I have a five and a three-gallon jar. Assuming there is an infinite supply of water, how can I measure one-gallon water?

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 number should come in place of the question mark below?

Four men were in a boat on the lake. The boat turns over, and all four men sink to the bottom of the lake, yet not a single man got wet! Why?

You can see three almost identical images below. Can you spot the odd one out from them?

I am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?

Prove that twice of ten is the same as twice of eleven.

A four-digit number (not beginning with 0) can be represented by ABCD. There is one number such that ABCD=A^B*C^D, where A^B means A raised to the B power. Can you find it?

Find three whole, positive numbers that have the same answer when multiplied together as when added together.

When can we add 2 to 11 and get 1 as the correct answer?