2, 3, 5, 9, 17, _ What is the next number in the sequence?

You knock a Table over in the library, and suddenly 20 eyes are looking at you.

Use the numbers 2, 3, 4 and 5 and the symbols + and = to make a true equation. Conditions: Each must be used exactly once and no other numbers or symbols can be used.

Rob is taller than Edwin, and Jurgen is shorter than Rob.
Of only one of the following statements, we now certainly know it is correct:

A.Edwin is taller than Jurgen
B.Jurgen is taller than Edwin
C.It cannot be determined if Jurgen or Edwin is the tallest.

I am 5 letters long.
My first two tell you who I am
My first 3 could be a medicine
My last three reversed could be a young boy.
My 4th, 3rd and 2nd in that order could be a fruit drink.
If you have me you may hang me round your neck
WHAT AM I ?

Replace the 'X' with any mathematical symbol to make the expression equal to 111.

18 X 12 X 2 X 3 = 111

A train full of passengers goes through a tunnel. When the train comes out from the other end, there is no single person on the train.

How did it happen?

What is the end of everything?

I am a prime number.
The double of myself is equal to the square of me.

which number am I?

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