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

Can you solve the tricky chess rebus puzzle below by ciphering the hidden meaning?

Assume there are approximately 5,000,000,000 (5 billion) people on Earth. What would you estimate to be the result, if you multiply together the number of fingers on every person's left hand? (For the purposes of this exercise, thumbs count as fingers, for five fingers per hand.) If you cannot estimate the number then try to guess how long the number would be.

A mile-long train is moving at sixty miles an hour when it reaches a mile-long tunnel. How long does it take the entire train to pass through the tunnel?

Can you count the number of blocks in the picture below?

An infinite number of mathematicians are standing behind a bar. The first asks the barman for half a pint of beer, the second for a quarter pint, the third an eighth, and so on. How many pints of beer will the barman need to fulfill all mathematicians' wishes?

Once while in his court, King Akbar asked Birbal to write something on a wall that makes one sad when read in good times and makes one happy when read in sad times.

He took only a few moment and wrote something that fit the requirements. What did he write?

An exterior architect is asked by a builder to plant seven trees in a manner that there are exactly six rows of trees in a straight line and each row has three trees in particular.

How will he do it?

I am quite hot but become too cold if you remove the first two letters. What am I?

Which tank will fill first?