What is the Surname of Barbie Doll?

Something Extraordinary happened on May 6th 19778 at 12:34am what was that?

A man started to town with a fox, a goose, and a sack of corn. He came to a stream which he had to cross in a tiny boat. He could only take one across at a time. He could not leave the fox alone with the goose or the goose alone with the corn. How did he get them all safely over the stream?

How many triangles are there in the picture below?

What does the following represent?

N N N N N N N

A A A A A A A

C C C C C C C

John said, "If yesterday was tomorrow, today would be Friday."

When did John make this statement?

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.

There is a jar in which there are two types of candies.
20 blueberries and 16 strawberries. You perform the following steps:
1) You take out two candies.
2) If the two candies are of the same flavour, you add a blueberry one otherwise, you add the strawberry one.

You repeat these two steps till there is just one candy remaining in the jar. Which flavoured candy will be left?

A bag contains 64 balls of eight different colours. There are eight of each colour (including red). What is the least number you would have to pick, without looking, to be sure of selecting 3 red balls?

I know a 5-digit number having a property that With a 1 after it, it is three times as large as it would be with a one before it.

Guess the number?