What is both possible and impossible at the same time?

What is the Surname of Barbie Doll?

Our product and our sum always give the same answer. Who are we?

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

We have arranged an array of numbers below. What you have to do is use any kind of mathematical symbol you know excluding any symbol that contains a number like cube root. You can use any amount of symbols but you have to come up with a valid equation for all of them.

0 0 0 = 6
1 1 1 = 6
2 + 2 + 2 = 6
3 3 3 = 6
4 4 4 = 6
5 5 5 = 6
6 6 6 = 6
7 7 7 = 6
8 8 8 = 6
9 9 9 = 6

Outside a massage parlour, there is a board that reads
"I only massage those who do not massage themselves."

Reading the above statement, does the masseur massage himself?

I can sizzle like bacon,
I am made with an egg,
I have plenty of backbone, but lack a good leg,
I peel layers like onions, but still remain whole,
I can be long, like a flagpole, yet fit in a hole.

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

This puzzle is for Harry Potter fans. Do you know why Tom Riddle is called Lord Voldemort?

Which word is least like the others? Third, fourth, fifth, sixth, seventh, eighth, ninth?