IMC Trading Interview Questions

Draw the payoff of a put option.

A robot is 3 cm from the left edge and 17 cm from the right edge of a table. The robot moves with equal probability 10 cm to the left or to the right in each step. What is the expected number of steps before the robot falls off the table?

There are 27 race cars and you can only race 5 of them at a time. You do not have a stopwatch. What is the minimum number of races required to determine the 3 fastest cars?

Draw a graph of profit versus price for a call option with a fee of £3. What features of this graph are of interest to traders?

What is the minimum number of cards required to build a card tower with 100 levels, given that you need 2 cards for 1 level, 7 for 2 levels, and so on?

Which type of graph is best used to describe time-series data?

There are 27 cars and only 5 cars can race at a time. How many races are needed to determine the 3 fastest cars?

Consider a game where you flip a fair coin: if it lands heads, you win $20, and if it lands tails, you lose $5. Would you like to play this game? In a second game, the payouts are $20 million for heads and lose $5 for tails. Would you prefer the second game? Lastly, if the payouts return to $20 for heads and -$5 for tails, but you can choose to play either once or 100 times, which option do you prefer and why? Please explain your reasoning.

What is the expected value (EV) of a standard six-sided dice roll?

Six people sit randomly around a round table. What is the probability that they are seated in increasing order by their age?

You have 12 identical balls, one of which is heavier than the rest (you don't know which). Using only a balance scale that can show which side is heavier, what is the minimum number of weighings needed to identify the heavier ball?

You have 27 horses. You can race up to 5 horses at a time. What is the minimum number of races required to determine the top 3 fastest horses?

What is the probability of landing on the Broadway street tile in Monopoly after 10 rotations? You can approximate the answer.

What are hashmaps, and how are they implemented?

Two teams are playing each other, and both have positive (plus) odds to win. How much should you bet on each team, and why?

You and a taxman are playing a game with N cards, each labeled with a natural number from 1 to N. You can pick a card only if at least one of its factors is still on the table, and for every card you pick, the taxman takes all available factors of that card from the table. How do you maximize your score?

When rolling a fair six-sided die repeatedly, what is the probability that, before rolling any odd number, you have rolled each even number (2, 4, and 6) at least once?

In a beer pong game with a 4x4 arrangement of cups, each time you land a ball in a cup, both the row and the column containing that cup are removed. Assuming each throw lands in any remaining cup with equal probability, what is the probability that you win the game in the minimum possible number of throws?

A drunk passenger boards an airplane and sits in a random seat. Each subsequent passenger sits in their assigned seat if it is available; otherwise, they choose a random unoccupied seat. What is the probability that the last passenger will be able to sit in their assigned seat?

Explain the Law of Large Numbers to someone with a non-STEM background. Also, explain one of the sorting algorithms to someone with a non-STEM background.

A fair coin is tossed repeatedly. What is the expected number of tosses required to first see the sequence 'HHH' (three consecutive heads)?

Explain a sorting algorithm to someone without a STEM background. Also, explain the law of large numbers to someone without a STEM background.

What is the expected number of times you need to roll a fair six-sided die to see an odd number?

There are some fish in a bucket. Three fishermen come to the bucket one after another. The first tries to divide the fish into groups of three but finds one fish left over, so he takes this one and a third of the remaining fish. The next fisherman tries to divide the rest into three, again finds one left over, and takes that one and a third of the remainder. The third fisherman does the same. What is the minimum number of fish that could have been in the bucket initially?

You are given two dice: one numbered 1 to 6 and the other numbered 1 to 4. You choose one at random and roll it twice. The first roll is a 2. What is the expected value of the second roll?

There is a 20 cm long table. You start 3 cm from the left edge. Each move, you go either 10 cm to the left or to the right with equal probability. If you reach either edge of the table, you fall off immediately. How many moves do you expect to make before falling off?

What is the variance of a six-sided dice roll?

Complete the function findValuation which returns the expected price of a house using linear interpolation of given data. The function must return the price rounded to the nearest integer. Function signature: findValuation(reqArea: int, area: list of int, price: list of int) -> int. Constraints: 500 < reqArea < 10^5, 500 < area[i] < 10^5 for all i.

Explain the concepts of a queue and a stack to a layperson.

What is the time complexity of different std::set operations?