What goes up but never comes down?

I am an odd number. Take away a letter and I become even. What number am I?

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?

A boy was locked in a room by some robbers. All that is in the room is a piano, a calendar, and a bed. The room is locked from the outside. What does he eat, drink, and how does he escape and get out?

A tree doubled in height each year until it reached its maximum height over the course of ten years. How many years did it take for the tree to reach half its maximum height?

Take number 1000 and then add 20 to it.
Now add 1000 one more time.
Now add 30.
Now add 1000 one more time.
Now add 40.
Now add 1000 one more time.
Now add 10.

What is the total?

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?

You have a three-gallon and a five-gallon measuring device. You wish to measure out four gallons.

I have a clock(12-hour format) and both the needles of the clock overlap at 12:00.
After how much time, they will overlap again?

How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?