Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?

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.

Can you find out the number of the parking space in which the car is parked?

Can you replace the question mark with the correct number?

I am lying and I always lie. Tell me whether I am lying or telling the truth.

A convention is held where all the big logicians are summoned. The master places a band on everyone's forehead. Now all of them can see others bands but can't see his own. Then they are told that there are different colours of bands. All the logicians sit in circle and they are further explained that a bell will ring at regular intervals. The moment when a logician knew the colour of band on his forehead, he will leave at the next bell. If anyone leaves at the wrong bell, he will be disqualified.

The master assures the logicians that the puzzle will not be impossible for anyone of them. How will the logicians manage ?

13 decks of cards have been mixed. What is the minimum number of cards that must be taken out from the above-mixed cards to guarantee at least one 'four of a kind?

I am a white box having no key or lid.
Yet there is a golden treasure inside it.

What Am I?

Once while in his court, King Akbar asked Birbal to write something on a wall that makes one sad when read in good times and makes one happy when read in sad times.

He took only a few moment and wrote something that fit the requirements. What did he write?

The average age of 10 members of a committee is the same as it was 4 years ago, because an old member has been replaced by a young member. Find how much younger is the new member ?