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?

Find the next number in the series below.

6 18 270 72090 ?

There were two grandmothers and their two granddaughters.
There were two husbands and their two wives.
There were two fathers and their two daughters.
There were two mothers and their two sons.
There were two maidens and their two mothers.
There were two sisters and their two brothers.
Yet there are only six, who are buried here,
All are born legitimate and relationships clear.
How can this happen?

Assume the given figure to be a delicious doughnut. Yes, now you can concentrate more on the puzzle. So you have this delicious doughnut in your refrigerator when your friends come knocking at the door. There are eight of them. Now you have to make three cuts in this doughnut so that each one of you nine people can enjoy a piece of it. Neither you nor your friends would mind the size of their piece as long as they are getting it. How will you do it?

If you toss a coin 10 times and it lands heads up every time, what are the chances it will land heads up if you toss it again?

John and his team plan to rob a safe. They got just one chance to break the code else the local police will be informed. Below are clues:
A) Exactly one number is perfectly placed: 9 8 1
B) Everything is incorrect: 9 2 4
C) Two numbers are part of the code of the safe but are wrongly placed: 0 9 3
D) One number is part of the code of the safe but is wrongly placed: 1 4 7
E) One number is part of the code of the safe but is wrongly placed: 7 8 3

There are three light switches outside a room. One of the switches is connected to a light bulb inside the room.
Each of the three switches can be either 'ON' or 'OFF'.

You are allowed to set each switch the way you want it and then enter the room(note: you can enter the room only once)

Your task is to then determine which switch controls the bulb?

You are given 2 eggs.
You have access to a 100-storey building.
Eggs can be very hard or very fragile means it may break if dropped from the first floor or may not even break if dropped from 100th floor, Both eggs are identical.
You need to figure out the highest floor of a 100-storey building an egg can be dropped without breaking.
Now the question is how many drops you need to make. You are allowed to break 2 eggs in the process

Use only one mathematical symbol and all numbers (0-9) to get a sum of 99

You walk into a creepy house by yourself. There is no electricity, plumbing, or ventilation. Inside you notice 3 doors with numbers on them. Once you open the doors you will die a particular way. Door No.1 You’ll be eaten by a lion who is hungry. Door No.2 You’ll be stabbed to death. Door No.3 There is an electric chair waiting for you. Which door do you pick?