Brain teasers are not there to test trivia. They test whether you can structure a problem you have never seen, state your assumptions, and stay calm when the first idea fails. Here are twelve common ones, worked.
A brain teaser feels unfair the first time. The interviewer asks how many golf balls fit in a plane, or whether you should spin the revolver again, and the room goes quiet. The point is not the golf balls. It is whether you can impose structure on a problem you have never seen, in front of someone who is watching how you think.
This guide covers the formats that come up most in finance interviews, with worked answers and a method for the ones you cannot prepare for. For the desk-specific questions that usually sit alongside the puzzles, read our sales and trading interview questions guide.
Why finance interviewers ask puzzles
Trading and quant desks care about decision quality under uncertainty. A junior trader will face incomplete information every day, and the job is to form a view, size a position, and update when new data arrives. A brain teaser is a compressed version of that.
Interviewers also use puzzles to see how you behave when you are stuck. Do you go quiet, guess wildly, or ask a clarifying question? Do you defend a wrong answer, or adjust when the interviewer pushes back? Those behaviours matter more than the puzzle itself.
Investment banking interviews lean more heavily on technicals and fit. If you are preparing for IB, spend your time on accounting and valuation first, and treat puzzles as a small side pocket.
The four-step method
Use the same structure for every puzzle, even the ones you recognise.
- Clarify. Repeat the question in your own words and check the constraints. Ask what is fixed and what can change.
- Assume. State the numbers or rules you need. "I will assume the plane is a 747 with roughly 900 cubic metres of interior space" is better than silence.
- Break it down. Split the problem into two or three pieces you can estimate or calculate separately.
- Sanity-check. Compare the answer with something you know. If the result implies a million coffee shops in Manhattan, something is wrong.
Say all of this aloud. The interviewer cannot score thinking they cannot hear.
Probability puzzles
1. Russian roulette
A six-chamber revolver has two bullets in consecutive chambers. You spin the cylinder, pull the trigger once, and survive. Should you spin again or pull without spinning?
Answer: Do not spin. After surviving the first pull, the empty chamber you fired from tells you the next chamber is more likely to be empty. Without spinning, the chance the next chamber holds a bullet is 1 in 4. With a fresh spin, it is 2 in 6, or 1 in 3. Pulling again is safer.
The lesson is conditional probability. The first outcome gives you information, and a good answer uses it.
2. Three coin flips
What is the probability of at least one head in three fair coin flips?
Answer: The complement is easier. The chance of three tails is 1/8, so the chance of at least one head is 7/8. Interviewers like this because candidates often try to add probabilities and double-count.
3. The birthday problem
How many people do you need in a room before the chance of a shared birthday passes 50%?
Answer: 23. The intuition fails because people compare one person's birthday with 22 others instead of counting the 253 pairs. You do not need to derive the full formula, but you should be able to explain why the number is lower than most people guess.
4. Expected value of a die roll
You roll a fair six-sided die and are paid the face value in dollars. What is a fair price to play?
Answer: The expected value is the average of 1 to 6, which is 3.5. If the game costs $3, it has positive expected value. If it costs $4, it does not. State whether you are risk-neutral before you answer, because the fair price and the price you would personally pay can differ.
Estimation questions
5. How many cups of coffee are sold in Manhattan each day?
Answer: Build it from population.
- Manhattan has about 1.6 million residents, of whom roughly 1.3 million are adults.
- Assume 60% drink coffee, so about 780,000 coffee drinkers.
- Assume the average drinker has two cups a day, but only half are bought outside the home. That gives about 780,000 cups.
- Add commuters and tourists, then round to somewhere between 800,000 and 1.2 million.
The exact number does not matter. The structure, the stated assumptions, and a sensible range do.
6. How many golf balls fit in a 747?
Answer: Estimate volumes.
- A 747 has roughly 900 cubic metres of usable interior space.
- A golf ball is about 4.3 cm across, so its volume is roughly 40 cubic centimetres, or 0.00004 cubic metres.
- Spheres do not pack perfectly. Assume 60% efficiency.
- That gives about 900 × 0.6 ÷ 0.00004, or roughly 13 million golf balls.
Again, the arithmetic matters less than choosing a method and checking the order of magnitude.
Logic puzzles
7. Two ropes and 45 minutes
Two ropes each burn for exactly 60 minutes, but unevenly. How do you measure 45 minutes?
Answer: Light both ends of rope A and one end of rope B. Rope A burns out in 30 minutes. At that moment, light the other end of rope B. It has 30 minutes of burn left, and burning from both ends halves that to 15. Total: 45 minutes.
8. Three switches and a bulb
Three switches outside a room control one bulb inside. You may enter the room once. How do you work out which switch controls the bulb?
Answer: Turn on switch 1 and leave it on for a few minutes. Turn it off, turn on switch 2, then enter. The lit bulb belongs to switch 2, a warm bulb belongs to switch 1, and a cold bulb belongs to switch 3.
The puzzle tests whether you think about heat as well as light. In finance, the equivalent is looking for a second signal when the obvious one is ambiguous.
9. Twelve coins and a balance scale
Twelve coins look identical, and one is heavier. You have a balance scale and three weighings. How do you find it?
Answer: Split the coins into three groups of four. Weigh two groups against each other. If one side is heavier, the heavy coin is in that group. If they balance, it is in the third group. You now have four candidates and two weighings left. Weigh two against two, then one against one.
The structure is to eliminate two-thirds of the possibilities each time. That is the same logic as a binary search.
10. The 3 and 5 gallon jugs
Using a 3 gallon jug and a 5 gallon jug, measure exactly 4 gallons.
Answer: Fill the 5, pour into the 3 until the 3 is full, leaving 2 in the 5. Empty the 3. Pour the 2 into the 3. Fill the 5 again, then top up the 3, which needs 1 more gallon. That leaves exactly 4 in the 5.
Mental maths and market questions
11. What is the angle between the clock hands at 3:15?
Answer: The minute hand points at 90 degrees. The hour hand has moved a quarter of the way from 3 to 4, so it sits at 97.5 degrees. The angle is 7.5 degrees.
This kind of question tests precision under mild time pressure. Say the steps, not just the answer.
12. How would you price a simple bet?
A friend offers to pay you $10 if a fair coin lands heads, and you pay $8 if it lands tails. Do you take the bet?
Answer: The expected value is (0.5 × 10) minus (0.5 × 8), which is $1 per flip. Positive expected value means you take it if you can afford the variance and can repeat it. If you can only play once, your answer can reasonably depend on risk tolerance. Say which assumption you are making.
How to behave when you are stuck
Everyone gets stuck. The difference is what happens next.
- Ask for a clarifying constraint. "Can I assume the balloon pops at random, or is there a fixed threshold?" shows you are thinking about the model.
- Simplify the problem. Solve a smaller version first, then scale up.
- Narrate the dead end. "I tried to add the probabilities, but that double-counts the overlap, so I will switch to the complement." That is a strong signal.
- Offer a range. If the exact answer is out of reach, give a bounded estimate and explain the bounds.
What not to do: go silent for two minutes, bluff a number with no reasoning, or refuse to change your approach when the interviewer hints that it is wrong.
Where puzzles fit in your prep
If you are preparing for a trading desk, pair puzzle practice with market and product questions. Our sales and trading interview questions guide covers the desk side. For hedge funds and quant roles, the hedge fund interview questions guide covers strategy and stock pitch rounds. If your process includes a paper LBO or a stock pitch, those are separate skills and deserve their own practice blocks.
For IB interviews, puzzles are a small part of the picture. Spend most of your time on accounting, valuation, and deal walkthroughs, then add a short puzzle session each week so you are not surprised.
What to do after reading this
Pick five puzzles from this guide and work them aloud, without notes, in front of a timer. Then find one you have never seen and apply the four-step method. The goal is not to memorise twelve answers. It is to make the method automatic.
If you are preparing across several applications, Finbound's study board ranks the next task by the firms and stages you are tracking, so technical practice follows the interviews you actually have. Start for free to add your first three applications.