Why 1729 is a magic number? Answer Logically.

In 1990, a person is 15 years old. In 1995, that same person is 10 years old. How can this be?

There is a shop where written:
Buy 1 for $1
10 for $2
100 for $3
I needed 999 and still only paid $3. How could this be financially viable for the shop-keeper?

What kind of tree can you carry in your hand?

A girl is twice as old as her brother and half as old as her father. In 50 years, her brother will be half as old as his father. How old is the daughter now?

I have cities, but no houses. I have mountains, but no trees. I have water, but no fish. What am I?

It comprises roots which nobody sees,
Much taller than those trees,
Up and up it goes,
Still it never grows?

You have two buckets of 11 liters and 6 litres.
How can you measure exactly 8 litres?

You are on a Boat in the mid of a river. You have two cigarettes with you. One of these two you have to light, how will you light the cigarette?

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?