The question is this:
I go south one mile, east one mile, north one mile, and end up where I started.
The usual answer is the north pole. But the thing is, that there are infinitely many points with this property, all but one of which are near the south pole.
To see this, here is a picture:
If we start at a point \(P_0\) which is exactly \(1+\frac{1}{2\pi}\) miles from the south pole, and walk one mile south, we find ourselves at a point \(P_1\) exactly \(\frac{1}{2\pi}\) miles from the south pole. If we then go east one mile, we complete a whole circle of radius \(\frac{1}{2\pi}\), so end up at \(P_1\) again. If we then go a mile north, we get back to \(P_0\).
Indeed, if we start at a point exactly \(1+\frac{1}{2n\pi}\) miles from the south pole, for any positive integer \(n\), we will also end up exactly where we started.
Image made with Blender. Earth texture came from here