When I get multiplied by any number, the sum of the figures in the product is always me. What am I?

What is a word made up of 4 letters, yet is also made up of 3. Sometimes is written with 9 letters, and then with 4. Rarely consists of 6, and never is written with 5.

I am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?

Count the squares in the matchstick puzzle below?

Find out a multi-digit number that if multiplied by the number 9 or any of its multiplications products (i.e. 18, 27, 36, 45,..) will result in the multiplication factor repeated (n) number of times.

A few friends are enjoying their sea voyage in a boat full of apples. On the way, they felt hungry and thus decided to eat the apples. Together, they ate two dozen of apples. When they have eaten the apples, will there be any change in the water level?

What 5-letter word typed in all capital letters can be read the same upside down?

A train leaves from point A for point B at 80 mph. After half an hour, another train leaves from point B for point A at 60 mph.

Which of the trains will be farther from point A when they meet ?

Railroad Crossing, look out for the cars. Can you spell that, without any R's ?

What kind of band never plays music?