IMC Trading Interview Questions

You have a 100-story building and two balls that break when dropped from too high a floor. What is the minimum number of drops needed on average to determine the highest floor from which a ball can be safely dropped?

Given 20 horses and 5 tracks, what is the minimum number of races required to determine the three fastest horses, assuming you can race up to 5 horses at a time and there is no timing, only order of finish in each race?

What is the probability of rolling an increasing sequence when you roll a die three times?

You have a 4x4 grid and three balls. If you manage to get at least 2 balls in the same row or column, you win. What is the probability of winning?

How much would the average global sea level rise if the mass of Mount Everest was submerged into the ocean?

Draw a payoff diagram for a put option.

If you remove the two squares that are diagonally opposite each other from a chessboard, can you use 2x1 domino tiles to exactly cover the remaining squares?

You have a deck of 3 black cards and 3 red cards in random order. In a game, you turn over one card at a time; if it is red, you win a dollar, and if it is black, you lose a dollar. What is the fair price to pay to play this game?

What is 72 multiplied by 73?

The profits of traders A, B, and C follow independent uniform distributions from 0 EUR to 100,000 EUR. What is the probability that A > B and B > C?

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 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?

Given a telephone keypad display with the numbers arranged as: 1 2 3 4 5 6 7 8 9 You press a random number, then move to a random adjacent number (no diagonals), then move again to a random adjacent number (again, no diagonals). You record the three numbers in order to form a three-digit number (e.g., 569). What is the probability that the resulting number is divisible by 2?

Given six distinct weights labeled 101, 102, 103, 104, 105, and 106, three weights are placed on each side of a balance scale. What is the probability that the weight labeled 106 is on the heavier side of the scale?

How many integers less than 100000 contain two consecutive '1's in their decimal representation?