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?

You are given 16 witch hats. The hats are divided in four different colours – red, blue, green and yellow. Every colour has been assigned to four hats. Now each of the hat will be glued with a label of an arithmetic sign – ‘+’, ‘-‘, ‘x’ or ‘/’. But you can label one sign only once on one colour. In such an arrangement, the hats can be uniquely defined by its colour and symbol.

Can you arrange all the 16 hats in a 4x4 grid in a fashion that no two rows and columns have a repetition of colour or sign?
We have arranged four hats in the below picture to assist you.

_ _ _ IE _ _
_ _ _ IE _
_ _ IE _ _
_ _ IE _
_ _ _ _ IE

Like you see, some letters have gone missing from these words that contain the IE pair at some or the other place. The letters that will be used to fill the blanks are given below. Use them and form meaningful words. Can you do that?

A, C, D, F, H, K, L, M, N, N, O, R, R, S, S, S, T, T, Y and Y.

A worker is to perform work for you for seven straight days. In return for his work, you will pay him 1/7th of a bar of gold per day. The worker requires a daily payment of 1/7th of the bar of gold. What and where are the fewest number of cuts to the bar of gold that will allow you to pay him 1/7th each day?

There are 2 cops parked along a one-way street looking for traffic violations. They spot a taxi driver going in the wrong direction, yet they do nothing.

Why?

A man is sitting in a pub feeling rather poor. He sees that the man next to him is extremely rich. He turns to the rich man and says to him, 'I have an amazing talent; I know almost every song that has ever existed.'
The rich man laughs.
The poor man says, 'I am willing to 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, Joanna Armstrong-Miller?'
The rich man goes home poor. The poor man goes home rich.

What song did he sing? A man is sitting in a pub feeling rather poor. He sees the man next to him pull a wad of £50 notes out of his wallet. He turns to the rich man and says to him, 'I have an amazing talent; I know almost every song that has ever existed.' The rich man laughs. The poor man says, 'I am willing to 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, Joanna Armstrong-Miller?' The rich man goes home poor. The poor man goes home rich. What song did he sing?

A man is trapped in a room. The room has only two possible exits doors. Through the first door there is a room constructed from magnifying glass. The blazing hot sun instantly fries anything or anyone that enters. Through the second door there is a fire-breathing dragon. How does the man escape?

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 fell off a smuggling boat into deep water. He could not swim and he was not wearing anything to keep him afloat. It took 30 minutes for the people on the boat to realize someone was missing. The missing man was rescued two hours later on the return trip. Why didn't he drown? Note:- He didn't know swimming, the sea was deep, and He wasn't holding anything

Intelligence Agency need to break the vault but the problem is that they are not able to break the vault.

On the vault, a text is written as:

31 11 33 33 43 45
21 25
31 24 11 31 51 41

To Break the code Intelligence Agency brings a mathematician named Joseph.
Minutes later he deciphers the code.

Whats the code?