What is both possible and impossible at the same time?

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

Solve the following series:
AZ, GT, MN, __, YB

1. Where does Easter come from before Valentine's Day?

2. Do you know what is in the middle of Valentine's?

3. What did the lady bee say to the man bee on the occasion of Valentine's Day

Considering the below equation:

V + II - VI = 10
IV - X + VIII = 20
IV - VII + VI = 30

Then, I + II + III = ?

After teaching his class all about Roman numerals (X = 10, IX=9 and so on) the teacher asked his class to draw a single continuous line and turn IX into 6. The teacher's only stipulation was that the pen could not be lifted from the paper until the line was complete.

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.

I have holes on the top and bottom. I have holes on my left and on my right. And I have holes in the middle, yet I still hold water. What am I?

If you say my name, I will no longer exist. What am I?

What breaks yet never falls, and what falls yet never breaks?