How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

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 girl was standing near the window thinking something. All of a sudden she decides something and throws something out of the window. She dies very soon after throwing it. She was perfectly healthy and had no disease or allergy. No one killed her and she did not commit suicide.

Can you think of any possible explanation that is logical as well for what happened there?

It is a six-letter word.
The first four letters are me.
The second and last letters are the same.
The fourth second and last letter is payment.

Who is it?

Two boys were admitted to a school. When the headmaster asks them about their parents, they tell him that they have same parents (father and mother). On further inquiry, it turns out that they both share the same date for their birthday.

"Are you twins," ask the headmaster.
"No," replies the boys.

Is it possible?

Using eight eights and addition only, can you make 1000?

A Car driver was heading down a street in Washington. He went right past a stop sign without stopping, he turned left where there was a 'no left turn' sign and he went the wrong way on a one-way street. Then he went on the right side of the road past a cop car. Still, he didn't break any traffic laws. Why not?

I look at you, you look at me, I raise my right, you raise your left. What am I?

A thief is convicted in Mexico. He gets the death penalty. The judge allows him to say the last sentence to determine how the penalty will be carried out. If the thief lies, he will be hanged, if he speaks the truth he will be beheaded. The thief tells the last sentence and to everybody's surprise some minutes later he is set free because the judge cannot determine his penalty. What did the thief say?

Can you figure out the logic I used to decide the order of the following words:
gun, shoe, spree, door, hive, kicks, heaven, gate, line, den