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)?

A 3 digit number is such that it's unit digit is equal to the product of the other two digits which are prime. Also, the difference between it's reverse and itself is 396.

What is the sum of the three digits?

We have arranged an array of numbers below. What you have to do is use any kind of mathematical symbol you know excluding any symbol that contains a number like cube root. You can use any amount of symbols but you have to come up with a valid equation for all of them.

0 0 0 = 6
1 1 1 = 6
2 + 2 + 2 = 6
3 3 3 = 6
4 4 4 = 6
5 5 5 = 6
6 6 6 = 6
7 7 7 = 6
8 8 8 = 6
9 9 9 = 6

Rearrange the letters in "new door" to make one word.

I cannot talk, but I always reply when spoken to. What am I?

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?

If you were to put a coin into an empty bottle and then insert a cork into the neck, how could you remove the coin without taking out the cork or breaking the bottle?

He digs out tiny caves and stores gold and silver in them. He also built bridges of silver and made crowns of gold. They are the smallest you could imagine. Sooner or later everybody needs his help, yet many people are afraid to let him help them. Who is he?

What can go through glass without breaking it?

I am the beginning of the end, and the end of time and space. I am essential to creation, and I surround every place. What am I?