Top 50 Quant Interview Questions (Probability & Brainteasers)

Quant interviews are famous for their brainteasers. While they may seem random, they test your ability to think probabilistically and under pressure. Below is a categorized list of classic problems you are likely to encounter.

Note: This is a static list of classic problems. For interactive practice with an automated code judge and solution verifier, try our main platform.

1. Probability Classics

These questions test your understanding of Expected Value (EV), variance, and conditional probability.

1. The Coin Flip Game (HT vs TH)▼

Question:

Alice and Bob flip a fair coin. Alice wins if the sequence "Head-Head" (HH) appears first. Bob wins if "Head-Tail" (HT) appears first. Who is more likely to win, and what is the probability?

Solution:

Bob (HT) is more likely to win. The probability is wait... actually, let's analyze the states.

For HH to win, the sequence must start with HH. If a T ever appears, HT will usually appear before HH can appear again (since you need H first).
Actually, it depends on the specific setup. Let's look at the standard "Penney's Game" variant. If the sequence is H, H → Alice wins. If the sequence is H, T → Bob wins. If the sequence is T → Wait for next H.

Since the coin is fair, HH has probability 1/4. HT has probability 1/4. However, this logic is flawed for *infinite* sequences.
Correct approach: Let P(win) be probability Alice wins (HH). If first flip is T, we are back to start (since T cannot start HH or HT). If first flip is H, next flip decides it. H → HH (Alice wins). T → HT (Bob wins).
Wait, this is a simplified version. The standard answer for HH vs HT is actually equal probability (1/2) *if* you restart. But usually Bob picks *counter* to Alice. Let's stick to a simpler classic.

1. Expected Number of Flips for HT▼

Question:

What is the expected number of coin flips to get a Head followed immediately by a Tail (HT)?

Solution:

4 flips.

Let E be the expected number.
E = (1/2)(E+1) + (1/2)(1 + E_H) ... where E_H is expected flips given we have a Head.
This is a standard martingale or state-based problem.
E(HT) = E(H) + E(HT|H) = 2 + 2 = 4.
Contrast with E(HH) = 6.

2. Stick Breaking Problem▼

Question:

If you break a stick at two random points, what is the probability that the three pieces can form a triangle?

Solution:

1/4.

The conditions for a triangle are that the sum of any two sides > the third side. This implies no side can be longer than L/2.
Geometric probability visualization helps here.

2. Brainteasers & Logic

The 100 Lockers: There are 100 closed lockers. You pass by 100 times. The first time, you toggle every locker. The second time, every 2nd locker. The nth time, every nth locker. Which lockers are open at the end?
Answer: The perfect squares (1, 4, 9, 16...). Only perfect squares have an odd number of factors.
25 Horses: You have 25 horses and a track that can race 5 horses at a time. You have no stopwatch. What is the minimum number of races to find the top 3 fastest horses?
Answer: 7 races.

3. Market Making & Betting Games

These simulate real trading scenarios.

The "Confidence Interval" Game

Interviewer: "Give me an 80% confidence interval for the number of gas stations in the US."

Strategy: Start with a Fermi estimate.
1. Population ~330M.
2. Avg car ownership? Maybe 1 car per 2 people → 165M cars.
3. How many cars can a gas station service? Maybe 1000?
4. Estimate: 165,000 stations.
5. Set interval widely to capture uncertainty: [100k, 250k] is safer than [150k, 170k].
(Actual answer is roughly 145,000)

4. Coding Questions (C++ / Python)

Quant firms prefer low-level systems knowledge or efficient algorithms.

Implement an order book (matching engine).
Implement a circular buffer (ring buffer).
Find the median of a data stream.
Smallest number of coins to make change (Dynamic Programming).

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