Before I ask the question, I want to be clear that I am NOT talking about magnetic mono-poles.
Gauss Law of Magnetism says that magnetic flux inside a closed surface is always zero, the reason being (what I understood), if there is a North pole, there has to be a South pole, so the number of magnetic field lines that enter the surface is equal to the lines that leave it.
So that got me thinking, what if we keep just the North pole of a magnet inside the surface and South pole outside it. Then the magnetic field lines will just leave the surface and I don't think the flux will be zero.
Where am I going wrong?