You need to arrange three 7 and mathematical symbols to form number 1?

In a supermarket, there is an intelligent glass pane before a refrigerating unit. This glass pane allows cherries and apples through it but does not allow grapes and Orange to pass through it.

Can you identify the rule that the glass pane is following?

You need to move three matchsticks to form three squares. Can you do it?

Replace the letters of words with a number so that the below equation holds true

BASE +
BALL
---------
GAMES
----------

What mathematical symbol can be put between 5 and 9, to get a number bigger than 5 and smaller than 9?

The centre of the third figure is empty. What digit should fit inside?

The host of a game show, offers the guest a choice of three doors. Behind one is a expensive car, but behind the other two are goats.
After you have chosen one door, he reveals one of the other two doors behind which is a goat (he wouldn't reveal a car).

Now he gives you the chance to switch to the other unrevealed door or stay at your initial choice. You will then get what is behind that door.

You cannot hear the goats from behind the doors, or in any way know which door has the prize.

Should you stay, or switch, or doesn't it matter?

I am a prime number.
The double of myself is equal to the square of me.

which number 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?

A woman who works in a sweet shop has a measurement of 32-26-36, is 5"4" tall, and wears size "6" shoes. What do you think she weighs?