What is the next number in this series?

4,12,84,3612....

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

Below, you can see three complete equations and one incomplete. Based on the three complete ones, can you complete the incomplete one?

5 $ 4 $ 3 $ 9 = 4215
6 $ 9 $ 2 $ 6 = 3816
4 $ 7 $ 3 $ 3 = 1122
7 $ 2 $ 7 $ 4 = ____

If you go to the movies and you're paying, is it cheaper to take one friend to the movies twice, or two friends to the movies at the same time?

Can you find a number that lies one third of the distance between 1/3 and 2/3?

I am the one who remains awake when you sleep. But I need to rest when you awake. Who Am I?

A plane crashed between the border of Mexico and America. Where do you bury the survivors?

I am the beginning of the end, and the end of time and space. I am essential to creation, and I surround every place. What am I?

I taste better than I can smell. Who am I?

For an extra income, John decided to work at a Hotel for one hour daily. The manager offers him that they will pay him $11 after every 11 days.
However, John offered a different proposition to the manager. The offers stand as:
He will be paid just a penny on his first day.
Two pence will be paid on the second day,
Four pence will be paid on the third day.
And so on till the 11th day.

Should the Hotel manager accept his offer?