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?

If two's company, and three's a crowd, then whats four and five ?

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

It comprises roots which nobody sees,
Much taller than those trees,
Up and up it goes,
Still it never grows?

Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

Jim and Sarah are in a long-distance relationship. Jim buys an engagement ring for Sarah and wants to mail it to her. Unfortunately, the only way to ensure the ring will be received is to place a lock on the package. Jim has locks and Sarah has locks, but neither has keys for each other’s locks. How can they make sure the ring isn’t stolen?

There is a place where if I stand up straight, I will still be considered sideways.

Complete the given grid with valid words. You can only use the letters AAEEIIMMPPTT.

Hint: The grid reads the same across as down.

I am the beginning of everything, the end of everywhere. I'm the beginning of eternity, the end of time and space. What am I?

Two girls were born to the same mother, on the same day, at the same time, in the same month and year and yet they're not twins. How can this be ?