What's the only room from which no one can enter or leave

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?

I go up and I go down.
I go up towards the beautiful sky and down toward the green ground.
I am present tense.
I am past tense too
Children love me.

Who Am I?

Speaking of rivers, a man calls his dog from the opposite side of the river. The dog crosses the river without getting wet, and without using a bridge or boat. How?

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?

A lion and its tamer are standing inside a cage that measures 1 unit in radius. Both of them can effortlessly run at the speed of 1 unit maximum.

1) Suppose the lion is hungry, will he be able to eat up the tamer?
2) If yes, how long can the tamer survive?

James ordered a fishing rod, priced at $3.56. Unfortunately, James is an Eskimo who lives in a very remote part of Greenland and the import rules forbid any package longer than 4 feet to be imported. The fishing rod was 4 feet and 1 inch, just a little too long, so how can the fishing rod be mailed to James without breaking the rules? Ideally James would like the fishing rod to arrive in one piece!

Our product and our sum always give the same answer. Who are we?

Name the three-letter word that can complete the below words?

A) L O _ _ _ E
B) E D U _ _ _ E
C) _ _ _ E R
D) _ _ _ T L E

You need to climb ten stairs. At every stair, you can either take one step up or you can jump two steps up.

In how many different ways you can climb 10 stairs?