81 x 9 = 801. What must you do to make the this equation true?

I never stop running even when I standstill. If I am formed by joining two identical bodies together, can you guess who I am?

You are on your way to visit your Friend, who lives at the end of the hill. It is his birthday, and you want to give him the cakes you have made. Between your house and his house, you have to cross 5 bridges, and as it goes in the land of make believe, there is a troll under every bridge! Each troll, quite rightly, insists that you pay a troll toll. Before you can cross their bridge, you have to give them half of the cakes you are carrying, but as they are kind trolls, they each give you back a single cake. How many cakes do you have to leave home to make sure that you arrive at a friend's house with exactly two

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

Can you name three consecutive days without using the words Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, or Sunday?

He does not have any heart but still, He manages to live.
If you kill him, you will eventually die but yet you kill him.
He cannot run, who is He?

If,
29 - 1 = 30
9 - 1 = 10
14 - 1 = 15

Based on similar logic, Can you prove that the below algebraic equation is true?
11 - 1 = 10 ?

In a boat, the father of a sailor's son is sitting with the son of the sailor. However, the sailor is not present on the boat.

Can this even be possible?

You are provided with a grid (as shown in the picture). Can you fill the squares with numbers 1-8 in a manner that none of the two consecutive numbers are placed next to each other in any direction (vertically, horizontally or diagonally?)

Can you find a rabbit in the given picture?