Ex-high-frequency trader in London reveals "the most ridiculous" interview question in HFT
Annanay Kapila is currently a founder at exchange startup QFEX, but once upon a time he was a London-based trader in high-frequency trading (HFT). He had stints at both Flow Traders and Tower Research Capital, and would interview junior candidates at the latter firm. He's recently released multiple questions he used to ask, including one he called "the most ridiculous thing I've seen in maths/physics."
The question "is not too hard" according to Kapila, rather it's the answer itself that is shocking. It reads as follows:
"I have a light ball of mass m, and a heavier one of mass M = 16 * 100^5 * m, and a wall. I kick the heavy ball at the light one. No friction, elastic collisions, etc.
i) Will the heavy ball change direction before hitting the wall (through the light ball)?
ii) At the time of changing direction, how many times will it have collided with the light ball?"
The problem might sound familiar to you. It was made famous from a video by Mathematics YouTuber 3Blue1Brown (using blocks instead of balls) which has amassed over 14 million views. The solution there shows that, eventually, both blocks eventually slide away from the wall forever and never touch again. As weight of the larger block increases, proportional to the size of the smaller one, the number of times the smaller ball collides with the wall shows more and more digits of Pi (π)
For example, when the larger ball is 10,000 times the mass of the first, the ball collides with the wall 314 times. When the ball is 1,000,000 times larger, it collides 3,141 times. At 10,000,000 times larger, the ball collides 314,159. And so on.
A comprehensive answer as to how this works can be found via 3Blue1Brown here, but as is often the case with algorithmic trading interview questions, the way you work it out might be more important than the answer. Rather than seeing whether or not you know how to calculate the answer, it might be a test for how passionate you are about mathematics, to the point that you'd be aware of this problem.
Kapila gave other questions he asked at Tower. Some are a bit more niche, for example, the following question:
"Suppose there are infinitely many people in the room wearing red or blue hats and each person can see everyone else’s hat except his or her own. They have to guess the colour of their own hat. Is there a collective strategy that guarantees finitely many wrong guesses?"
Think you can answer that one? Put your answer in the comments below.
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