IMC filters with game-based cognitive tests before any human sees your application, then spends a Superday watching whether you update a price when the information changes.
A dealer shuffles a standard -card deck and turns one card face up. Ranks run from ace low () to king (); suits are irrelevant. Looking at that card, you call whether the *next* card off the deck will be higher or lower in rank. A tie -- the next card matching the rank of the face-up card -- counts as a loss.
Playing optimally, what is your probability of winning, and what is the fair price to enter a game that pays on a win and nothing on a loss?
A mountain gondola makes three stops on its descent, and the same thing happens at every stop: three-quarters of the riders currently aboard step off, and then new riders climb on. Nobody recorded how many riders started at the summit. What is the smallest possible number of riders aboard after the third stop?
You are the sole market maker in a one-off contract. Everyone agrees the contract will settle at either or , each equally likely, so its unconditional fair value is .
Orders arrive one at a time, in unit size. Each order comes from an informed counterparty with probability -- that trader already knows the settlement value, and will buy from you whenever your offer sits below it and sell to you whenever your bid sits above it. Otherwise (probability ) the order comes from a noise trader who buys or sells with probability each, regardless of price.
(a) Why is quoting bid at offered a losing strategy, even though is the honest fair value? (b) Find the bid and offer at which you break even on the next order. (c) What happens to your quote if informed flow rises to ?
Graded automatically, and a hard gate
One of them is technical
Freezing on one brainteaser is enough to exit
The trading game is about updating, not winning
A lottery drum holds balls numbered through . After a thorough mixing, five balls are drawn out one at a time. A ticket costs and pays if the five numbers emerge in strictly increasing or strictly decreasing order; otherwise it pays nothing. What value of makes the ticket exactly break-even in expectation?
A barnyard fair hosts geese, goats, and spiders. A careful tally turns up legs in total. There are twice as many geese as goats, and twice as many spiders as geese. How many spiders are at the fair? (Geese walk on legs, goats on , spiders on .)
Three junior traders — Arjun, Mei, and Tomas — each get a year-end bonus drawn independently and uniformly from . What is the probability that Arjun's bonus exceeds Mei's, and Mei's in turn exceeds Tomas's?
Take a standard chessboard and count every square whose sides lie along the grid lines — not just the 64 unit cells, but squares of every size. How many are there? As a follow-up, count all the grid-aligned rectangles the board contains.
Five hundred point-sized beetles land at independent, uniformly random spots on a taut 1-foot wire. Each one immediately flips a fair coin to pick a direction and crawls at 1 foot per minute. Whenever two beetles meet head-on, both instantly turn around and continue crawling; a beetle that reaches either end of the wire drops off. How long, in expectation, until the wire is completely clear?
Roughly how many haircuts are given each day in a metropolitan area of million people? No lookups and no calculator -- build the estimate out loud from assumptions the interviewer can audit, then check it a second, independent way.
A vendor sells you a coin-flipping machine and claims it is unbiased. You suspect it actually lands heads of the time. Flips are independent and you may run as many as you like.
(a) Using a quick two-sigma argument, roughly how many flips do you need before a machine would show up as clearly non-random? (b) Do it properly: how many flips give a one-sided test an chance of detecting the bias? (c) A colleague flipped the machine times, got heads, and wants to declare victory. What do you tell him?
An equity index has an annualised volatility of , and there are about trading days in a year. Model daily log returns as independent and normally distributed with that volatility.
(a) Under this model, how often should the index move more than in a single day? More than ? (b) The real index has had well over a dozen daily moves beyond in the past century, several of them within the same few weeks. What is wrong with the model, and what is the smallest change that repairs it?
An interviewer asks you to estimate an unknown quantity and to give an interval around it. The scoring is stated up front: you collect if the true value lands inside your interval, and you are charged for every standard deviation of width you use. Formally, if your belief about the quantity is normal with mean and standard deviation , and you quote , your expected score is
Which maximises the score, what coverage does it correspond to, and what does that tell you about how confident an interval a trader should volunteer?
Two parts. BrainsFirst NeurOlympics is a set of about four short game-based tasks, around 45 minutes in total, measuring working memory, attention, reaction speed and decision-making rather than arithmetic. Alongside it sits a psychometric battery: a work-style questionnaire and a timed inductive reasoning test on diagram sequences. It is scored automatically and a weak result ends the process.
Four or five back-to-back interviews of about 45 minutes with senior traders, a behavioural round, informal time on the desk, and a trading simulation in which you quote two-sided prices and keep updating them as new information arrives. Interviewers say the point of the game is not to win but to see whether you update sensibly. Teamwork and fit are assessed separately and can override a strong technical day.
Roughly three to eight weeks from application to decision: the online assessment, a recorded video interview, a recruiter call, a trader interview, then the Superday. Graduate trader roles reopen each year around September for the following graduating class, and successful trainees go through about six weeks of Trading School followed by a 6 to 14 week local traineeship.
It can. Prosperity is the multi-day algorithmic trading challenge IMC runs for STEM students, with tens of thousands of entrants per edition, and IMC describes it as a recruiting funnel. Strong finishers can be fast-tracked into the interview pipeline, but they still go through the trader interview and Superday.
