First, there was a 35-minute logic test. The content was very simple, just some pattern recognition and things like that. After that, the difficulty went up.
After asking a few questions about my resume, the first interviewer gave me a graph theory brainteaser:
Let there be a polygon with n vertices. What is the maximum number of edges you can draw between them without making a triangle (three vertices are connected to each other)?
This one was pretty easy. He wanted me to write a general formula for n vertices. The answer is (n/2)^2 if n is even, and (n-1/2)^2+n/2+1/2 if n is odd.
Then there was another question:
Let's say you toss a coin 1,000 times, and you win if you get 10 heads in a row before you finish flipping. Then you try a different strategy, where you restart every time you get tails. Every time you restart, that is one round, and you get 1,000 rounds. Which strategy is better?
He asked whether I could write a recurrence formula for the first strategy, something like:
P(x = flips in a row, y = flips) = 1/2 * P(x + 1, y + 1) + 1/2 * P(0, y + 1)
He also asked me some very general questions like, "Can you estimate which one is better?"
The second interviewer asked a lot of technical questions.
If there are n students, what is the probability that two or more of them have the same birthday?
Can you estimate what n would be for the probability in your previous answer to equal 1/2?
There are n = 300 students. What is the gap between any two of their birthdays? The answer should be smaller than one, and assume the birthdays are uniformly distributed.
What is the probability of getting more than 60 heads out of n = 100 coin flips? This was a normal distribution and standard deviation question.
Can you use normal distributions if the probability of flipping heads is much lower and n is much higher?
How would you calculate P(>5 heads) if p(heads) = 1/1000 and you have 1,000 flips?
If x1 has a correlation of 0.8 with x2, and x2 has a correlation of 0.8 with x3, what is the correlation between x1 and x3? Can you give examples?
The third interview was just a very casual lunch interview, with no technical questions.
There was actually supposed to be one final data analytics coding round, but I had already been rejected 😭😭😭
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