Kapila’s Insights on Math and Physics Questions
Ananay Kapila is the founder of the exchange startup QFEX and has a background as a high-frequency trading (HFT) trader in London. He’s worked at firms like Flow Traders and Tower Research Capital, where he even interviewed young candidates. Recently, he shared some of the questions he used during those interviews, including one he described as “the most ridiculous thing I’ve ever seen in math/physics.”
Kapila noted that the questions themselves weren’t particularly hard, but the answers often surprised him. One of the questions he posed is framed like this:
“We have a light ball of mass m, a heavy ball of mass M = 16 * 100^5 * m, and a wall. We kick the heavy ball towards the light ball. There is no friction, no elastic collision, etc.
i) Does the heavy ball change direction (pass through the lighter ball) before hitting the wall?
ii) How many times will it collide with the photosphere when changing direction?”
This problem rings a bell for many. It gained popularity from a video by YouTuber 3Blue1Brown, which has amassed over 14 million views. The conclusion there indicates that, eventually, both blocks will slide off the wall without touching again. If the larger block’s weight increases proportionally to the smaller one, the collisions grow significantly according to pi (π).
For instance, if the larger ball is 10,000 times the mass of the lighter one, it will collide with the wall 314 times. If it’s a million times larger, the collisions rise to 3,141. At 10 million times the size, the number of collisions would be 314,159, and so on.
A more in-depth exploration of this can be found at 3Blue1Brown. While understanding how to derive the answer is valuable, the interview’s purpose might lean more towards gauging the candidate’s passion for math rather than just their mathematical prowess.
Kapila has also asked other interesting questions during interviews. For instance:
“Imagine an infinite number of people in a room wearing red or blue hats, where each can see everyone else’s hat but not their own. Is there a way for them to guess their hat color, minimizing wrong guesses?”
Think you could solve that? Feel free to share your thoughts in the comments!
