Can you fill the blank with the correct number?

6 30 870 756030 _____

You have two buckets of 11 liters and 6 litres.
How can you measure exactly 8 litres?

John and his wife were living in a rural place. On a particular day, John's wife fell ill and he called the local doctor. When the doctor picked up, he said, "Doctor, my wife is ill. She might have appendicitis."

"This can't be possible! I took out her appendix two years ago myself," the doctor explained.

When diagnosed, John's wife was found to have appendicitis. How can this be possible?

Move four matchsticks to the below square to form three squares?

Only one colour, but not one size,
Stuck at the bottom, yet easily flies.
Present in sun, but not in rain,
Doing no harm, and feeling no pain.
What is it?

There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.

2, 3, 5, 9, 17, _ What is the next number in the sequence?

There was a blind man. He had four socks in his drawer either black or white. He opened it and took out two socks. Now the probability that it was a pair of white socks is 1/2.

Can you find out the probability that he had taken out a pair of black socks ?

You have two rectangular wires.

Both of them have property that when you light the fire from one end , it will take 60 minutes to get completely burn.

However, they do not burn at consistent speed (i.e it might be possible 1st 20% burn in 50 minutes and 80% can burn in 10 minutes).

So how could you measure 45 minutes ?

In the figure that has been attached to this question, each digit represents a digit. The similar letters carry the same integer value. Can you expose the original digits?