Why do people go to bed?

Birbal was jester, counsellor, and fool to the great Moghul emperor, Akbar.
The villagers loved to talk of Birbal's wisdom and cleverness,
and the emperor loved to try to outsmart him.
One day Akbar (emperor) drew a line across the floor.
"Birbal," he ordered, "you must make this line shorter, but you cannot erase any bit of it."
Everyone present thought the emperor had finally outsmarted Birbal.
It was clearly an impossible task.
Yet within moments the emperor and everyone else present had to agree that Birbal had made the line shorter without erasing any of it.
How could this be?

Replace the question mark in the picture below.

Below the four parts have been reorganised. The four partitions are exactly the same in both arrangements. Why is there a hole?

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?

How many pluses should we put between the digits of 987654321 to get a total of 99, and where?

What is the fewest number of coins that would be required in order to make sure each and every coin touches exactly three other coins?

One of the leprechaun is missing if you see the two pictures attached to this question. Where did he go? When he comes back, do you know where has he been?

Jigsaw captured 100 people and make them stand in a circle and all these people are labelled as Person1, Person2, Person3... Person100. He made them play a crazy game in which Person 1 shot Person 2 and pass the gun to the next person and so on until one stands alive.

Which person will survive in the end?

I can be made.
I can be cracked.
I can be told.
I can be played.

Who am I?