n the Northern Hemisphere, only one point P satisfies the conditions of this puzzle --the North Pole {Hypernote#1}. The Southern Hemisphere is quite another matter. Pick any point P located exactly...

one mile 840 feet 4 inches

...from the South Pole and follow the same instructions:

 Starting at some point P, a sophisticated person travels one mile south, one mile east, and one mile north, arriving back at P.
• The first mile travels a straight pathway south from point P reaching a point Q exactly 840 feet 4 inches from the South Pole.

 The sophisticated solver will recognize that distance as one mile divided by 2..
• The second mile, traveling east from point Q, takes the puzzle solver on a circular pathway, exactly one mile in circumference, around the South Pole back to point Q {Hypernote#2}.
• The third mile travels a straight pathway north from point Q to point P, retracing the first mile.

Hypernote #1 -- Birds and Bears

The juvenile version of this puzzle asks for the color of a bear killed by a hunter after following the triangular journey. That statement of the puzzle eliminates the southern solution, since most people know that there are no bears at all in Antarctica (only the most precocious child or petulant grown-up will complain that a polar bear would never be found within a mile of the North Pole either).

There are penguins down under, though, which invites the question, What kind of bird did our hunter kill? The sophisticated explorer knows that penguins are aquatic birds; their habitat must be located many miles from the South Pole and therefore safe from a hunter at point P.

By the way, apart from places like the Vancouver Zoo, there are no penguins inhabiting the Northern Hemisphere. Anymore. Sophisticated solvers know that the great auk lived in northern regions and was called a 'penguin' before being hunted to extinction in the 19th century.

Hypernote #2 -- Questions for Puzzle Solvers

In the Antarctic solution, how many time zones are crossed in traveling that second mile?

Since the International Date Line will be crossed going east, which way will the date have changed upon arrival back at point Q?

In the Arctic solution, how many time zones are crossed in traveling that second mile?