Can you find a number that lies one third of the distance between 1/3 and 2/3?

Find The Next Number in this series.
1, 2, 6, 42, 1806 ?

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.

You are given a cube that is made with the help of 10x10x10 smaller cubes summing up to a total of 1000 smaller cubes. You are asked to take off one layer of the cubes.
How many remain now?

Can you find out the next digit in the following series ?

0, 0, 1, 3, 2, 6, 3, 9, 4, 12, 5, ?

In the four images below, can you find the odd one out?

These types of puzzles are known as charades. What you have to do is to find two words that are referred to in the first stanza and the second stanza and put them together to form the third word in the third stanza.

Just for example, if my first refers to 'off' and my second refers to 'ice', then my whole will be the 'office'.

My first is present - future's past -
A time in which your lot is cast.

My second is my first of space
Defining people's present place.

My whole describes a lack of site -
A place without length, breadth, or height.

Can you identify the Oscar-winning movie from the rebus below?

A new Engineering building containing 100 offices had just been completed. John was hired to paint the numbers 1 to 100 on the doors. How many times will John have to paint the number nine (9)?

What can go up a chimney down, but can’t go down a chimney up?