Why is a river so rich ?

Eight Chelsea player makes the following statements :

1. Seven of us are lying here.
2. Six of us are lying here.
3. Five of us are lying here.
4. Five of us are lying here.
5. Four of us are lying here.
6. Three of us are lying here.
7. My name is Torres.
8. My name is Lampard.

The last two are Lampard and Torres or maybe Torres and Lampard.
So can you deduce which of the last two is Lampard or Torres?

I am thinking of a five-digit number such that:
The first and last digits are the same, their submission is an even number and multiplication is an odd number and is equal to the fourth number. Subtract five from it and we obtain the second number. Then divide into exact halves and we get the 3rd number.

What number I am thinking of?

Two trains start at the same time, one from Bangalore to Mysore and the other from Mysore to Bangalore. if they arrive at their destinations one hour and four hours respectively after passing one another, how much faster is one train running than the other?

P is the father of Q and S is the son of R. T is the brother of P and has a daughter U. If R is the sister of P, then what is the relation between U, Q and S?

John was piloting a plane behind a car but was never able to overtake it. Why?

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?

It's pretty hard to give up.
If you remove a part of it, you will be left with a bit.
Even if you remove another part, the bit still remains.
Remove one more and it still remains.

What is it?

Can you find out the remainder when 3^300 is divided by 5?

What do you call a fish without an eye?