All the walls face south.

Can you guess the color of the bear?

What kind of question is that?

How is the color of a bear linked to a house?

Think.

I have no idea man.

The color of the bear is white.

Confused?

Obviously.

Let me explain.

The Earth is a sphere.

At any point on the Earth, any direction will point towards the antipode.

That is, the point directly opposite on the sphere.

Now, when the house is exactly at the north pole.

Every direction will point directly opposite to the north pole on the sphere, which is south.

That is why all the walls face south.

Now, in the north pole, we can only find polar bears which are white in color.

Hence, the color of the bear is white.