In the early years of rocket company SpaceX, CEO Elon Musk liked to set job applicants the following problem:
You’re standing on the surface of the Earth. You walk one mile south, one mile west and one mile north. You end up exactly where you started. Where are you?
The most common response was the North Pole, which is a correct answer. Indeed, the question is an old chestnut. (The earliest known reference to a version of this puzzle is 1821.)
According to Musk’s biographer Ashlee Vance, however, Musk would then ask: “Where else could it be?”
That is today’s first puzzle: where else could it be?
The shape of the Earth (and Mars, fwiw) leads to many other excellent puzzles. Here are three of them:
1. One direction
You are standing on the surface of the Earth. You head north and travel for ten miles in a straight line. After a quick stop, you again head north and travel another ten miles in a straight line. You end up exactly where you started. Where are you?
2. Squaring the circle
You are standing on the surface of the Earth. You walk ten miles north, ten miles west, ten miles south and then ten miles east. You end up exactly where you started. Where are you?
(Note: this is not a trick question. Since the Earth is spherical, almost all starting points will not get you back to where you started.)
If you think you have an answer, I will Elon Musk it right back at ya: where else could it be?
3. Brain Fogg
In the Jules Verne story Around the World in Eighty Days, Phileas Fogg leaves London on October 2, 1872. He travels via Egypt, India, Japan, the US and his final leg is across the Atlantic. As the book’s title indicates, the trip takes him 80 days. What day did he arrive back in London?
(Note: the eightieth day after October 2 is December 21.)
Clarification for pedantic astronomers, geographers and physicists: assume the Earth is a perfect sphere.
I’ll be back at 5pm UK with the answers.
Meanwhile NO SPOILERS. Please instead discuss the shape of the world.
I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
I’m the author of several books of puzzles, and also the children’s book series Football School. The latest instalment, The Greatest Ever Quiz Book, is just out.
I give school talks about maths and puzzles (online and in person). If your school is interested please get in touch.
Sources: 1) Adapted from a puzzle by David Singmaster, 2) Murray S Klamkin, Mathematics Magazine 1958/9