This is a solution to problem 10 on the hard interview questions
There are infinite points where walking one mile south
, one mile east
and one mile north
you reach the place where you started.
- The North Pole
. Walk a mile south (i.e. any direction), then one mile east (an arc of 1 rad around the pole), then walk back north one mile.
- Exactly 1 + 1/(2π
) miles from the South Pole
. You walk south one mile, ending up exact 1/(2π) miles from the South Pole. You walk east one mile, around the South Pole and back (drawing a circunference
of 1/(2π) miles and length of 1 mile). Walk north one mile, and you're back where you started.
- Exactly 1 + 1/(4π) miles from the South Pole
. Just as above, except you go around the South Pole two times.
- Exactly 1 + 1/(2xπ) miles from the South Pole
, where x is a natural number
. You got the idea.
This, of course, assuming both poles can be walked and circled around at will.