SDS 088: Fermi questions

Hey guys, and welcome back to the SuperDataScience podcast. Today we’ve got an interesting episode. I would like to share something with you that might help you on your interview as a data scientist. So, Fermi questions, what are they? Well, Fermi questions are questions designed to test your logic, and you may have encountered them before. So, they usually are formed or phrased in a way where the person asking you this question designs a scenario, asks you about a real world scenario, and asks you to provide an estimate very quickly. And we’ll have an example just now, but I wanted to touch on where they come from.

So, Fermi questions, they originally come from Enrico Fermi, who estimated the power of the atom bomb tested at the Trinity test simply through some pieces of paper which he had in his hand. So, when the bomb blew up, he dropped the papers from his hand. And as they were flying, the explosion moved them. So basically, the shock wave from the explosion moved the papers, and by how far it moved them, he was able to estimate that this was a 10 kilo-ton bomb, which is a very close estimate. In reality, it was a 20 kilo-ton bomb, and that was calculated afterwards. But, as you can imagine, by estimating that from just some pieces of paper in your hand, that’s very, very close to the real value, and very impressive as well.

And so that’s exactly what you need to do at an interview, you need to show your thinking and actually impress the interviewer with your logic and how quickly you can come up with this estimate. It doesn’t have to be accurate. It doesn’t have to be precise. But it has to just show your thinking. That’s what they’re all about. And that’s what a lot of people get wrong. They start trying to get the exact right answer, or provide a very accurate estimate, whereas in reality, people just want to see how you think on your feet, how your logic works, how your mind works.

And so, let’s have a look at an example of one of these questions. So, this was a question I was asked when I was interviewing for Sunsuper, the superannuation or pension fund which I went to after Deloitte. It was quite a complex interview because I had less years of experience than they were looking for, so already I was at a disadvantage in their perspective, as I can imagine. And also, I was about to double my salary based on this interview. And so, as you can imagine, it was a challenging interview, and at the very end, there was this question. So I really had to show my thinking. And so this was the question: Can you estimate how many red cars there are in Australia?

And that’s all. They don’t give you any additional information, they don’t tell you anything else, that’s the question. How many red cars are there in Australia? And off you go. And so the trick here is of course to take a few minutes to think about it. You just say, “Ok, let me think about this for a second, get everything lined up in my head.” But as soon as you start talking, you should keep going and not pause or not stop. That’s the way I approached it.

So basically, the calculation goes as follows: There’s approximately 24 million people in Australia. For calculation’s sake, we’ll say 24. We know that on average, there’s about four people per family in Australia, from my personal experience. So that means about 6 million families in Australia. And, also from my personal experience, I know that there’s about 2 cars per family, plus or minus, give or take, but on average, it would be 2 cars per family. So that makes it 6 x 2 = 12 million personal vehicles in Australia. Ok, that’s great. So now, why aren’t we taking into account commercial vehicles, you can say this as a side note, because commercial vehicles are rarely red. They’re mostly white or black. So we’re going to stick with just personal vehicles, 12 million personal vehicles.

And now we need to figure out the colour as well. Just as a benchmark, we’re going to take the 7 colours of the rainbow, then we’ll add white and black to that. That makes 9 colours because white and black are not included in the colours of the rainbow, and cars come in white and black, and then we’re going to count the colour white twice, because in Australia, it’s very hot, and a lot of people choose white cars because they absorb the least amount of sun, so it’s cooler to have, inside you feel cooler, you don’t feel as hot to have a white car, and so we’re going to count white cars twice, and therefore we don’t have 9 colours, we actually have 10 colours. And that’s really good, because it helps us with counting, makes it very easy to divide, and we have 12 million personal vehicles divided by 10, makes it 1.2 million red cars in Australia approximately. And there you go. That’s your answer.

As you can see, that was very quick, and all I needed was the population of Australia. Some people might approach this wrong, they might start thinking oh, how would I solve this problem? I would sit outside, and I would start counting the cars, and then I would extrapolate into the total amount. So they do describe their logic, but you need to just take what you already have, the population of Australia, or you might even know how many personal vehicles are in Australia. But usually it’s something like common knowledge. You might need to do some basic mathematics to calculate the volume of a cube, or something during your calculation process, but basically, all the things that are available to you in your mathematical apparatus, and your common knowledge, you can apply to come up with an answer.

And, by the way, that estimate of the number of personal vehicles in Australia is quite accurate. As of 2017, as of this year, as of 31 January this year, this is stats from the Australian Bureau of Statistics, I’m just looking it up now. There was 18.8 million registered motor vehicles in Australia, but that’s total, and 75% of them are passenger vehicles. So basically, that means 14.1, if you take 75% of 18.8, you get 14.1 personal vehicles in Australia, versus the 12 that I provided in my estimate. So quite an accurate number. If you take into account what I started with, what information is available to you when you are actually performing this, which is very, very little information, which is just the population of Australia.

So there you go, that’s how to answer a Fermi question. Look them up, there’s whole websites devoted to them. There’s lots of interesting ones, you know, how many tennis balls in America, how many ping pong balls fit into a Boeing 777, how many trucks would it take to move the whole of Mt Everest to another location, and stuff like that. So lots of interesting questions. It’s good fun going through them. You know how people sometimes sit and solve sudoku in their free time, on a bus or something? It’s really cool to just take one of these questions and not read the answer right away, but actually think it through and try to apply your own logic, and then compare what you got to the logic that’s described in the solution. And that way you will train your brain for these Fermi questions.

And even if you’re not applying for a data scientist role, they’re really cool because in consulting, these questions are often asked when you’re applying for jobs. You might get asked these questions when you’re applying for analyst jobs. Basically, any kind of job where you need to apply logic, they can ask you this question. And if you’re a manager, or an executive yourself, you might find an interesting question yourself, and ask people who you’re hiring to provide that estimate.

And there are different levels. Some of them require a bit more mathematics, like with the Mt Everest, you’ll need to calculate based on its height, you might be given the diameter or something, and you’ll need to calculate the volume and things like that. So it requires some geometry, or some mathematics, algebra. Some are easier, some are harder. So have a look at the different options. But a lot of my friends – not a lot, but people who have applied for consulting roles and data science roles, have very often been asked these questions, so it’s good to have them in mind. And even if you’re completely happy with your job, and you won’t be in an interview any time soon, or you won’t be interviewing anybody any time soon, it’s a really cool way, a really fun way, to discover things about the world and train your brain at the same time.

So there you go. I hope you enjoyed this episode. Hope that helps you out, or maybe you might help out a friend who is looking for an interview. If they are, then send them this episode, and they can catch up on Fermi questions. And I look forward to seeing you here next time. Until then, happy analyzing.