Find the correct statement

A sheet of paper has statements numbered from 1 to 100. Statement
N says "Exactly N of the statements on this sheet are false."

How many statements are true?

Tough probability riddle

A stick of length 1 metre is divided randomly into 3 parts.
What is the probability that a triangle can be made with
those three parts?

Rooks problem

Consider a chessboard with a single Rook. A Rook can move any
number of square sideways/forward, but not diagonally.
What is the minimum number of moves the Rook needs to make, in
order to pass over all the squares on the chessboard and return
to the original position?

Note: Take any square as a starting position for the Rook.

Hot Dogs

If a boy and a half can eat a hot dog and a half in a minute and a half,
how many hot dogs can six boys eat in six minutes?