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

I am lying and I always lie. Tell me whether I am lying or telling the truth.

The ages of a father and son add up to 66.
The father's age is the son's age reversed.
How old could they be?
(3 possible solutions).

I am a five-letter word under you,
Remove the first letter and I am above you,
Remove the second as well and I am around you.

Who am I?

When Jack was six years old he hammered a nail into his favourite tree to mark his height. Ten years later at age sixteen, Jack returned to see how much higher the nail was. If the tree grew by five centimetres each year, how much higher would the nail be?

How can one talk without saying a single word?

How many times do a clock's hands overlap in a day ?

You need to pick one entry from pot A and one from pot B to have a perfect match. Can you do it?

What 8 letter word can have a letter taken away and it still makes a word. Take another letter away and it still makes a word. Keep on doing that until you have one letter left. What is the word?

People make me, save me, change me, raise me. What am I?