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.

A tree doubled in height each year until it reached its maximum height over the course of ten years. How many years did it take for the tree to reach half its maximum height?

An octopus has 8 legs. A hippogriff has 6 legs and 2 pairs of wings. A sphinx has 6 legs and one pair of wings. Now we have all 3 kinds and a total of 18 insects in a cage. We have a total of 118 legs and 20 pairs of wings. How many insects do we have of each kind?

What is the word or phrase?

Consider this about a word: The first two letters signify a male, the first three letters signify a female, the first four letters signify a great, while the entire world signifies a great woman. What is the word?

Can you solve the maths in the below-given picture equation?

John is 45 years older than his son Jacob. If you find similarities between their ages, both of their ages contain prime numbers as the digits. Also, John's age is the reverse of Jacob's age.

Can you find their ages?

A thief is convicted in Mexico. He gets the death penalty. The judge allows him to say the last sentence to determine how the penalty will be carried out. If the thief lies, he will be hanged, if he speaks the truth he will be beheaded. The thief tells the last sentence and to everybody's surprise some minutes later he is set free because the judge cannot determine his penalty. What did the thief say?

Birbal was jester, counsellor, and fool to the great Moghul emperor, Akbar.
The villagers loved to talk of Birbal's wisdom and cleverness,
and the emperor loved to try to outsmart him.
One day Akbar (emperor) drew a line across the floor.
"Birbal," he ordered, "you must make this line shorter, but you cannot erase any bit of it."
Everyone present thought the emperor had finally outsmarted Birbal.
It was clearly an impossible task.
Yet within moments the emperor and everyone else present had to agree that Birbal had made the line shorter without erasing any of it.
How could this be?

A bank customer had $100 in his account. He then made 6 withdrawals. He kept a record of these withdrawals, and the balance remaining in the account, as follows:

Withdrawals Balance left
$50 $50
$25 $25
$10 $15
$8 $7
$5 $2
$2 $0
----- -----
$100 $99

Why are the Totals not tallying?