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?

Replace the question mark with the number below given a simple math problem.

I have cities, but no houses. I have mountains, but no trees. I have water, but no fish. What am I?

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?

Today is a very icy and cold morning in Newcastle. Mr Shearer, an office bus driver arrived to pick up the employees from the last stop. Shearer suddenly remembers that he needs to pick a newly joined 4miles to the north. Mr Shearer lost his direction compass, a few minutes later Shearer is able to figure that he is moving in the correct direction i.e. north. How did Shearer know that he is moving in the correct direction?

I am a ten letters word
The first four letters have the power to rule,
Next, four-letter can be eaten.
The next three-letter represents a lady.
I can fly as well

what am I looking for?

A dead body is found outside a multi-story multinational company. The case is reported and a homicide detective is called on the crime scene.

He looks at the body and then towards the building. From the position of the body, it is evident that the victim committed suicide. He goes to the first floor of the building and then walks in the direction of the dead body, opens the window and toss a coin in the air.

He goes to second floor and again repeats the process. He keeps doing this till he is done on all the floors. Then he returns back to the floor and tells his team that it is a murder.

How in heaven did he deduce that?

I can write cow in 13 letters.

Can You?

What is red and smells like blue paint?

I am a normal creature, but I have five hands. I can even have more but even then I will be considered normal.

Who am I?