How many tangerines fit in this room?

How a person answers simple questions can tell a lot about what type of thinker they are.

It's not that you need to know a lot of math to answer this question (it's basic geometry and arithmetic), but rather that people who think quantitatively as part of their day-to-day life can be identified by their attitude towards this question.

There's a big difference between someone who thinks like a quant and someone who can do math on demand, so to speak. Thinking like a quant means that you generally look at the world through the prism of math; that when you're solving a work problem, you're not just applying knowledge from your education, but also something you practice every day. And that practice makes a difference.

 It's like the difference between an athlete (even if amateur) and someone who goes to gym class.

To illustrate, consider your typical "lone inventor can upset entire industry" story, in particular this one that was in the last Fun With Numbers.

I didn't read the article, but from the photo [which is deceptive, in the article the 1500-mile battery is bigger, though still small enough to make the result non-credible] we can see that the '1500-mile battery' volume is about 2 liters, so a little bit of arithmetic ensued: 

1. 1500 miles w/ better-than-current vehicles [a google search shows that they're all over 250 Wh/mi], say 200 Wh/mi: 300 kWh (1.08 GJ)
2. Volume of battery, from article photo [estimated by eye], let's say 2 l, so energy density = 504 MJ/l
3. Current Li-Ion battery energy density [google search] ~2.5 MJ/l to  5 MJ/l (experimental) 

Home inventor creates something 100 to 200 times more dense than
current technology (and about 15 times more energy-dense than gasoline)?! Not credible.

Are we to believe that the journalists can't do the simple search and arithmetic needed to raise the concerns we can see? Or that they expect none of their audience to? (This second question assuming that the journalists know that the battery can't work, but are willing to write these clickbait headlines because they assume their credibility is not going to be questioned by innumerate audiences.)

Back to the tangerines, and a tale of three people.

Person one gets confused by the question, takes a while to think in qualitative terms (sometimes verbalizing those), then eventually realizes it's a geometry question and with more or less celerity solves it. Person one can do math "on demand," but doesn't think like a quant.

Person two grasps the geometric nature of the problem immediately, estimates the size of the room and of an average tangerine, reaches for a calculator, and gives an estimate. Person two "groks" the problem and is a quant thinker.

Person three sketches out the same calculation as person two, but then adds a twist: instead of a calculator, person three reaches for a spreadsheet, to create a model where the parameters can be varied to allow for sensitivity analysis. Person three is an advanced version of a quant thinker, a model-based thinker.

The problem with "puzzle" interview questions: I - The what

I like puzzles. I solve them for fun; I don't like when companies use them for recruiting, though.

Some companies use puzzle-like questions as interview devices for knowledge workers. Other than the obvious inefficiency of using proxies when there are direct measures of performance, many of these questions penalize creativity and thinking outside the box defined by the people who are conducting the interview (usually the potential coworkers).

Here's a thought: if hiring a programmer, ask a programming question. For example, give the interviewee a snippet of code and ask what its function is; ask how it could be optimized; ask what would happen with some change to the code or how a bug in a standard subroutine would affect the robustness of the code.

Here's a second though: if hiring statisticians, instead of trying to trip them with probability puzzles (especially when your answer might be wrong), show them a data-intensive paper and ask them to explain the results, or to consider alternative statistical techniques, or to point out limitations of the techniques used. Perhaps even -- oh what a novel idea -- consider asking them to help with an actual problem that you're actually trying to solve.

My job interviews, in academe, were like these thoughts: I was asked, reasonably enough, about my training, my research, my teaching, and to demonstrate the ability to present technical material and answer audience questions; job-related skills, all, even though some interviewers were interested in puzzles.

In social events, however, some acquaintances have asked me questions from interviews; here are a couple of responses one could give that are correct but unacceptable to most interviewers:

How would you move Mount Fuji?

Well, in a universe in which the Japanese people and government would allow me to play around with one of their most important landmarks, I'd probably be too busy simuldating Olivia Wilde and Milla Jovovich to dabble in minor construction projects. But if I had to, I'd use a location-to-location transport beam from my starship, the USS HedgeFund.

Or did you want to know whether I can come up with the formula for the volume of a truncated cone?

What is the next number in this sequence: 2, 3, 5, 7, 11,...

It's pi-cubed. You are enumerating in increasing order the zeros of the following polynomial
\[ (x - 2) (x - 3) (x - 5) (x- 7) (x - 11) ( x - \pi^3).\]
Or did you think that there was only one sequence starting with the first five prime numbers?

Bob has two children, one is a boy. What is the probability that the other is a boy?

I made a video about that. (Even after that video, or my live explanation, some people insist on the wrong answer, 1/3; proof that there are few things more damaging than a little knowledge matched with a big insecure ego.)

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I'll have a later post explaining the deeper problem with using puzzles (and its dynamics), part II of this.