What is the next number in this series?

4,12,84,3612....

You have two buckets - one holds exactly 5 gallons and the other 3 gallons. How can you measure 4 gallons of water into the 5 gallon bucket?

(Assume you have an unlimited supply of water and that there are no measurement markings of any kind on the buckets.)

There is one thing that goes round the house and also inside the house but never even share a brief touch. What is it?

The great emperor Akbar once ruled India. He was well known for his intelligence. But along with that, he was known for the Nine Gems in his court. One of the nine gems was Birbal, a quick witted and extremely intelligent man. The stories of his wit were widely popular.

Once a king ruling in a distant land heard of Birbal. To check his wit, he sent an invitation and called him to visit his land. Akbar allowed Birbal to go and he took off on the journey.

Upon reaching that kings kingdom, he was welcomed with flowers. He was then escorted to the palace of the king. Upon entering the palace, Birbal found that there were six people sitting in front of him adorning the same robe. They were also lookalike and it was hard to judge who the real king was.

After a couple of minutes, Birbal approached one of them and bowed in front of him greeting him.

That was the real king. How did Birbal know who was the real king ?

Can you find out the smallest number that can be conveyed as the sum of three squares in three unique ways?

John is pretty weird. He likes toffees but hates chocolates. He loves books but never reads. He likes to build his troops in an online game but does not proceed with the war. He likes to go swimming but is afraid of water.

Seeking this behaviour, can you tell whether he likes balloons and parties?

I cannot talk, but I always reply when spoken to. What am I?

A newspaper is supposed to have 60 pages, but pages 24 and 41 are missing.
Which other pages won't be there?

I had an infinite supply of water and 5 litres and 3 litres jars.

How would you measure exactly 4 litres in the least number of steps?

The first two letters signify a male, the first three letters signify a female, the first four letters signify a great, while the entire world signifies a great woman. What is the word?