Why is the Hole below a Lock?

Replace the question mark with the correct number, given the pair of numbers exhibits a similar relationship?

? : 3839 :: 11 : 1209

Mr Black, Mr Gray, and Mr White are fighting in a truel. They each get a gun and take turns shooting at each other until only one person is left. Mr Black, who hits his shot 1/3 of the time, gets to shoot first. Mr Gray, who hits his shot 2/3 of the time, gets to shoot next, assuming he is still alive. Mr White, who hits his shot all the time, shoots next, assuming he is also alive. The cycle repeats. If you are Mr Black, where should you shoot first for the highest chance of survival?

A man embarked on a questionnaire game. He kept asking the same question to whomever he found. The answer each time was different.

Can you guess what the question was?

A beggar on the street can make one cigarette out of every 6 cigarette butts he finds. After one whole day of searching and checking public ashtrays the beggar finds a total of 72 cigarette butts. How many cigarettes can he make and smoke from the butts he found?

Outside a massage parlour, there is a board that reads
"I only massage those who do not massage themselves."

Reading the above statement, does the masseur massage himself?

They came out at night, without being called.
They lost at day, without being stolen.
Who are they?

Out of the nine cats that you can see in the picture, there are only two that are completely identical. Can you find them out?

A frog is at the bottom of a 30-meter well. Each day he summons enough energy for one 3-meter leap up the well. Exhausted, he then hangs there for the rest of the day. At night, while he is asleep, he slips 2 meters backwards. How many days does it take him to escape from the well?

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 ?