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

What is the riddle which can be asked all day with a different correct answer each time.

In the attached figure, you can see a chessboard and two rooks placed on the chess board. What you have to find is the number of squares that do not contain the rooks. How many are there?

A little girl goes to the store and buys one dozen eggs. As she is going home, all but three break. How many eggs are left unbroken?

What am I?

Can you name any English verb that becomes its past tense by simply rearranging the alphabets ?

The following four words might seem abrupt to you. But you can make them meaningful by just adding vowels.
RDSH
GGPLNT
TMT
NN

Hint: All of them are vegetables.

Can you find the missing letter in the sequence?
S - T - I - L - ? - T - F - Y - C

Detective Rockford was jogging near the beach at 4:30 am.
He hears a sound near the shack "No Michael, Please Do not shoot me".
Next instance he heard the sound of gunfire. Rockford rushes to the shack where he finds women lying dead and a gun in close proximity of three "Doctore Lawyer and a Teacher".

Rockford immediately knew that the Lawyer has committed the crime. How?

I am quite hot but become too cold if you remove the first two letters. What am I?