There is a long tradition of posing puzzles at interviews for technical positions. Despite my respect for puzzles, I don’t believe one’s ability to solve one quickly in a high-pressure situation provides an accurate forecast for their future job performance. Google, once known for its notoriously difficult interview puzzles, retired the practice in 2013, with the senior VP of people operations at the time stating that they were “a complete waste of time. They don’t predict anything. They serve primarily to make the interviewer feel smart.” This week, your interviewer is Elon Musk. Try to solve his preferred puzzle to give to engineers vying for a job at SpaceX. While the puzzle is not rocket science, it will require some ingenuity.
Did you miss last week’s puzzle? Check it out here, and find its solution at the bottom of today’s article. Be careful not to read too far ahead if you haven’t solved last week’s yet!
You are standing somewhere on the surface of the Earth. You walk 1 mile south, then 1 mile west, and then 1 mile north, and you end up back at the same point where you started. Where are you? Assume the Earth is a perfect smooth sphere.
The most natural answer to this question is the North Pole. And it’s correct! Walking a mile south from the North Pole, then a mile west, and a mile north again will land you right back at the top of the planet. According to Musk’s biographer, Ashlee Vance, when engineers would get this correct, Musk would respond, “Where else could you be?” That problem is significantly tougher, and solving it is your task for the week.
The South Pole doesn’t work. Traveling south from the South Pole isn’t even a meaningful concept, since moving south is by definition moving toward the South Pole. It helps to remember that we’re on a big sphere. Think of lines of latitude not actually as horizontal lines but as circles traced around the globe that get progressively wider toward the equator and narrower toward the poles.
Good luck solving the puzzle this week, and rest easy that your career doesn’t depend on it.
I’ll be back next Monday with the solution and a new puzzle. Do you know a cool puzzle that I should cover here? Send it to me at firstname.lastname@example.org
Were you able to snare the mouse from last week’s puzzle? You can guarantee that you catch the mouse in six days. There are several solutions. Numbering the cabinets in order from 1 to 5, one solution is to check them in this order: 2, 3, 4, 2, 3, 4. A clever observation is that the mouse must alternate between odd- and even-numbered cabinets each day.
Suppose the mouse begins in an even-numbered cabinet. How could you catch it in this case? On day one, you open cabinet 2. If the mouse is in there, you win. Otherwise, the mouse must have been in cabinet 4. This means that on day two, the mouse will either be in cabinet 3 or cabinet 5 (because these are the only cabinets adjacent to 4). Open cabinet 3 on day two. If you find the mouse, you win. Otherwise, it means the mouse was in cabinet 5 that day. But this means that on day three, you know the mouse will be in cabinet 4 (the mouse’s only legal move from cabinet 5). So by checking the cabinets 2, 3, 4, on the first three days, you are guaranteed to catch a mouse that begins in an even-numbered cabinet.
If these are your first three moves and you do not uncover a mouse, this means that the mouse must have begun in an odd-numbered cabinet. So where is the mouse the morning of day four? Since it started in an odd-numbered cabinet and it alternates between even and odd each day, the mouse must be in an even-numbered cabinet on day four. Luckily, we already have a strategy that catches the mouse when it begins in an even-numbered cabinet! Repeating it by guessing cabinets 2, 3, and 4 again on days four, five, and six is then guaranteed to catch the mouse.
Notice that in the solution, we could run the argument in reverse and start with door 4 before proceeding to 3 and 2. We can even mix the two strategies. For example, the order: 2, 3, 4, 4, 3, 2 catches the mouse. It turns out that this latter backtracking approach is what is needed when you have an even number of cabinets. In fact, this generalizes to any number of cabinets. This means that even if the mouse had 100 places to hide, if you simply open 2, 3, 4, up to 99, and then begin backtracking to 98, 97, and back down toward 2, the mouse has no hope of evading you.