What always comes into a house through the keyhole?

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?

A beggar on the street can make one cigarette out of every 6 cigarette butts he finds. After one whole day of searching and checking public ashtrays the beggar finds a total of 72 cigarette butts. How many cigarettes can he make and smoke from the butts he found?

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

I was speeding and ran through a stop sign, yet two traffic officers who were there do nothing about it.

why?

Find The Next Number in this series.
1, 2, 6, 42, 1806 ?

Once upon a time, there was a castle on a square island. The entire island was surrounded by a 14m wide trench. The Romans had wanted to invade the castle and had brought a few wooden planks along with them to facilitate themselves in crossing the moat. The planks were however found to be only 13m long.

The Romans still managed to cross the trench. How did they do it?

All of the flowers I have are orchids except two. All of the flowers I have are hibiscuses except two. All of the flowers I have are roses except two.

Can you tell me how many flowers I have?

"That Restaurant always remains crowded. This is the reason why nobody goes there".

Can you find a flaw in this statement?

In a rainy season, one day 3 huge ladies walked under a normal-sized umbrella.
The umbrella is not huge enough to accommodate all 3 ladies yet not a single lady got wet. Why?