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.

In a mathematical quiz, you are asked the following question:

Use three 9s in a mathematical expression without dividing or multiplying to form the number one.

Can you answer the question?

You have a basket containing ten apples. You have ten friends, who each desire an apple. You give each of your friends one apple.
Now all your friends have one apple each, yet there is an apple remaining in the basket.
How?

There are two insects on a tile. Insect X is sitting on one side of the tile (point A) and Insect Y is sitting opposite on the other side of the tile (point B). Now both of them decide to change their position and thus X starts crawling to point B and Y starts crawling to point A. When they meet and pass each other in between, X takes 20 seconds to reach B and Y takes just 5 seconds to reach A.

Can you calculate the total time each of the insects took to change their positions?

Solve the below puzzle by replacing the question mark with the correct number.

3 6 12

4 8 16

5 10 ?

Can you decipher these quotes by Albert Einstein?
Blf xzm mvevi hloev z kilyovn lm gsv ovevo lm dsrxs rg dzh xivzgvw.

I add 5 to 9 and get 2. The answer is correct, so what am I?

What 8 letter word can have a letter taken away and it still makes a word. Take another letter away and it still makes a word. Keep on doing that until you have one letter left. What is the word?

There are a number of books on a shelf. If one book is the 4th from the left and 6th from the right, how many books are on the shelf?

Below the four parts have been reorganised. The four partitions are exactly the same in both arrangements. Why is there a hole?