Why is 6 afraid of 7?

I have no doors but I have keys, I have no rooms but I have space, you can enter but you can’t leave! What am I?

By adding four matchsticks, can you divide the square shown in the picture into two equal parts?

You find yourself in a strange place guarded by two guards.One of the guard always say truth while other always lies.You don't know the identity of the two.You can ask only one question to go out from there. What should you ask?

If you say my name, I will no longer exist. What am I?

James Bond is caught up in a mysterious scenario where the evil villain has him blindfolded. He somehow breaks through the handcuffs but is unable to get the blindfold off. Upon searching, he comes across a bow and 3 arrows. He can hear the villain speak, and thus tries to take a shot at him. He launches the first arrow, it misses the villain. He then launches the second arrow and it misses by a greater margin.

What is the probability that this third shot our James bond takes will be worse than the second shot?

We have arranged an array of numbers below. What you have to do is use any kind of mathematical symbol you know excluding any symbol that contains a number like cube root. You can use any amount of symbols but you have to come up with a valid equation for all of them.

0 0 0 = 6
1 1 1 = 6
2 + 2 + 2 = 6
3 3 3 = 6
4 4 4 = 6
5 5 5 = 6
6 6 6 = 6
7 7 7 = 6
8 8 8 = 6
9 9 9 = 6

Christina has four daughters, and each of her daughters has a brother. How many children does Christina have?

If,

6 / 7 = 2
3 / 9 = 7
8 / 2 = 6

Then

4 / 5 = ?

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