How can a man go eight days without sleep?

What are the next two letters in the following series and why?
W A T N T L I T F S _ _

*Hint: Check Puzzle Title

I start and end with 500 and carry a 5 in my heart. But I require the first letter and the first number to be complete. I am the name of a King.

Who am I ?

By including only four matchsticks in below picture, you have to make "Four Triangles And Two Squares"

We have four gears with below features=> Both Gear A and D has 60 teeth=> Gear B has 40 teeth=> Gear C has 20 teeth=> Every two minutes, Gear B makes 25 full turns.What is the relative speed of Gear A and Gear B?

Decode the below four famous ciphers:

8P of the SS
1M of the E
1S of the SS
60M in 1H

If Rajina's daughter is my daughter's mom, who am I to Rajina?

In the Wild West, you are challenged into a death match by two bounty hunters nicknamed Golden Revolver (GR) and Killer Boots (KB). You accept the challenge. None of you want to waste any of the bullet and so a certain rules are laid down:

1) All of you will shoot in a given order till the last man standing.
2) Each of you shoots only once upon his turn.
3) If any one of you is injured, the other two will finish him off with an iron rod.
4) The worst shooter of all (which is you) shoots first and the best one shoots at the last.

Now, how will you plan things if you know that you hit every third shot of yours, KB hits every second shot and GR hits every shot ?

In the addition below, all digits have been replaced by letters.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?

What is the coolest letter in the alphabet?