What is the next number in this series?

4,12,84,3612....

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

I am a type of room you cannot enter or leave. Raised from the ground below, I could be poisonous or a delicious treat. What am I?

Who always enjoys poor health?

Once upon a time, there was a castle on a square island. The entire island was surrounded by a 14m wide trench. The Romans had wanted to invade the castle and had brought a few wooden planks along with them to facilitate themselves in crossing the moat. The planks were however found to be only 13m long.

The Romans still managed to cross the trench. How did they do it?

What makes this number unique: 8,549,176,320?

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?

If you had an infinite supply of water and 5-quart and 3-quart pails, how would you measure exactly 4 quarts? What is the least number of steps you need?

What has many keys but can’t open a single lock?

I make a loud sound when I’m changing. When I do change, I get bigger but weigh less. What am I?