What is the centre of gravity?

Our product and our sum always give the same answer. Who are we?

What can run but never walks, has a mouth but never talks, has a head but never weeps, has a bed but never sleeps?

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?

There’s a girl who has a large family. She has an equal amount of brothers and sisters, but each brother only has half as many brothers and sisters. What’s the correct amount of brothers and sisters?

Who has married many women but was never married?

Jenifer and Jesica are having a conversation.

Jenifer: I am definitely not over 30.
Jesica: I am 28 and you are surely 5 years older to me at least.
Jenifer: No, you are at least 29.

You are told that both of them are lying throughout in the conversation. Can you find their respective ages?

Consider this about a word: 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?

What runs around the whole yard without moving?

Which city is three-fifths chick two third cat and 50% goat?