There are an unbounded number of places near the south pole where you can go 10 miles south, ten miles east (or west) and ten miles north, ending up at your starting point.

For example, Consider a place near the South Pole where a circle of constant latitude is 5 miles in circumference. Any spot ten miles north of that lattitude would fit the conditions.

Then consider places near the South Pole where a circle of constant latitude has a 10 mile, 2.5 mile, or 1.25 mile circumference.

On earth, if they said they saw a few bears while taking their trip, it would have to be the North Pole because there are no bears near the South Pole.