The story of one interview, or how in the company X candidates “hung up”

    Actors:
    X - a large well-known company in which an analyst vacancy is open (conditionally)
    A - an employee of company X who conducted interviews
    B - a representative of the HR department of company X
    C - a candidate for an analyst vacancy.


    Brief background

    I want to say right away that I probably would not write and discuss my interview here if I hadn’t accidentally discovered that A (an employee of Company X), who was interviewing me, decided for some reason in his account on Facebook in the evening of the day the interview took place, lay out a couple of questions that I was asked in this interview. And also, as it seemed to me, to describe this in a somewhat negative connotation, including using the terms “hung” (as applied to the applicant), “enter into a stupor”, “took pity”, etc.
    It’s also very unusual for me, it can be said, this is the first time I’ve met such that the details of my interview, albeit in anonymous form, are made public, and this was not done first by the candidate (i.e. by me), but It is a representative of the company.

    His post was quoted by other Facebook users. A discussion unfolded in one of the branches, and I also entered into it, having promised the other day in detail to tell me about the look at this interview on my part (i.e., on the part of the candidate).

    The next morning, A (the one who interviewed me) deleted his original message, and along with this, all discussions of other participants were erased. What exactly led him to do this, I don’t know, maybe A realized that his message in itself causes reputational damage to Company X in the eyes of the applicants, but I also admit that it is connected with the fact that I wanted to give my comments.
    However, since I promised to answer this topic, I still do it, despite the fact that the topic itself has been erased.

    Some limitations

    I will not disclose the true names X, A and B here, as well as comment on, confirm or refute any guesses, questions and statements regarding them. Also, I will not talk in more detail about the vacancy itself, about the contents of the rest of the interview and any other details, since they do not relate to the essence of the issue. I only note that, despite the fact that I have a mathematical education that I received more than 10 years ago, the job description did not say that it requires deep, wide, or any specific knowledge in the field of mathematics, with the exception of experience application of mathematical statistics methods in the list of requirements.

    Message A (of an employee of the company) on his Facebook account after interviewing me

    Today I “hung” the candidate (mathematician) with a question about how to calculate the integral from 0 to Pi of the function sin (x), without using the cosine.
    After 10 minus, the candidate sagged, and I finished him off with the question of what would happen in the world if Pi were equal to 3. The
    good analyst (the name of colleague A is indicated here) still suggested Pi ^ 2 = 10, but I took pity on the candidate

    I note that this quote is almost verbatim, if necessary, those who saw it can confirm it.
    In his response to one of the comments on this post, A also writes the following (exact quote):
    About tasks from the category: "What if?". Sometimes a person goes into a stupor. Sometimes a riot of imagination about one thing begins. Sometimes a person decomposes the situation into components and through them comprehensively evaluates the situation as a whole. Such a “game” helps to understand how a person will think with a reduced induced effect from experience. Actually, the main thing in analytics is how he thinks. When asking about knowledge, it is very difficult to learn about thinking.


    A look at the interview from the candidate side

    So, we will consider the first question I was asked: how to calculate the integral from 0 to Pi of the function sin (x).
    In my quick answer that you can take the antiderivative, and then use the Newton-Leibniz formula, I was told that a new condition is being added: cosine cannot be used in calculations.
    I must say right away that I like such questions, I like to solve non-standard and entertaining mathematical problems. Therefore, the question itself seemed immediately interesting to me, and I began to think about it.

    But then one important point should be made. I was forbidden to use a paper with a pen (of course, I didn’t even talk about the Internet). And no suggestive questions or clues (I clearly asked about this if there would be any clues).

    A (the one who interviewed me) wrote on Facebook that he “hung me” for 10 minutes.
    Firstly, I don’t like this term “hung” on its own, since any process of reflecting on a task (especially not trivial) can also be formally described as “hung”. People who solve problems in the standings or at the Olympics in silence - are they also in a "hanged" state? So what?
    Secondly, this phrase gives the impression that I just sat there, was silent, did not offer at least any approaches to the solution, any assessments.
    But this is not so.
    On the contrary, knowing that in Company X they want to hear from candidates not only the decision itself, but also its reasoning, even if they do not lead to the right decision, I tried to say what ideas came to my mind in order to somehow demonstrate my thoughts .

    In order:

    I immediately said that, since the sine function is odd, for example, the integral from -Pi / 2 to Pi / 2 will be 0. To which A expressed doubt that the sine is an odd function, and also at zero it takes a zero value. But after I demonstrated my confidence in this, he nodded in agreement. I was a little puzzled by this reaction A, although I admit that in this case it’s just a test of the candidate’s confidence, and nothing more.
    At the same time, A asked me if it could be used somehow in answering the original question. I did not understand how to use this right away, I said so (I repeat, you cannot use a piece of paper with a pen).

    Further, I proposed (as an idea) to expand sin (x) in a series (xx ^ 3/3! + ...) and calculate the integral of the polynomial. Later, after the interview, I realized that this decision is a dead end, because after integrating this polynomial, the decomposition for minus cosine will just turn out, but it never occurred to me how to calculate the sum of the series otherwise. Another thing is that this method will allow you to quickly calculate the approximate value, but in your mind this obviously will not work.

    OK, let's move on.
    For lack of any clues, I proposed to evaluate the integral above and below. Bottom - “house”, the left side of the “roof” which is formed by the function y = x * 2 / Pi. Here, without explanation in the figure it was completely inconvenient to do, so I dared to draw this house so that it was more clear what I was talking about. A again had some doubt in my words, and I said that evaluation is possible, since the function sin (x) is convex upward in the interval from 0 to Pi. Therefore, from below, the simplest estimate from below will be equal to the area of ​​these two triangles under the sine graph, namely, Pi / 2. The simplest upper estimate is determined by the rectangle formed above the line y = 1. So, as a top grade, I suggested Pi.

    Then I clarified with him what it means "you cannot use cosine." He asked for a strict logical definition of this. At first glance, this is obvious and does not require any explanation, and my question seemed naive, but if you think about it, then from a formal point of view the function (-cos x), considered as an independent function, is not a cosine function, so how does not coincide with her.
    So, A evaded to give a more rigorous and formal explanation of what he puts in the concept of "you cannot use cosine." Thus, in my opinion, he did not answer my clarifying question.

    Further, I proposed the following idea (a trick, if I may call it that): since in fact I knew the value of the integral (2, through the Newton-Leibniz formula with a “forbidden” cosine), I said that we can analyze why it turns out to be an integer, perhaps this will lead to the right decision. Knowing the answer, in some cases it turns out to guess which way the solution could go. In response, I was told that doing so is not good.

    In the end, I asked for permission to move on to the next question, as I doubted that I would come up with a solution to this problem in the next few minutes, and the interview time was limited.

    Decision(my version). I note that after the interview, at home, in a calm environment, I still found a solution to this problem. Namely, it was necessary to recall the formula sin (x) = (exp (ix) -exp (-ix)) / (2i), which is a consequence of the well-known Euler formula. After applying this formula, the antiderivative of the original function sin (x) will be - (exp (ix) + exp (-ix)) / 2. In fact, this is the same minus cosine written in an alternative form.
    Further, applying the Newton-Leibniz formula, we obtain: - (- 1-1) / 2 + (1 + 1) / 2 = 2.

    I’m not sure, by the way, that this solution would fit A, maybe he would get me some other transformation or representation, and this solution would also be rejected. I can only guess. I sent this decision A in a message via Facebook on the evening of the interview, but he ignored my message.
    Yes, by the way, the time that I spent trying to solve this problem myself, I would rather rate closer to 5 minutes, and not 10, as A reported, since it should be noted that for some part of this time I explained the ideas that came to me to the head (see above).

    Next, I was asked what would happen if Pi were equal to 3 in our world.
    I immediately said that I had heard about such a thing as fine tuning the universe. The Pi constant is itself fundamental and can enter various physical constants. With a small change in these constants, the world will change so much that life may be impossible, and even the existence of molecules will remain in doubt, etc. In general, this is a difficult conversation, here, if you think deeply, you need to start the conversation with a discussion of space and its metrics (the last phrase is my comment made after the interview).

    I was asked an additional question about how the rotation of the Earth will change (apparently, the rotation period was implied) if the Pi constant would be different, for example, 3.
    I said I don’t know, because I don’t remember the formula. But I answered the following: even if Pi is not directly included in the formula, however, it is likely that Pi is included in some formulas from which these formulas are derived. Or it is implicitly “wired” in some other constants. That is, I meant that I fully admit that the period of the Earth's rotation could be different. This is purely from a formal point of view, simply using calculations for a given isolated case.

    Honestly, in the second question (about Pi) I could make some gross errors in the reasoning.
    But ask yourself: what would you answer in a few minutes, being at the interview and not having access to the Internet? Even if it is a formula from the school curriculum and is very simple, should you remember it, especially if it does not apply to your specialization at the university and to your previous work? If so, then answer the question: "what is the formula of the flower for the Rosaceae"?

    Let me remind you once again, on Facebook I then wrote the following:
    About tasks from the category: "What if?". Sometimes a person goes into a stupor. Sometimes a riot of imagination about one thing begins. Sometimes a person decomposes the situation into components and through them comprehensively evaluates the situation as a whole. Such a “game” helps to understand how a person will think with a reduced induced effect from experience. Actually, the main thing in analytics is how he thinks. When asking about knowledge, it is very difficult to learn about thinking.


    OK, the thought as a whole is not bad, but it all depends on the implementation. Below are examples.

    You can offer one universal method for this kind of interviews.
    It is necessary to collect all the known proofs of the Pythagorean theorem (and there are 367 of them, according to Wikipedia) and sort them by simplicity and visualization. Then ask candidates to prove the Pythagorean theorem. If suddenly the candidate proves it, inform that another proof is required, which follows a different scheme (" What if you need to propose another proof?") And so on. After the candidate, exhausted, stops, say, on the first or second proof of the theorem, offer him the simplest and most obvious of the remaining versions of the proofs.

    Another option: take an exotic example that has a simple solution. For example, ask a candidate to give an example of a metric space in which such a situation is possible when a ball of a larger radius lies inside a ball of a smaller radius. This is one of my favorite puzzles, by the way. Its mere formulation is enough to, as A put it, introduce a person into a “stupor”.
    In terms of A, one can reformulate the problem in the following form: “ What if a ball of a larger radius is inside a ball of a smaller radius? Is it possible? Give an example of the corresponding metric space »
    And let the candidate think, cooked in his juice. Fantasy. Let decomposes the situation into components and comprehensively assess the situation. Structures, analyzes. I wonder if all this toolkit of his brain will help him in this case. What do you think? And the solution is very simple, by the way.
    But if a person has never encountered a similar example before, he will not come up with such an example in 10 minutes, unless he is very talented.

    If a person gushes with some kind of bizarre or just wrong ideas, is this necessary? If the candidate is not only completely unaware of the subject area about which he is asked, but he doesn’t even have anything to push fromhow can he decompose the problem into its components and comprehensively evaluate it? By the way, here a lot depends on the experience of the person, and this also needs to be taken into account, and sometimes the interviewer himself may not take this into account. Different candidates may have different experiences in different areas of life.

    Example. Probably, if you want to estimate how many gas stations are in the city of Moscow, then it is easier for a Muscovite car enthusiast to give an estimate, since he can start, for example, from the number of gas stations in his area (which he most likely knows with an accuracy of plus or minus 1-2 ), then, based on the population in the area and the population of the city, give some estimate for the number of gas stations in the whole city. It is difficult for a person who does not have a car to act according to this scheme, because, most likely, he has a much less accurate estimate of the number of gas stations in his area.
    If the subject area is close to the candidate, but they want some special solution from him, will he always understand what exactly they want from him without the appropriate hints?

    In general, the topic that A formulated is actually interesting.
    Is it possible to measure some abstract analytical abilities of a person in general, without reference to any experience? Is it possible? Just keep in mind that the experience of solving mathematical puzzles is also an experience (sorry for the tautology).
    Your opinions

    Supplement

    One . I do not blame A for how he conducts interviews. He, as a leader, is recruiting for himself those employees with whom he will work. And he does it as he sees fit. If he does not like the candidate with something, he can refuse them simply without giving reasons.

    The second one . Despite the previous paragraph, I was flustered that in his Facebook account A described how he “hung me” for 10 minutes (you can evaluate the objectivity of this statement yourself from this piece of interview described in detail by me), as well as the epithets “dropped off”, "Took pity", etc. In fairness, it should be noted that he did not mention my name and surname, perhaps for reasons of tact. Therefore, I answer him in return.

    Third (rhetorical question). Would I like to work with a person who describes the process of communicating with candidates in this way? I might have got the wrong idea, but probably not.

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