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 wooden log balances equally on the scales when weighed with three-quarters of a pound and three-quarters of a wooden log.

Can you calculate the weight of the entire wooden log?

How can you drop a raw egg from a height onto a concrete floor without cracking it?

In the addition below, all digits have been replaced by letters.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

Can you divide numbers from 1 to 9 (1 2 3 4 5 6 7 8 9) into two groups so that the sum of the numbers of each group is equal?

Note: 9 cannot be turned over to make it 6.

What is both possible and impossible at the same time?

I have no doors but I have keys, I have no rooms but I have space, you can enter but you can’t leave! What am I?

Count the number of squares in the picture below.

I make two people out of one. What am I?

If we add four times the age of John four years from now to five times his age five years from now we get ten times his current age.

How old will John be two years from now?