The more of this there is, the less you see. What is it?

What word is represented by this rebus?

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?

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?

A bus driver was heading down a street in Mexico. 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 left side of the road past a cop car. Still - he didn't break any traffic laws. Why not?

Why do we preferably have round manhole covers and not square ones?

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?

What is full of holes but still holds water?

Things are just as they seem, right? Well, check again.
Can you count the number of tigers in this picture ?

If I put in one bird per cage, I have one bird too many. If I put in two bird per cage, I have one cage too many. How many cages and birds do I have?