Can you solve the maths in the below-given picture equation?

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?

Which number should replace the question mark?

How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

What came first, the chicken or the egg?

Why do we preferably have round manhole covers and not square ones?

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?

Today, I celebrated my 32nd birthday but I was born in 1972.
How is this possible?

John named his first son Alpha, second Beta, third Charlie and fourth Delta. What is the fifth son's name?

A sundial has the fewest moving parts of any timepiece. Which has the most?