What is both possible and impossible at the same time?

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

Nodes are shown below and you need to connect them based on the following rule: Every node can be connected to the number of nodes inside them, i.e. the first node there is a value of 1 which indicates that the first node can connect to exactly one node only.Can you do it?

A doctor and a boy were fishing. The boy was the doctor’s son, but the doctor was not the boy’s father. Who was the doctor?

What does below pictogram mean?

f you were running a race, and you passed the person in 2nd place, what place would you be in now?

The peacock is a bird that does not lay eggs. How do they get baby peacocks?

A word I know,
Six letters contain,
Subtract just one,
And twelve is what remains.

When you say goodbye, I am what you need to tie.
I come as a couple and go wherever you run.
Who am I?

Look at this sequence from top to bottom. What is the next number in the sequence?
1
11
21
1211
111221
312211