I travel all around the world but always stay in the corner. What am I?

Here is a mathematical expression that also secretly tells a movie name. What movie is that?

There are 2 sand hourglasses.

The small one can measure 5 hours and the large one can measure 7 hours.

How can we measure 16 hours with 2 sand hourglasses running together ?

A woman lives in a Tall building thirty-six floors high and served by several elevators which stop at each floor going up and down. Each morning she leaves her apartment and goes to one of the elevators. Whichever one she takes is three times more likely to be going up than down. Why?

You walk into a room that contains a match, a kerosene lamp, a candle and a fireplace. What would you light first?

A network of 20 x 10 squares is given to you.

Can you calculate how many unique squares and rectangles can be formed combining two or more individual squares ?

Can you find the missing letter in the sequence?
S - T - I - L - ? - T - F - Y - C

What does this simple rebus mean?

Manish and Manoj play 5 games of chess.
Both Manish and Manoj win the exact same number of games. There is no tie at all.

How?

A time long back, there lived a king who ruled the great kingdom of Trojan House. As a part of the renovation of the kingdom to meet future security needs, he asked his chief architect to lay down a new play in a manner that all of his 10 castles are connected through five straight walls and each wall must connect four castles together. He also asked the architect that at least one of his castles should be protected with walls. The architect could not come up with any solution that served all of King's choices, but he suggested the best plan that you can see in the picture below. Can you find a better solution to serve the king's demand?