If you're reading this article, you're interested in learning about the skills required to solve quantitative puzzles. Well, you've arrived at the right place. In this article you'll see me making heavy reference to Jane Street Puzzles. While Jane Street Puzzles are not an exhaustive list of quantitative puzzles, they are the gold-standard for widely attempted puzzles in the space of quantitative trading. Keep this in mind as you think of how to apply the tips below to puzzles you Since I hate long blog posts whose sole purpose is to get your to stay on a webpage for as long as possible, let's get right into it.
I know, this point seems extremely obvious, but hear me out. Not all quantitative puzzles are written equally. There is a misconception that quantitative puzzles, or puzzles written by quantitatives are all about math. That could not be further from the truth! Quantitative puzzles come in all shapes and sizes, and many are not at all quantitative in nature. I've even worked on, and solved, poetry-based quantitative puzzles (see Poetry in Motion). Given the diverse nature, there are many different skillsets that are all applicable to solving quantitative puzzles.
This brings me to my first point, understand what skills are in your toolkit! The following are a set of commonly tested forms of intelligence in the context of quantitative puzzles. Think carefully about the tools in your arsenal that may be applicable to each form of intelligence. For example, I rely on programming as one of strengths to break down puzzles that would traditionally require superior spatial reasoning, such as Tri, Tri Again, Again.
As examples of different forms of tested intelligence appear, I'll make sure to expand on this list.
Nobody is a Jack-of-all-Trades. This is especially true in the world of quantitative trading, which relies on the harmonious co-operation of traders, developers, and researchers, along with other equally important teams such as trade support, risk, and operations. Hence, both in the workplace and outside of it, you will need to be comfortable relying on others for assistance. This doesn't mean that you offload your responsibility onto someone who has more experience than you. It means you attempt a problem, detail your current approach, brainstorm several ways forward, and run those paths by someone who can guide you down the best approach to take.
Being resourceful in the context of quantitative puzzles involves humility; it involves understanding that you don't understand everything. When I hit a wall when I attempt a quantitative puzzle, I pursue one or more of the following options:
Notice how the list above does not include "Ask a colleague". While asking a colleague may be appropriate, often times your work-colleagues may be uninterested in a puzzle, especially if they are busy, and so using work-time to go through something you should be doing on your own time is inappropriate.
This one is obvious. By virtue of being in the industry, you are most likely already running in circles of people who take interest in solving problems. If so, there is no doubt that several will take intrigue in helping you solve a puzzle, or at least giving you advice. Turn to those who are close to you when you find yourself stuck.
If you don't have any friends, or you don't have any friends interested in solving quantitative puzzles, you can always turn to the internet. The internet is riddled with forums on every subject from chess to Dota 2. There is no shortage of forums you can leverage to help you through an impasse. Simply search for a forum that contains subject matter relevant to the question you'd like to ask, and I'm more than certain there will be a forum participant willing to help you. You'll be surprised how many people you can convert into Jane Street puzzle solvers by introducing them to a puzzle or two, and how many are willing to help you!
This tip sounds ridiculous, doesn't it? Of course I should persevere, you're telling yourself. Well, not everyone understands what I really mean when I say 'persevere'. In the West we've come to think of intelligence as a binary, you either know something or you don't. This is why Western children give up on problems they haven't encountered within 30 seconds of their initial attempt, while students in the East can exhaust an entire hour before quitting. The American school system teaches students that intelligence is an acquired skill, and if you don't possess the intelligence required to solve a problem, you will never be able to solve said problem. The East, on the other hand, teaches students that intelligence is gained through struggle and hard work. As a natural extension of this phenomenon, people who approach quantitative problems tend to give up a lot easier if they were taught that they are "simply not smart enough" to solve the puzzle.
I've solved countless puzzles by which, if I was to give up, I would have lost out miserably. Many of my breakthroughs occurred at one in the morning, whereby I was able to make more progress during the last hour before solving the puzzle than I was able to during the first five. Quantitative puzzles are made to be difficult. There are rare exceptions in which, after your initial read through of the puzzle, you know how to solve the puzzle immediately. Most people struggle through quantitative puzzles and that's just fine as long as you arrive at the correct answer.
It's important to understand what a puzzle is asking before attempting the puzzle. This involves doing some preparation. I like preparing the old-fashion way - take out a piece of paper and a pen and start drawing. This is where your spatial reasoning skills comes into play. Often times, simply drawing out a puzzle can help you come to conclusions you would have never been able to had you either dived directly into the puzzle, or simply sat there and thought about it.
For example, in the June 2020 Jane Street puzzle Circle Time, I wrote a monte carlo simulation to find the maximum proportion of the area of the circle that can be covered by rings entirely contained within the circle. If I was to go into writing the simulation without doing any thinking beforehand, the simulation would have taken weeks to run and most likely would have spat out an answer to a tolerance that would disqualify my submission. I knew that I would need to remove a large amount of cases hexagonal orientations from within the circle when running my simulation. After drawing out the shape detailed in the question, and thinking about it, I came to the conclusion that there are only two orientations that the hexagon contained within the circle can be positioned in to maximize the area of the mutually disjoint circles contained within the larger circle, C. These orientations were having the hexagon in its original upright orientation (which I called '0 degrees' in the source code) and another slightly tilted (30 degree) orientation.
This helped me eliminate an infinite amount of hexagon orientations and cut the runtime of my puzzle-cracking algorithm dramatically. The algorithm runs and arrives at the correct answer in under 1 second. See a link to the source code below.
Quantitative puzzles are hard. They are meant to discriminate against people who neither have the fortitude nor creative capability to think through problems that require a higher level of reasoning and a skillful understanding of one's own toolkit. You'll notice that, while I solved quite a few Jane Street puzzles in 2020, I stopped solving them in 2021 (the last puzzle I solved was the January 2021 puzzle Figurine Figuring). This is because I simply have other priorities which have taken precedence. Hopefully the information I've imparted with you can help you carry my torch as I retire to building on my other endeavors.