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

Pronounced as one letter,
And written with three,
Two letters there are,
And two only in me.
I am double, I am single,
I am black blue and grey,
I am read from both ends,
And the same either way.

Two friends were stuck in a cottage. They had nothing to do and thus they started playing cards. Suddenly the power went off and Friend 1 inverted the position of 15 cards in the normal deck of 52 cards and shuffled it. Now he asked Friend 2 to divide the cards into two piles (need not be equal) with equal number of cards facing up. The room was quite dark and Friend 2 could not see the cards. He thinks for a while and then divides the cards in two piles.

On checking, the count of cards facing up is same in both the piles. How could Friend 2 have done it ?

What is the centre of gravity?

Evil warlock dislikes dwarfs and therefore he selects four of them and buries them. The dwarfs are buried in the ground and they are in such a way that except for their heads, their body is inside the ground. The dwarfs cannot move their body and they can view only forward. They are all buried in a line, and amongst the four, one of the dwarfs is separated by a wall. All the dwarfs are in the same direction. The last dwarfs can see two heads of friends in the front and a wall. In the last second dwarf can see one head of his friend and a wall. The second dwarf can see only the wall. The dwarf can see nothing.
Warlock comprehends the situation and tells the dwarfs that he has placed hats on their heads. There are two blue hats and two red ones. In all four dwarfs, one of them has to say what colour hat he is wearing. If the dwarf says the correct colour of the hat, they will be left free. If the answer is wrong, then they will be dug inside the ground till the very end.

What will be the answer by the dwarf and how will they answer?

I have no doors but I have keys, I have no rooms but I have space, you can enter but you can’t leave! What am I?

A Japanese ship was en route to a mission on foreign seas. The captain of the ship felt tired and thought of taking a bath. He went for taking the shower and removed his diamond ring and Rolex and kept them on the table. When he returned after taking the bath, he found that the ring and watch were stolen.

He called the five members of the crew whom he suspected and asked them what they were doing for the last 15 minutes.

The Italian cook (with a butcher knife in hand): I was in the fridge room getting meat for cooking.

The British Engineer (with a high beam torch in hand): I was working on a generator engine.

The Pakistani seaman: I was on the mast correcting the flag which was upside down by mistake.

The Indian Radio officer: I was trying to make a contact with the company to inform them about our position.

The American navigation officer: I am on night watch, so I was sleeping in my cabin.

Upon listening to them, the captain caught the lying member. Who do you think stole the valuables?

A man is sitting in a bar when a rich man sits next to him. He turns to the rich man and says, “Did you know I know almost every song that has ever existed?”

The rich man laughs. The man then says, “I bet you all the money you have in your wallet that I can sing a genuine song with a lady’s name of your choice in it. The rich man laughs again and says, “OK, how about my daughter’s name, Jamie Armstrong-Miller?” Minutes later, the man collects his cash and the rich man goes home cashless. What song did the man sing?

You along with your friend are standing in front of two houses. Each of those houses inhabits a family with two children.

Your friend tells you the below two facts:
1) On your left is a family that has a boy who likes accounts but the other child loves science.
2) On the right is a family with a seven-year-old boy and a newborn baby.

You ask him, "Does either of the family have a girl?"

To this, he replies, "I am not quite sure. But can you guess that? If you are right, I will give you $500."

Which family do you think is likely to have a girl?

John went to a parrot shop in Mexico, and the parrot owner told him that his parrot is so unique that he repeats everything he hears. John got excited and immediately bought the parrot. John went home and spoke many words, but the parrot does not repeat anything.
He went again to the parrot shop and complaint to the shopkeeper, but the shopkeeper never lied. Explain?