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The Horse Race Problem

Jan. 12, 2020 4-minute read

The point of this post is simply to illustrate the importance of putting in the work and prep prior to your quant interviews. It is 10 times easier to recall a (similar) quant interview question that you have already practiced ahead of time than to actually solve a question, you have never seen before, live and under pressure. And you may be saying to your self "There must be an infinite pool of interview questions that are constantly changing that I need to practice". Well, there are certainly a lot of questions that may be asked, but you may be surprised by the persistence of some of these questions.

The rise, fall or persistence of quant interview questions

Some questions fall out of favor because they have been overdone or never actually tested the candidate in any meaningful way. New questions emerge and gain popularity to keep interviewees on their toes or reflect changes in focus of the industry. But some old time classics never seem to fade year after year after year. There is no worse feeling than stumbling over a question during your interview only to see that exact same riddle, brainteaser or probability question on the first page of a google search or in a math or finance text book.

Back in 2010, when I was first trying to land a quant job, the interviewer asked me the horse race problem (quant interview question #15 on our site). For those of you who do not know it, it reads as follows:

There are 25 horses, each of which runs at a constant speed that is different from the other horses. Since the track only has 5 lanes, each race can have at most 5 horses. If you need to find the 3 fastest horses, what is the minimum number of races needed to identify them?

I wouldn't consider this question to be particularly technical or difficult for that matter, but this did get asked and you should know it. And if you do a bit of google searching, you will find many instances on forums, books, blogs, etc. where this EXACT question is discussed. So a decade later, is this still a relevant quant interview question? Let's look at the data below:

Frequency of the horse race problem per year

Yes. Ten years later, this question is still getting asked to evaluate whether or not a candidate will make a good quant hire.

What makes certain questions persistent?

Easy to remember
In this case, this question is more of a dinner party style riddle than a more technically involved quant problem. But I think that is part of the appeal, it is easy for the interviewer to remember. They may in fact have heard it at a dinner party with his or her lawyer, doctor and other finance friends (thus some recency bias). And the question being relatively simple to solve makes it easy to remember.

Your interviewer was asked that same question

Most people will have this sort of ego bias. I answered question "X" when I was interviewed, and I'm a smart person and I would hire myself, so therefore any quant I hire should go through the same hoops and hurdles as I have. Also, most interviewers don't seek out new interview questions (that's not their job after all). They will simply use the questions they have used in the past, plus say new questions they have discussed with colleagues and not think twice about it.

The standardization of the quant interview

Some more "advanced" firms have started standardizing the quant interview process. This means that putting in the time to prepare has just become even more valuable. The same question, or extremely similar variations of the same question are now just asked to every candidate to eliminate any biases that interviewers may have. Yes, they will change the format of these over time, but generally the same principles and concepts will be at play. You will be in a great position to succeed with enough practice.

Already seen an interview question?

If you go into an interview and they ask you a question you have already seen before. Just answer the question in a straightforward way. No need to pretend that you are solving this question for the first time ever. It will come off much better to just answer the question to play any games with the interviewer. You are likely not great at acting and will come off as being inauthentic. If the interviewer asks you if you have ever seen this question before, feel free to tell them the truth and say "yes". You will not be dinged for this. You prepared well, answered the question accordingly and you will come off in a positive manner. However, you also don't need to tell the interviewer prior to even answering the question that you have seen this before. Just answer the question. If the interviewer asks you if you have seen it after you have answered it fine, but no need to bring it up preemptively.