When I get multiplied by any number, the sum of the figures in the product is always me. What am I?

Why 1729 is a magic number? Answer Logically.

There is a square piece of paper with a hole that is denoted by the circle on the top right side in the given picture. You have to cut the paper in a manner that it forms two and only two separate pieces of paper and then rearrange the pieces in a manner that the holes come in the centre of the paper.

I look at you, you look at me, I raise my right, you raise your left. What am I?

I left my campsite and hiked south for 3 miles. Then I turned east and hiked for 3 miles. I then turned north and hiked for 3 miles, at which time I came upon a bear inside my tent eating my food! What colour was the bear?

If we change the South-East direction into North and North-East into West and all others similarly.
Can you find out which direction will be in the place of South-West direction?

Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

Imagine you are in a room with no windows or doors. How will you get out?

Can you solve the below tricky visual equation?

Can you identify the Oscar-winning movie from the rebus below?