour and symbol.

Can you arrange all the 16 hats in a 4x4 grid in a fashion that no two rows and columns have a repetition of colour or sign?
We have arranged four hats in the below picture to assist you.

The first two letters signify a male, the first three letters signify a female, the first four letters signify a great, while the entire world signifies a great woman. What is the word?

Move four matchsticks to the below square to form three squares?

Can you name three consecutive days without using the words Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, or Sunday?

We have shown you a regular water barrel as below. Without using any measuring device can you check if the barrel is more than half-filled or less than half-filled?

There was a strange boy who was born before his father. How can this be possible?

A boy was at a carnival and went to a booth where a man said to the boy, "If I write your exact weight on this piece of paper then you have to give me $50, but if I cannot, I will pay you $50." The boy looked around and saw no scale so he agrees, thinking no matter what the carny writes he'll just say he weighs more or less. In the end the boy ended up paying the man $50. How did the man win the bet?

John is on an island and there are three crates of fruit that have washed up in front of him. One crate contains only apples. One crate contains only oranges. The other crate contains both apples and oranges.

Each crate is labelled. One reads 'apples', one reads 'oranges', and one reads 'apples and oranges'. He know that NONE of the crates have been labeled correctly - they are all wrong.

If he can only take out and look at just one of the pieces of fruit from just one of the crates, how can he label all of the crates correctly?

What number comes next in this sequence:
7 8 5 5 3 4 4 _