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?

What is black when you buy it, red when you use it, and gray when you throw it away?

As easy as you can get into me, it is as hard to get out of me.

Do you know what I am?

A man calls his dog from the opposite side of a river. The dog crosses the river without a bridge or a boat and manages to not get wet. How is this possible?

I’m orange, I wear a green hat and I sound like a parrot. What am I?

What is the end of everything?

Vin Diesel is pulling a theft and has planned to run away with all the cash kept in the safe. But the only way to open the safe is the 13 character password. He has a set of five clues given to him by a trustworthy source.

Exactly two of the below statements are false.
The password is contained within this sentence.
The password is not in this hint.
The password is within only one of these statements.
At least one of the above statements is a lie.

I sleep during the day and fly at night, but I have no feathers to aid my flight. What am I?

What has hands, but can’t clap?

A woman lives in a skyscraper thirty-six floors high and is 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?