What has one letter and starts with an E?

What are the 50th, 63rd and 100th numbers in the sequence below?
4, 5, 8, 8, 9, 9, 12, 13, 13, 13, 17, 18, ...

A word I know has six letters it contains, remove one letter and 12 remain. What is it?

The square root of number 121 is "11". What is the square root of the number "12345678987654321."?

You have a roll of cloth 1km long. You have a machine which cuts this roll into pieces of 10-meter-long cloth.

How long would it take for the machine to cut the roll if each cut took 4 secs?

Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?

Which tank will fill first?

In the Chess Board picture below white army is arranged. You need to add a black army on the board such that no piece is under any threat.
Note: Army comprised of 1 king, 1 queen, 2 rooks, 2 bishops, 2 knights, and 8 pawns.

You have two strings whose only known property is that when you light one end of either string it takes exactly one hour to burn. The rate at which the strings will burn is completely random and each string is different. How do you measure 45 minutes?

In the addition below, all digits have been replaced by letters. Equal letters represent equal digits and different letters represent different digits.
ABCABA
BBDCAA
ABEABB
ABDBAA
------- +
AAFGBDH
What does the complete addition look like in digits?