Walk south, east, north, and end up home

Question

You start at some point on Earth, walk exactly 1 mile south, then 1 mile east, then 1 mile north, and find yourself back at your starting point.

From how many points on Earth can you do this? (The North Pole is one, but it is far from the only one.)

Accepted Answer

There are infinitely many such starting points: the North Pole, plus infinitely many rings of points clustered near the South Pole. The North Pole. Start at the North Pole. Walk 1 mile south (down some meridian). Walk 1 mile east, this traces an arc along a circle of latitude, but you stay at the same distance from the pole. Walk 1 mile north, straight back up the meridian to the pole. You're home. The sneaky southern solutions. Near the South Pole, circles of latitude get tiny. Find the circle of latitude whose circumference is exactly 1 mile. Now start at any point 1 mile north of that circ…

Walk south, east, north, and end up home

Your answer

More Brainteasers questions