Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not rounded numerals equals 24.

Always in you, Sometimes on you;

If I surround you, I can kill you.

What am I?

You stand in front of two doors. A guard stands next to each door. You know the following things: one path leads to paradise, the other leads to death. You cannot distinguish between the two doors. You also know that one of the two guards always tells the truth and the other always lies. You have permission to ask one guard one question to discover which door leads to paradise. What one question would you ask to guarantee you enter the door to paradise?

There are nine letters in the below-given diagram. You have to form a nine-letter word using these letters.

John is selling fruits.
He sells grapes at $30, Dates $25, and a Wolfberry $45.
At what price does he sell fig?

PS: Logical Thinking

A word I know,
Six letters contain,
Subtract just one,
And twelve is what remains.

Many have heard it, but nobody has ever seen it, and it will not speak back until spoken to. What is it?

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.

Replace the question mark with the correct number.

What do you see in the given picture?