What is the fewest number of coins that would be required in order to make sure each and every coin touches exactly three other coins?

Two boys were admitted to a school. When the headmaster asks them about their parents, they tell him that they have same parents (father and mother). On further inquiry, it turns out that they both share the same date for their birthday.

"Are you twins," ask the headmaster.
"No," replies the boys.

Is it possible?

A man plots the murder of his wife. His plan is full proof. Nobody saw them leaving their house. He stabbed her with a knife while driving. She died on the spot. He threw her body in a valley. He threw the knife carefully wiping his finger prints on a random garbage bin. Then he went back to his home and no one was watching him this time as well.

After an hour, he was called by the local police department who informed him that his wife was murdered. They asked him to reach the scene of crime immediately. But as soon as he arrived at the crime scene, he was arrested by them.

How did the police know that he himself is the murderer?

It's pretty hard to give up.
If you remove a part of it, you will be left with a bit.
Even if you remove another part, the bit still remains.
Remove one more and it still remains.

What is it?

You are in a room with no metal objects except for two iron rods. Only one of them is a magnet.
How can you identify which one is a magnet?

A train full of passengers goes through a tunnel. When the train comes out from the other end, there is no single person on the train.

How did it happen?

Can you tell a 3D object that has just two surfaces?

There’s a one-story house in which everything is yellow. Yellow walls, yellow doors, yellow furniture. What colour are the stairs?

When 99 is considered higher than 100?

I never stop running even when I standstill. If I am formed by joining two identical bodies together, can you guess who I am?