Why 1729 is a magic number? Answer Logically.

Prove that twice of ten is the same as twice of eleven.

Can you decipher the below rebus?

PBLUESAISNUERSES

Find the missing letter in the last circle logically in the given below picture.

100 prisoners are stuck in the prison in solitary cells. The warden of the prison got bored one day and offered them a challenge. He will put one prisoner per day, selected at random (a prisoner can be selected more than once), into a special room with a light bulb and a switch which controls the bulb. No other prisoners can see or control the light bulb. The prisoner in the special room can either turn on the bulb, turn off the bulb or do nothing. On any day, the prisoners can stop this process and say "Every prisoner has been in the special room at least once". If that happens to be true, all the prisoners will be set free. If it is false, then all the prisoners will be executed. The prisoners are given some time to discuss and figure out a solution. How do they ensure they all go free?

A bomb goes off.
Carnage.
One person, only a few feet away, survives! How can this be?

Can you make a fire with just a single stick?

You can find some missing letters in the picture. By placing two particular letters in the spaces, you can form a nine lettered word beginning from one of the corners and going clockwise direction to the middle. Can you find out the letters and the word?

In the image below, you can see two glasses and two matchsticks.You need to move four matchsticks in such a manner that the crosses come inside the glasses. Note: you cannot move the crossed.

I have teeth but i don't bite. Who Am I ?