Top 50 Quant Interview Questions (With Full Solutions)

The 50 problems that cover roughly 80% of what trading firms actually ask — grouped by topic, with one fully worked example and the traps to avoid.

Updated July 3, 2026 · QuantVault

Quant interviews look intimidating from the outside, but the question pool is surprisingly small. Interviewers at Jane Street, Citadel Securities, Optiver, SIG, and their peers draw from the same few dozen archetypes, because those archetypes test the things the job actually needs: conditioning correctly, computing expectations fast, and staying calm when a follow-up changes one assumption. If you can solve the 50 problems below cold — and, more importantly, re-derive them from scratch when the interviewer perturbs the setup — you have covered the bulk of the technical rounds at most firms.

Why every firm asks from the same list

Interviewers are not trying to be original. They want a question with a known difficulty curve, clean follow-ups, and a solution path that reveals how you think under time pressure. Classics like the Monty Hall problem or gambler's ruin survive because a candidate's first thirty seconds on them are diagnostic: do they set up states, or start guessing? That is also why memorizing answers fails — the real question is always the second or third variant, not the base case.

The 50 questions, grouped by topic

Here is the breakdown by archetype. Each row links to the corresponding question bank where the full set lives with worked solutions.

Topic	#	Representative questions
Probability & counting	12	Birthday problem, airplane seat problem, Monty Hall, drawing aces without replacement, Bayes with false positives
Expectation & variance	8	Expected flips until HH, coupon collector, expected max of two dice, St. Petersburg paradox
Brainteasers & logic	7	25 horses, two eggs and 100 floors, burning ropes, 100 prisoners and lockers
Markov chains & random walks	5	Gambler's ruin, ant on a cube, drunkard's walk hitting times
Statistics & regression	6	Interpreting a p-value, OLS assumptions, testing whether a coin is biased
Options & market intuition	6	Put-call parity, delta of an ATM option, “make me a market on X”
Betting & bankroll	3	Kelly sizing on a biased coin, repeated favorable bets, when to stop
Coding & algorithms	3	Reservoir sampling, fair coin from a biased coin, simulate and price

That is 50 problems, but really about 15 techniques: conditioning, linearity of expectation, state equations, symmetry, indicator variables, and no-arbitrage logic. Learn the techniques and the count stops mattering.

Worked example: expected flips until HH (and why HT is different)

This one appears in some form at nearly every trading firm. Flip a fair coin repeatedly. What is the expected number of flips until you first see HH? What about HT?

Set up states. Let $E_0$ be the expected flips remaining with no progress, and $E_1$ the expected flips remaining having just seen an H. For the target HH:

$$E_0 = 1 + \tfrac{1}{2}E_1 + \tfrac{1}{2}E_0, \qquad E_1 = 1 + \tfrac{1}{2}\cdot 0 + \tfrac{1}{2}E_0.$$

The first equation gives $E_0 = 2 + E_1$. Substituting into the second: $E_1 = 1 + \tfrac{1}{2}(2 + E_1)$, so $E_1 = 4$ and $E_0 = \mathbf{6}$.

Now repeat for HT. The equations change in one crucial place: from state $E_1$, flipping another H does not reset you — you still hold a usable H:

$$E_1 = 1 + \tfrac{1}{2}\cdot 0 + \tfrac{1}{2}E_1 \;\Rightarrow\; E_1 = 2, \qquad E_0 = 2 + E_1 = \mathbf{4}.$$

So HH takes 6 flips on average, HT only 4, even though both patterns have probability $\tfrac{1}{4}$ on any given pair of flips. The intuition interviewers want to hear: when hunting HH, a failure (T) destroys all your progress; when hunting HT, a failure (H) preserves it. The natural follow-up — “which pattern appears first more often in a race?” — leads into martingale and Penney's game territory, so be ready for it.

The traps that actually cost offers

Answering the memorized version. If you blurt “6” instantly, the interviewer switches to HTH or a biased coin. Show the state setup every time; the method is the answer.
Ignoring the follow-up ladder. Most questions have three tiers. Solving tier one fast just means you reach tier three, where the offer is decided.
Silent arithmetic. Narrate your reasoning. A wrong answer with a correct framework outperforms a right answer produced silently.
No sanity checks. After any expectation, check limits and units. Saying “6 is plausible because it must exceed the 4 flips HT needs, since HH overlaps with itself” is exactly the habit trading desks screen for.
Confusing $P(A|B)$ with $P(B|A)$. Roughly a fifth of the list is Bayes in disguise. Write the conditioning explicitly.

How to use this list

Do not read solutions passively. Attempt each problem on paper with a 10-minute timer, then study the solution, then re-derive it two days later with one parameter changed — a biased coin, an $n$-sided die, an asymmetric payoff. For breadth beyond the core 50, work the full topic banks; for the classics with deep follow-up trees, our dedicated guides on coin-flip problems and dice probability go several variants deep. Keep formulas fresh with the quant interview cheat sheet the week before your interview.

Ready to drill? Work the full probability question bank with step-by-step solutions, test yourself under time pressure in the QuantVault problem set, and practice the market-making rounds with our trading games.

Frequently asked questions

What are the most common quant interview questions?

The most common quant interview questions are probability and expectation problems: the airplane seat problem, expected coin flips until a pattern like HH, gambler's ruin, the Monty Hall problem, and Bayes' rule with false positives. Brainteasers like 25 horses and two eggs, plus market-intuition questions like 'make me a market,' round out the core set. Roughly 50 archetypes cover the majority of technical rounds at trading firms.

Do Jane Street, Citadel, and Optiver ask the same questions?

The underlying archetypes overlap heavily, but the emphasis differs by firm. Market makers like Optiver and SIG lean on mental math, expected value, and market-making games, while Citadel and Two Sigma push harder on statistics, regression, and coding. Jane Street is known for deep follow-up ladders on probability problems rather than exotic new questions.

Should I memorize the answers to the top 50 questions?

No — memorize the techniques, not the answers. Interviewers deliberately perturb classic problems (a biased coin, an n-sided die, an asymmetric payoff) precisely to catch candidates who memorized the base case. If you can set up states, apply linearity of expectation, and condition correctly, you can re-derive any variant on the spot.

How long does it take to prepare for a quant interview?

Most successful candidates spend 4 to 8 weeks of consistent practice, working 5 to 10 problems per day with full written solutions. The first two weeks should cover the core 50 archetypes; the remaining time goes to timed drills, mental math speed, and firm-specific formats like online assessments and market-making games.

Practice the real thing

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