What is so fragile that saying its name breaks it?

I have a mouth but I don't eat.
I have a bank but have no money.
I have a bed but i dont sleep.
I wave but have no hands.

Who Am I ?

Three people enter a room and have a green or blue hat placed on their heads. They cannot see their own hat but can see the other hats.
The colour of each hat is purely random. They could all be green, blue, or any combination of green and blue.
They need to guess their own hat colour by writing it on a piece of paper, or they can write 'pass'.
They cannot communicate with each other in any way once the game starts. But they can have a strategy meeting before the game.
If at least one of them guesses correctly they win $10,000 each, but if anyone guesses incorrectly they all get nothing.
What is the best strategy?

Count the number of triangles in the picture below:

The day before yesterday I was 25 and the next year I will be 28. This is true only one day in a year. What day is my birthday?

There are hundred red gems and hundred blue gems. The blue gems are priceless while the red gems equal wastage. You have two sacks one labeled Heads and the other Tails. You have to distribute the gems as you want in the two sacks. Then a coin will be flipped and you will be asked to pick up a gem randomly from the corresponding sacks.

How will you distribute the gems between the sacks so that the odds of picking a Blue gem are maximum?

I look at you, you look at me, I raise my right, you raise your left. What am I?

What's the next in the series?

H, Be, F, S, Mn, Kr, In, Gd, Tl, ?

A deaf and mute man goes to the train station. Tickets for the train are 50 cents each. The man goes to the ticket booth and hands the man inside just a dollar. The man in the booth hands him two tickets.

How did the man in the booth know to give him two tickets without even looking at him?

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