In the early years of the SpaceX rocket company, CEO Elon Musk liked to ask job applicants the following problem:
You stand on the surface of the Earth. You go one mile south, one mile west and one mile north. You end up exactly where you started. Where are you?
The most common answer was the North Pole, which is the correct answer. The question really is an old chestnut. (The earliest known mention of a version of this puzzle is 1821)
However, according to Musk biographer Ashley Vance, Musk will ask, “Where else can he be?”
This is the first puzzle today: where else can 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 ten miles in a straight line. After a quick stop, head north again 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 go 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 take you back to where you started.)
If you think you have an answer, I’ll give it back to Elon Musk right away: where else can it be?
3. Brain Fog
In the story of Jules Verne Around the world for eighty days Phileas Fogg left London on October 2, 1872. He traveled through Egypt, India, Japan, USA and his last leg was across the Atlantic. As the title of the book shows, his journey takes 80 days. What day did you return to London?
(Note: the eightieth day after October 2 is December 21.)
Explanation for meticulous astronomers, geographers and physicists: accept that the Earth is a perfect sphere.
I will be back at 17:00 UK with the answers.
In the meantime, WITHOUT SPOILERS. Please discuss the shape of the world instead.
I put a puzzle here every two weeks on Monday. I’m always on the lookout for great puzzles. If you would like to suggest one, send me an email.
I am the author of several books with puzzles, as well as the series of children’s books Football School. The latest part, The Greatest Ever Quiz Book, has been released.
I give student lectures on mathematics and puzzles (online and in person). If your school is interested, please contact.
Sources: 1) Adapted from a puzzle by David Singmaster, 2) Murray S. Klamkin, Mathematics Magazine 1958/9
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