What has to be broken before you can use it?

There is a square of a particular number which when doubled, becomes 7 more than its quarter.

Can you find the number?

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?

Can you find out the remainder when 3^300 is divided by 5?

What famous saying does this rebus mean?

COME SERVED <---
COME SERVED
COME SERVED
COME SERVED
COME SERVED

What goes up but never comes down?

John, Jack and Jill are in a desert. John doesn't like Jill and hence decides to murder him. He poisons the water supply of Jill. Since it is a desert area, Jill must drink or he will die of thirst.

Jack does not know of the actions of John and also decides to murder Jill. To succeed in his ill motives, he removes the water supply of Jill so he dies of thirst.

Jill dies due to thirst. Who murdered Jill?

I make a loud sound when I’m changing. When I do change, I get bigger but weigh less. What am I?

There is a box full of marbles,
all but two are blue,
all but two are green,
and all but two are red.

How many marbles are in the box?

After a heavy Thanksgiving meal, the night watchman went to work. In the morning, he told his boss he had dreamed that a saboteur planted a bomb in the factory and that he felt it was a warning. The boss promptly fired him. Worker confused, Why boss fire him?