O.R. Brainteasers

Question

In finance, they have lots of books and sources for interview questions. Especially, 'brainteasers' are pretty famous. A brainteaser can be logical deduction questions or questions like 'when does the hour and minute hands of a wall-clock are exactly at the same place after 3 PM'. There are also questions dedicated to the finance field.

My question is the following: how kind of questions can we ask for OR & Analytics jobs? Of course, it can not be very detailed mathematical questions since the expertise in OR can vary from financial modeling to discrete optimization. Hence, I am thinking about a good way to measure the analytical thinking skills of applicants for the OR & Analytics fields.

Hence, I will be happy to see whether:

1. We have good sources for such questions
2. We can give some good examples here showing what kind of skills does this question measure

Let me list some examples. An OR & Analytics applicant needs to be really good at induction, so without going in much detail we can ask:

Use induction to show that \begin{align*} \sum_{k=1}^n k^3 = \frac{n^2 (n+1)^2}{4}. \end{align*} Hint: For induction you need to define a base case, ....

Or, even to measure mathematical modeling skills we can again stay in the high school level and ask questions like:

George is 1 year more than twice Luke's age. 3 years from now, Maggy will be 27 less than twice George's age. 4 years ago, Maggy was 1 year less than 3 times Luke's age. How old will Maggy be 3 years from now?

Or, with a very simple question, we can measure the knowledge of functions and calculus with:

On what interval(s) is the function $f(x) = x^3 e^x$ increasing?

Note: I am aware that there is a similar discussion here, but I think it can be nice to give some problems here as a resource for applicants and application receivers.

Answer 1

Even if brainteasers are not sufficient to test the ability of candidates to be good OR engineers and scientists, they can be useful to test some specific hard or soft skills. For example, at LocalSolver, we use brainteasers to check if candidates love computer programming (assuming that loving means practicing) or if candidates are able to react positively faced with "hard" clients (assuming that a good reaction to a tedious question is not just to dismiss the question).

Here are examples of the brainteasers we use at LocalSolver:

• Give two ordered sequences of numbers, could you describe an algorithm that merges the two sequences in one ordered sequence? Then we can discuss the computational complexity of the algorithm.

• Given a graph with vertices and edges that connect these ones, we want to compute the largest subset of vertices such that these ones are all pairwise connected (this is what we call a clique). How do you proceed? Again, this is the opportunity to launch a discussion about computational complexity and algorithm efficiency.

If the candidate has difficulty to go ahead, we help her/him. The goal is to create a conversation to evaluate the skills mentioned above. We always take a step back from the answers given by candidates, taking into account, in particular, their professional experience and their education. This is just a part of the exchanges we have with the candidates. Nevertheless, this part is important for us at LocalSolver since we always find it useful to get an accurate evaluation of the candidates.