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

Twenty frogs are sitting on a log floating on the surface of a river. Two of them decide to jump off into the water.

How many frogs are there on the log at this moment?

I shave every day, but my beard stays the same. What am I?

I have a head like a cat and feet like a cat, but I am not a cat. What am I?

I am something people love or hate. I change peoples appearances and thoughts. If a person takes care of them self I will go up even higher. To some people I will fool them. To others I am a mystery. Some people might want to try and hide me but I will show. No matter how hard people try I will Never go down. What am I?

Look at the below sequence of letters and tell us what the next letter should be:

O T T F F S S ?

Find the next number in the series.
1 10 24 43 67 ?

Below toothpicks/matchsticks indicate the group of fishes moving from west to east direction. Can you make them move from east to west by just moving three toothpicks/matchsticks?

What always comes into a house through the keyhole?

I can turn polar bears white.
I can make anyone dance.
I can make everyone cry
I can make your hands clap
I can make you thin.
I can make you smile.
I can make you smile

Can you guess the riddle?