Giving Smart Answers Under Pressure

I recently decided to sell my vinyl collection, lovingly kept for years. The traditional hi-fi takes up too much space, changing sides of albums is a chore and (the way it’s set up) it’s primarily for just one room. I now find Sonos and Spotify (and others) a much more flexible and convenient arrangement. I’m not bothered by the slight decrease in sound quality. The latter also allows easy search for known artists and it’s fascinating to discover loads of great new musicians I never knew existed.

For selling the vinyl (that I had an obvious emotional attachment to), I had to come to a rough valuation. As I was moving house at the time and things were hectic, in the end I didn’t pay too much attention to this. I did find sites that gave estimates for individual prices (depending on their condition and the pressing) but going through the whole collection would have taken ages. Also there were comments that the prices were very subjective. So to get a quick solution I did some very rough guesswork and negotiated from that.

What I should have done (obvious in hindsight) was do some guesstimates. At the very least, put records into categories (rock, folk, jazz and classical), estimate average prices plus identify any special items of value which presumably would be few eg early pressings. This valuation is not what you may achieve but at least gives a better starting point to negotiate from. As they say, in negotiations, the one with most knowledge wins! The issue is what is the smartest thing you can do under strict time pressure. I’m not saying I got a bad price it’s just that I’d have a nicer feeling inside if I’d thought things through (I know, that’s life!).

This got me thinking about more general guesstimates, sometimes called Fermi Problems or back-of-the-envelope calculations. Fermi was a highly creative scientist and won the Nobel Prize for his ground breaking work in nuclear physics. He was one of the last ‘giants’ that could encompass and contribute to both experimental and theoretical physics (disciplines that require very different skills). He had a reputation for his seemingly uncanny ability to give good estimates to tricky problems even with little actual data.

A famous example of a Fermi Problem (that he used to tantalise students with) is: How many piano tuners are there in Chicago?

This at first site seems an impossible problem but on reflection some educated guesses can be made that give a good approximation to the answer (see here):

  1. Assume population of Chicago is roughly 3,000,000 (actually 2,693,976 in 2019)
  2. Assume average family size is 4, so number of families is about 750,000
  3. If one in five families owns a piano (seems a bit high but rounds things for easy calculation), then 150,000 pianos to be tuned in principal
  4. If the average piano tuner works 5 days a week and tunes 4 pianos a day for 50 weeks a year (2 week vacation), he/she can service 1,000 pianos.
  5. So, for these two estimates to match, there must be about 150 piano tuners in Chicago.

Obviously you can contest each assumption, see how sensitive it is to changes and so on. But the main point is that some simple and quick reasoning can give an initial ball-park figure (ie order of magnitude 100 tuners). You’re now working from a situation of some knowledge rather than no knowledge.

Recently I came across a site, Street of Walls, that goes through a number of these problems in a business setting. For instance, they might be the sort of question you get in a demanding job interview for management consultancy.

Examples they give (with typical ‘answers’) include:

  • How many flat screen televisions have been sold in Australia in the past 12 months?
  • How many iPhones are currently being used in China?
  • What is the revenue of Peugeots sold in France per year?

These questions might all sound crazily difficult but using the approach of the piano tuner example above, it might be educational to try the above questions prior to looking at the answers. Remember, you’re not looking for ‘the’ answer rather a reasonable and quick approximation to it. In some sense, this is the first step, to reframe the question into something manageable. Also, to keep your cool.

This approach to developing intelligent guesses also reminds me of something that the famous physicist Richard Feynman said (and probably many others too). When you start a problem make some bold educated guesses. If a more careful analysis gives a very different answer, figure out what you missed in the back-of-the envelope approach and try to learn from it. With a bit of luck, your intuition and guesswork will steadily improve and deepen as a result.

I’ve written about the topic of guesstimates previously, motivated by some thoughts of Seth Godin:

“When I interview people for jobs, I always ask, “How many gas stations do you think there are in the United States?” Not because I care how many gas stations there are, but because it gives me an insight into how people solve problems.

The vast majority of people who answer this question (Iʼve asked it more than 1,000 times over the years) start their answer with, “Letʼs see…there are 50 states.” They then go on to analyze their town, figure out how many gas stations there are, and multiply from there…”

He mentions this is not a good approach as it doesn’t deal with easily scalable quantities and ends up with another totally different way forward:

“Instead of starting the business that makes stuff for people just like you, do some real re-search. Go to the library. Donʼt invent something that requires you to have a handle on the purchasing habits, the psychographics, and the changing demographics of the whole country. Instead, find a thriving industry and emulate and improve on the market leader. Sheʼs already done your homework for you.”

This could be an additional point you could use in the interview. More details in my original post here.

Finally, as an aside, on the topic of extremely demanding and somewhat crazy interview questions, see here.


  1. How many gas stations? With a population of 330 million, and an average age of death of 70, and a driving age of 18, that’s about 74.3% of the population that drives (245.2 million), and probably works a job. Assuming that 80% of these people own a car, that’s about 196 million drivers. If the average car drives 50 miles a day, and the average tank gets 400 miles, then drivers will refuel every 8 days, so every day 24.5 million drivers are refueling. If the average gas station has 8 pumps, and takes 10 minutes to fill a tank, that’s 1,152 cars a day. Let’s assume that these cars all refuel four hours a day on their way home from work. That’s about 200 cars a day. That’s about 122,500 gas stations. If the average tank is 15 gallons, and the cost per gallon is $2.00, then a gas station is averaging about $6,000 per day, or $2,190,000 a year in gas revenue. That sounds about right.

    1. Hi William, thanks for commenting and for the interesting and detailed analysis. Out of curiosity, I quickly googled and found there were c 111,000 in 2016 so the estimate is very near. Anything up to a reasonable factor is fine of course reflecting all the many approximations made. Once again, thanks for the comment.

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