Quant Interview Brain Teasers

Brain teasers might seem like an arbitrary interview tool, but top quant firms use them for good reasons:

• They test raw problem-solving ability. Unlike textbook problems, brain teasers can't be solved by applying a memorized formula. They require you to think from first principles — exactly the skill needed when facing novel market situations.
• They reveal how you handle ambiguity. Many brain teasers have intentionally vague phrasing or multiple valid approaches. How you clarify assumptions and navigate uncertainty mirrors how you'd handle real trading scenarios.
• They test communication under pressure. The interviewer isn't just listening for the answer — they're watching how you structure your thinking, ask clarifying questions, and recover from wrong turns.
• They're fun. Quant traders are, by nature, puzzle enthusiasts. Brain teasers help identify candidates who genuinely enjoy intellectual challenges — a strong predictor of cultural fit at firms like Jane Street and SIG.

Brain teasers are especially prevalent at prop trading firms. SIG is famous for poker-based decision problems, Jane Street loves expected-value puzzles, and Optiver includes estimation problems in their process.

Most brain teasers fall into one of these categories:

• Weighing & Measurement Puzzles: "You have 12 balls, one is heavier. Using a balance scale at most 3 times, find the odd ball." These test systematic elimination and information theory — each weighing should maximize information gained.
• Logic Riddles: "There are 100 lockers, all closed. 100 students walk by — student 1 toggles every locker, student 2 toggles every 2nd locker, etc. Which lockers are open at the end?" These test pattern recognition and number theory.
• Optimization Problems: "You need to get to the top of a 100-story building. You have 2 identical eggs. What's the minimum number of drops to guarantee finding the highest safe floor?" These test dynamic programming thinking and minimizing worst-case scenarios.
• Fermi Estimation: "How many piano tuners are in Chicago?" These test your ability to break a complex question into estimable components and compute reasonable bounds.
• Game Theory & Strategy: "You and your opponent alternately remove 1-3 stones from a pile of 20. The player who takes the last stone wins. Do you go first or second?" These test strategic thinking and backward induction.
• Lateral Thinking: "A man lives on the 20th floor. Every morning he takes the elevator down to the lobby. When he comes home, he takes the elevator to the 15th floor and walks up 5 flights. Why?" These test the ability to challenge assumptions.

Let's solve four classic brain teasers step by step.

Problem 1: The Two Egg Problem

You're in a 100-story building with 2 identical eggs. There's a critical floor F: eggs break when dropped from floor F or above, and survive when dropped from below. Find F using the minimum number of drops in the worst case.

Solution: With one egg, you'd have to go floor by floor (up to 100 drops). With two eggs, we can do much better.

Let n be the minimum number of drops needed. On the first drop, try floor n. If it breaks, use the remaining egg on floors 1 through n-1 (at most n-1 drops, total = n). If it survives, try floor n + (n-1). If it breaks, check floors n+1 through n+(n-2) (at most n-2 drops + 2 already used = n). Continue this pattern.

We need: n + (n-1) + (n-2) + ... + 1 ≥ 100, so n(n+1)/2 ≥ 100.

Solving: n ≥ 13.65, so n = 14. First drop at floor 14, then 14+13=27, then 27+12=39, etc.

Problem 2: The Locker Problem

100 lockers are initially closed. Student 1 toggles every locker. Student 2 toggles every 2nd locker. Student k toggles every k-th locker. After all 100 students pass, which lockers are open?

Solution: Locker n is toggled once for each of its divisors. A locker ends up open if it's toggled an odd number of times — i.e., if it has an odd number of divisors.

A number has an odd number of divisors if and only if it's a perfect square (because divisors come in pairs, except when d = n/d, i.e., d = √n).

The perfect squares from 1 to 100 are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

Answer: Lockers 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100 are open — exactly the 10 perfect squares.

Problem 3: The Burning Rope Problem

You have two ropes. Each burns in exactly 60 minutes, but they burn at non-uniform rates (you can't cut them in half to get 30 minutes). How do you measure exactly 45 minutes?

Solution: At time 0, light Rope A at both ends and Rope B at one end.

Rope A burns at both ends, so it's consumed in 30 minutes. At that moment (t=30), immediately light the other end of Rope B. Rope B has 30 minutes of burning left, but now it's burning from both ends — so it takes 15 more minutes.

Total: 30 + 15 = 45 minutes.

Problem 4: The Game of Nim

There are 20 stones in a pile. Two players alternate turns, removing 1, 2, or 3 stones. The player who takes the last stone wins. Should you go first or second?

Solution: Work backward. If it's your turn and there are 1-3 stones, you win (take them all). If there are 4 stones, you lose — whatever you take (1, 2, or 3), your opponent can take the rest.

Pattern: you lose when stones are a multiple of 4, win otherwise. Since 20 = 5 × 4, the player who goes first is in a losing position (assuming optimal play by the opponent).

Answer: Go second. Whatever your opponent takes (call it k, where 1 ≤ k ≤ 3), you take 4-k. After each pair of moves, exactly 4 stones are removed. After 5 rounds, the pile is empty and you took the last stone.

When facing an unfamiliar brain teaser in an interview, use this framework:

• 1. Clarify the problem. Repeat it back. Ask about edge cases and assumptions. This buys thinking time and prevents solving the wrong problem. "Just to confirm — the eggs are identical, and we want the worst-case minimum?"
• 2. Start with small cases. If the problem involves 100 of something, solve it for 2, 3, or 5 first. Patterns often emerge from small cases that generalize to the full problem.
• 3. Think out loud. The interviewer is evaluating your process, not just your answer. Say things like "My first instinct is X, but let me check that..." or "I notice this has a recursive structure..."
• 4. Look for invariants. What stays the same as the problem evolves? In the Nim game, the key invariant is the pile size modulo 4. In weighing puzzles, the key is information (each weighing gives at most log₂(3) bits).
• 5. Work backward. Many puzzles are easier to solve from the end state. Start with the simplest winning/losing position and work backward to the start.
• 6. Don't panic if stuck. Take a breath, revisit your assumptions, try a completely different approach. Interviewers have seen candidates struggle — what they're looking for is resilience and adaptability, not instant brilliance.
• 7. Sanity check your answer. Does it make intuitive sense? Try it against small cases you solved earlier. Catching your own errors is a strong signal.

Build your brain teaser skills with these resources:

• Books: "Heard on the Street" by Timothy Crack (the classic quant puzzle book), "How Would You Move Mount Fuji?" by William Poundstone, and "Puzzles for Programmers and Pros" by Dennis Shasha.
• Online: Our interview question database includes brain teasers from Jane Street, SIG, Optiver, and other top firms.
• Practice partners: Brain teasers are best practiced out loud with a partner who can ask follow-up questions and challenge your reasoning.
• Related prep: Brain teasers overlap significantly with probability questions — prepare for both simultaneously. See our complete interview prep guide for a structured study plan.

Aim to solve 50-100 brain teasers before your interviews. After each one, identify the key insight and think about what category of problems it belongs to. Over time, you'll develop pattern recognition that makes even novel puzzles feel approachable.

Ready for personalized coaching? Book a free consultation with an industry quant who can assess your problem-solving skills and recommend targeted practice.