I travel all around the world but always stay in the corner. What am I?

A famous swimmer can swim downstream in a lake in exactly 40 minutes with the lake current.
He can swim upstream in that lake in exactly 60 minutes against the lake current.
The length of the lake is 2 km.

How long he can cover the distance of one side at a still lake with no current?

John enters a small room. The Door Closes.
When the door opens, John is in a larger room.

Explain?

The product of three consecutive numbers is 7980.
Then the sum of these consecutive numbers would be?

Two in a corner, one in a room, zero in a house, but one in a shelter. What am I?

The centre of the third figure is empty. What digit should fit inside?

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 always drive my customer away.

Who am I?

An octopus has 8 legs. A hippogriff has 6 legs and 2 pairs of wings. A sphinx has 6 legs and one pair of wings. Now we have all 3 kinds and a total of 18 insects in a cage. We have a total of 118 legs and 20 pairs of wings. How many insects do we have of each kind?

I sleep during the day and fly at night, but I have no feathers to aid my flight. What am I?