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?

Coffee machine

A drinks machine offers three selections - Tea, Coffee or Random
(Either tea or Coffee)but the machine has been wired up wrongly
so that each button does not give what it claims. If each drink
costs 50p, how much minimum money do you have to put into the
machine to find out which button gives which selection?

Blindfold game

A blindfolded man is asked to sit in the front of a carrom board.
The holes of the board are shut with lids in random order, i.e. any
number of all the four holes can be shut or open. Now the man is
supposed to touch any two holes at a time and can do the following.
* Open the closed hole.
* Close the open hole.
* Let the hole be as it is.
After he has done it, the carrom board is rotated and again brought
to some position. The man is again not aware of what are the holes
which are open or closed.

How many minimum number of turns does the blindfolded man require
to either open all the holes or close all the holes?
Note that whenever all the holes are either open or close, there
will be an alarm so that the blindfolded man will know that he has won.

Birthday Probability Problem

What are the chances that at least two out of a group of fifty people
share the same birthday?