Which is the rope you never skip with?

A four-digit number (not beginning with 0) can be represented by ABCD. There is one number such that ABCD=A^B*C^D, where A^B means A raised to the B power. Can you find it?

There is one four-digit whole number n, such that the last four digits of n2 are the original number n

When it is alive we sing, when it is dead we clap our hands. What is it?

Who has married many women but was never married?

There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.

If,

A + B = C
D - C = A
E - B = C

Based on the above equations, find out the answer for:

D + F = ?

Can you identify the direction in which this bus is moving; left or right?

Hint: The bus is moving on the roads of London.

What goes up but never comes down?

How is the moon similar to a dollar?