Why 1729 is a magic number? Answer Logically.

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.

I am a five-letter word and comprises two different vowels and three same consonants. I am so strong that I can spoil your entire work.

Can you find out who am I?

What numbers should go on the bottom line?
3 6 9 15
8 2 10 12
11 8 19 27
19 10 29 39
? ? ? ?

I have branches, but no fruit, trunk or leaves. What am I?

Replace the question mark with the correct number, given the pair of numbers exhibits a similar relationship?

? : 3839 :: 11 : 1209

John bought 150 chocolates but he misplaced some of them. His Father asked him how many chocolates were misplaced.
He gave the following answer to him:
If you count in pairs, one remains
If you count in threes, two remain
If you count in fours, three remain
If you count in fives, four remain
If you count in sixes, five remain
If you count in sevens, no chocolate remains.

Can you analyze the statements and tell us how many chocolates were lost?

Alex is stranded on an island covered in forest.
One day, when the wind is blowing from the west, lightning strikes the west end of the island and sets fire to the forest. The fire is very violent, burning everything in its path, and without intervention the fire will burn the whole island, killing the man in the process.

There are cliffs around the island, so he cannot jump off.

How can the Alex survive the fire? (There are no buckets or any other means to put out the fire)

How can a man go eight days without sleep?

You are in a land where thirty men and two women were dressed in classic black and white dresses.
They begin to fight as soon as any of them move.

Where are you?