Key Highlights
- Brain teasers test how you think under pressure, not how much finance you know.
- Interviewers want to see your problem-solving process, not just the final answer.
- You can improve with practice by learning structured thinking and staying calm during tough questions.
Brain Teasers in Banking: Necessary Evil or Just Evil?
If you’ve ever been blindsided by an interviewer asking how many ping-pong balls fit in a 747, you’re not alone.
Brain teasers in banking interviews are a necessary evil we all love to hate. One minute you’re nailing your DCF, and the next you’re guessing how many pigeons live in New York City.
Banks throw these curveballs to see if you can stay cool and think on your feet under pressure. In high-stress finance, keeping a cool head is a must.
Brain teasers might feel cruel, but they have a purpose, they show how you tackle the unknown and whether you crack or shine.
What Are Investment Banking Brain Teasers?
Investment banking brain teasers are puzzles or logic questions that test your mental agility – not your finance knowledge.
They can range from guesstimate questions to quirky riddles or lateral thinking problems.
Think of questions like “Why are manhole covers round?” or “How many ping-pong balls fit in a jet?” – anything that makes you pause and think creatively.
They’re basically stress tests for your brain.
The goal isn’t about getting the exact right answer; it’s about showing how you analyze an unfamiliar problem and whether you can think outside the box.
Why Investment Banks Use Brain Teasers in Interviews
So, why do investment banks insist on tossing brain teasers at candidates?
They’re not being sadistic (mostly); they’re assessing how you think.
Banking is a high-pressure, unpredictable business – one minute you’re cranking on a valuation, the next a client throws an absurd curveball at you. Interviewers want to see if you can handle surprises with grace.
Brain teasers test a few key things:
Composure Under Pressure
Can you stay cool and think clearly when you’re put on the spot? Many interviewers believe a tough puzzle is a good way to test your “battle-worthiness”. If you freeze or freak out in a brain teaser, what will happen when a real client problem hits?
Analytical Thinking
Banks want to watch you break down an unfamiliar problem and work toward a solution. It’s not about getting the exact answer. In fact, being correct comes secondary in these interviews – what matters is showing a rational thought process. If you explain your approach and demonstrate strong reasoning, you’ve done your job.
Creativity & Lateral Thinking
Some brain teasers are intentionally weird or open-ended to see if you can think outside the box. Can you approach problems from different angles?
Interviewers also love when you think aloud, because it shows them your analytical pathway. In other words, they learn more from how you work it out than from whether your final answer is correct.
Types of Brain Teasers Commonly Asked in Investment Banking Interviews
Brain teasers come in many flavors.
Knowing the types can help you prepare for whatever they throw at you:
Market Sizing / Estimation
These ask you to estimate a big, random number on the fly. For example, “How many elevators are there in the United States?”
There’s no single correct answer, the interviewer wants to see a structured approach (sizing the market, making reasonable assumptions) and basic math under pressure.
Riddles & Lateral Thinking
These are the quirky “trick” questions that often have an unexpected twist. Classic example: “Why are manhole covers round?” They test if you can catch the trick or think non-literally rather than get stuck on an obvious-but-wrong path.
Math & Probability
These test your quantitative reasoning. They could be simple-but-deceiving math problems or counterintuitive probability scenarios. You might also face quick mental math questions.
Rapid math under pressure shows you can handle numbers when it counts.
Logic Puzzles
These involve scenarios you solve with clear logical steps. Think of puzzles like the fox, chicken, and corn across a river, or weighing balls to find a heavier one, or the two guards where one always lies.
They test your ability to methodically work through constraints and rules. Often there’s a clever trick to simplify the problem, so lateral thinking helps here too.
Pattern Recognition
Less common but possible, you might be given a sequence of numbers or letters and asked what comes next. These test your observation skills to find hidden patterns.
How to Get Better at Solving Investment Banking Brain Teasers
The good news: you can get better at brain teasers.
It’s like hitting the gym, but for your brain’s problem-solving muscles.
Here are some strategies to level up:
Practice, Practice, Practice
Do brain teasers regularly. Use real prep resources like Heard on the Street (Timothy Crack’s famous book) and the Vault Guide to Finance Interviews – they’re full of “classic” interview puzzles that show up year after year.
You can find many of these online, in puzzle forums or brainteaser subreddits. You can even have ChatGPT quiz you with random brain teasers.
Focus on the Process, Not Memorizing Answers
Don’t be that candidate who just memorizes 50 brain teasers and blurts out answers. Interviewers will see through that. Instead, practice breaking down problems and explaining your reasoning. If you understand why an answer is what it is, you can tackle new puzzles you haven’t seen before.
Learn a Systematic Approach
Even though brain teasers can be wild, you can impose structure. Clarify the question first.
Then break the problem into parts. For estimation, lay out your assumptions clearly (e.g. “Assume X million people, each does Y…”).
For logic puzzles, list possibilities or draw a quick sketch. For math, write down any formula or relationship that might help.
Taking notes is a pro move, it keeps you organized and shows the interviewer you’re methodical.
Think Out Loud
Make it a habit to narrate your thought process as you solve a puzzle. In an interview, silence can be misinterpreted as frozen panic.
When you talk through it, even if you’re unsure, the interviewer sees your logical approach. Plus, if you’re slightly off track, they might give you a nudge.
Essentially, you’re letting them into your thought process, which is exactly what they want.
Stay Calm and Buy Time if Needed
If a brain teaser stumps you for a moment, don’t panic. It’s perfectly fine to say, “Hmm, let me think for a moment…” and gather your thoughts.
Take a breath, jot down a couple notes. Start tackling a part of the problem that is clear. Interviewers care as much about your composure as your solution.
Showing that you can stay cool and systematic when faced with the unexpected is
30 Common Investment Banking Brain Teasers (with Answers + Explanations)
Enough theory!
Let’s get into some real examples.
Below are 30 common brain teasers that interviewers have been known to ask.
I’ll give the question, answer, and a quick explanation for each.
Market Sizing / Estimation
1. Question: How many elevators are there in the United States?
Answer: On the order of a few hundred thousand (say, ~100,000–200,000).
Explanation: Break it down with assumptions. For example, assume ~330 million people in the U.S. If you figure one elevator per, say, 1,000 people, that’d be 330,000 elevators. The exact number isn’t important, what matters is explaining a sensible approach and doing the math step by step.
2. Question: How many ping-pong balls can you fit inside a Boeing 747 airplane?
Answer: On the order of tens of millions of balls.
Explanation: First, estimate the volume of a 747’s cabin. Suppose it’s roughly 200 feet long, 20 feet wide, and 30 feet tall (just an estimate). That’s 200×20×30 = 120,000 cubic feet of space. Convert to cubic inches (multiply by 1,728) to get about 207 million cubic inches. A ping-pong ball is about 1.5 inches in diameter; its volume ~1.8 cubic inches. If you filled every inch of the plane (which you can’t, but theoretically), 207,000,000 / 1.8 ≈ 115 million balls. Now, account for empty space between balls – packing efficiency might be ~60%. So maybe around 70 million ping-pong balls. The key is walking the interviewer through these assumptions calmly and clearly.
3. Question: How many gas stations are there in the United States?
Answer: Roughly 100,000 to 150,000 gas stations.
Explanation: Approach with a population or car-based estimate. One way: U.S. population ~330 million, and maybe there’s 1 gas station per 2,000 people. 330,000,000 / 2,000 = 165,000. That feels a bit high, so maybe use the number of cars: ~250 million vehicles in the U.S. If each gas station can service about 2,000 vehicles, that’d be 125,000 stations. It’s in the same ballpark. Any reasonable set of assumptions is fine, just state them and do the math. The interviewer cares about your structured thought process more than the exact figure.
Riddles & Lateral Thinking
4. Question: How would you move Mount Fuji?
Answer: Break it into pieces and move it one truckload at a time.
Explanation: This famous question isn’t expecting a realistic plan, it tests how you’d approach an impossible task. A good approach is to outline a method, showing that you can logically tackle a huge problem step by step instead of panicking.
5. Question: Why are manhole covers round?
Answer: Because a round cover can’t fall through its own opening, and it’s easy to roll and align.
Explanation: A round manhole cover won’t drop into the hole no matter how you position it – unlike a square cover, which could fall in if turned diagonally. Also, you don’t need to orient a round cover to put it back on; any rotation fits. The question tests if you see the practical logic behind the design.
6. Question: A farmer has 17 sheep. All but 9 die. How many sheep are left?
Answer: 9 sheep.
Explanation: It’s a wording trick. “All but 9 die” means 9 did not die. Interviewers use simple riddles like this to see if you get thrown by unusual phrasing.
7. Question: If a plane crashes exactly on the border of the United States and Canada, where do they bury the survivors?
Answer: You don’t bury survivors.
Explanation: Read that again – survivors wouldn’t be buried because they’re alive. This classic riddle tests your attention to detail..
8. Question: A man is pushing his car along a road when he comes to a hotel. He shouts, “I’m bankrupt!” Why?
Answer: He’s playing Monopoly.
Explanation: This riddle paints a strange scenario, but the clue is the word “hotel. The interviewer is checking if you can leap out of the literal scenario and realize it’s describing a game. It’s all about lateral thinking – seeing the non-literal context behind the words.
9. Question: I have two U.S. coins that add up to 30 cents, and one of them is not a nickel. What are the coins?
Answer: A quarter (25¢) and a nickel (5¢).
Explanation: The trick is in the phrasing “one of them is not a nickel.” That coin is the quarter. The other coin is a nickel. Together they make 30¢, and it’s true that one of them isn’t a nickel. The riddle tests if you get tangled in the wording.
10. Question: Three people pay $30 ($10 each) for a meal. The actual bill was $25, so the waiter returns $5. They each keep $1 and leave $2 as a tip. Now each person effectively paid $9, totaling $27, and $27 + $2 tip = $29. Where did the missing $1 go?
Answer: There is no missing $1 – the addition is done wrong.
Explanation: The $27 already includes the $2 tip (making the cost $25). Adding 27 and 2 is mis-framing the math. The correct total is $25 (bill) + $2 (tip) = $27. The riddle works only because it tricks you into an illogical addition.
11. Question: Why are images in a mirror flipped horizontally but not vertically? For example, your reflection switches left vs right, but it isn’t upside down.
Answer: A mirror actually flips front-to-back, not left-to-right – we perceive it as a horizontal flip because of how we turn ourselves.
Explanation: A mirror flips along the front-back axis (into the mirror), not truly left-right or up-down. We perceive a left-right swap because we turn ourselves horizontally to face the mirror, but there’s no upside-down flip because we don’t flip ourselves vertically when facing it.
Math & Probability
12. Question: If it’s 3:15 on an analog clock, what’s the angle between the hour hand and the minute hand?
Answer: 7.5 degrees.
Explanation: At 3:15, many people instinctively say “0°” because both hands seem to be on the 3. But the hour hand moves continuously – by 3:15 it has moved a quarter of the way toward 4. A full hour is 30°, so a quarter-hour is 7.5°. The minute hand is at 3 (15 minutes = 90° from 12), and the hour hand is 7.5° past 3, so the difference is 7.5°. This tests whether you remember that the hour hand moves between the marks.
13. Question: A bat and a ball together cost $1.10. The bat costs $1.00 more than the ball. How much does the ball cost?
Answer: $0.05 (5 cents).
Explanation: Most people’s gut says “10 cents,” but that’s wrong. If the ball were $0.10, the bat would be $1.10, totaling $1.20. Let the ball be $x. Then bat = $x + $1.00. Together: $x + ($x + $1.00) = $1.10 ⇒ 2x + $1.00 = $1.10 ⇒ 2x = $0.10 ⇒ x = $0.05. So the ball is $0.05 and the bat $1.05. This puzzle checks if you can set aside intuition and use basic algebra under pressure.
14. Question: If 5 machines take 5 minutes to make 5 widgets, how long would 100 machines take to make 100 widgets?
Answer: 5 minutes.
Explanation: It’s tempting to say “100 minutes,” but look closer. 5 machines → 5 widgets in 5 minutes. That means 5 machines produce 1 widget per minute (together). So 1 machine produces 1 widget in 5 minutes. If you have 100 machines, each can make a widget in 5 minutes. Working simultaneously, 100 machines make 100 widgets in 5 minutes. It’s a rate problem in disguise – the machine-to-widget ratio stays the same, so time remains constant.
15. Question: You’re on a game show with 3 doors. One door has a prize, the other two have goats. You pick Door #1. The host, who knows where the prize is, opens Door #3 and reveals a goat. He then asks if you want to switch to Door #2. Should you switch?
Answer: Yes – you should switch (it doubles your chance of winning).
Explanation: When you pick initially, you have a 1/3 chance of being right – meaning a 2/3 chance the prize is behind one of the other doors. The host’s goat reveal doesn’t change those odds; it just eliminates one losing door. Therefore the remaining unopened door has a 2/3 probability of hiding the prize, so switching wins two-thirds of the time.
16. Question: There’s a patch of lily pads on a lake that doubles in size every day. If it takes 48 days to cover the entire lake, how long would it take to cover half the lake?
Answer: 47 days.
Explanation: If the coverage doubles daily and it’s full on day 48, it must have been half-full on day 47. (Because on day 48 it doubled from half to full.) This puzzle is meant to illustrate exponential growth – the intuitive (but wrong) guess is often 24 days, instead of the correct 47. The lesson: sometimes things grow slowly then suddenly right at the end.
17. Question: What is the sum of all the integers from 1 to 100?
Answer: 5,050.
Explanation: You can pair the numbers in clever ways. 1 + 100 = 101, 2 + 99 = 101, 3 + 98 = 101, … there are 50 pairs each summing to 101. So 50 × 101 = 5,050. (This is the classic Gauss trick.) Alternatively, use the formula n(n+1)/2 for n=100. Either method shows quick thinking under pressure.
18. Question: Your sock drawer has 8 red socks and 11 blue socks, all mixed together. The light is out, and you need to grab socks in the dark. What is the minimum number of socks you must take out to be guaranteed you have at least one matching pair?
Answer: 3 socks.
Explanation: This is the pigeonhole principle in action. There are two colors, so if you blindly pick 3 socks, even in the worst case you’d have 2 of one color. With 2 socks you might have a pair or you might have one of each color – 3 socks guarantees a match. (It doesn’t matter that there are 19 socks total; only the two color categories matter.) Interviewers use this to test whether you understand basic combinatorics logic.
19. Question: A snail is at the bottom of a 10-foot well. Each day it climbs 3 feet up, but each night it slides 1 foot back. How many days will it take the snail to reach the top of the well?
Answer: 5 days.
Explanation: Be careful – it makes net 2 feet per full day (3 up, 1 down), but it doesn’t need a full day on the last one. After 4 days and 4 nights, the snail has climbed 8 feet (net). On day 5, it climbs from 8 to 11 feet and reaches the top; it doesn’t slide back that night. Many people calculate 10/2 = 5 and think 5 days (which in this case happens to be right), but if the well height were different, a simple division could mislead. It’s better to simulate day by day to avoid off-by-one errors.
Logic Puzzles
20. Question: You have 3 switches outside a closed room, and each switch controls one of 3 light bulbs inside. You can flip the switches however you want, but you can only enter the room once to figure out which switch goes to which bulb. How do you do it?
Answer: Turn on two switches (say, #1 and #2) and leave them on for a few minutes. Then turn off switch #2, leave switch #1 on, and quickly go into the room. One bulb will be on (controlled by switch #1). Of the two bulbs that are off, feel them: the warm one corresponds to switch #2 (it was on for a while then off), and the cold one is switch #3.
Explanation: The trick was to use more than just on/off – you used time (heat) as a clue. By leaving one switch on long enough to heat its bulb, then turning it off, you created a distinct state (off but warm). This puzzle tests creative logic: realizing you have an extra piece of information (bulb temperature) to exploit.
21. Question: You have two ropes that each take exactly 1 hour to burn from one end to the other. They burn non-uniformly. How can you measure exactly 45 minutes using these ropes and a lighter?
Answer: Light one rope at both ends and the other rope at one end, at the same time. When the first rope finishes, 30 minutes have passed. At that moment, light the other end of the second rope. That second rope had 30 minutes of burn time left; lighting the other end now makes it burn twice as fast, so it will finish in 15 more minutes. 30 + 15 = 45 minutes.
Explanation: The key insight is burning a rope from both ends cuts its burn time in half (even if it burns irregularly). So the first rope gives a 30-minute timer. The second rope then is used to get the remaining 15. This puzzle checks whether you can find an indirect way to measure time with non-standard “clocks.”
22. Question: You have a 5-gallon jug and a 3-gallon jug, and an unlimited water supply. How can you measure out exactly 4 gallons of water?
Answer: Fill the 3-gallon jug and pour it into the 5-gallon jug. Refill the 3-gallon and pour into the 5 until the 5-gallon jug is full. That leaves 1 gallon in the 3-gallon jug. Empty out the 5-gallon jug. Pour the 1 gallon from the small jug into the big jug. Now fill the 3-gallon jug one more time and pour it into the 5. The big jug now has 1 + 3 = 4 gallons.
Explanation: The classic water jug solution. In short, you used the difference in jug sizes (5–3) to measure 2 gallons, and eventually got to 4. This tests logical planning: setting up a sequence of steps to reach an exact measurement. The explanation is just walking through those steps, showing you approached it methodically.
23. Question: You’re standing before two doors. One door leads to your dream job offer, the other leads to nothing. Each door has a guard. One guard always tells the truth, the other always lies. You can ask one question to one guard to decide which door is the correct one. What do you ask?
Answer: Ask either guard: “If I asked the other guard which door leads to the job offer, what would he say?” Then choose the opposite door.
Explanation: This question is a classic. By asking one guard what the other would say, you always get the wrong door as the answer. If you ask the truthful guard, he truthfully tells you the lie the other guard would give – so you get a wrong door. If you ask the liar, he lies about the truthful guard’s answer – again giving you the wrong door. Either way, the indicated door is incorrect, so you pick the opposite. It’s all about constructing a question that accounts for both possibilities. Interviewers use this to see if you can navigate a tricky logical setup clearly.
24. Question: A farmer needs to cross a river with a fox, a chicken, and a sack of corn. His boat can only hold him and one other item. How can he get everything across safely?
Answer: Take the chicken across first. Then come back alone, take the fox across, and bring the chicken back. Next, take the corn across, and finally return to get the chicken again.
Explanation: By following that sequence, the farmer never leaves the chicken alone with the fox or the corn. The chicken is the one that can’t be left with either of the other items, so he shuttles it back and forth to avoid disaster.
25. Question: You have 8 balls that look identical, but one of them is slightly heavier than the others. You have a pair of scales (balance scale) and no weight references. What’s the minimum number of weighings needed to guarantee you find the heavier ball?
Answer: Two weighings.
Explanation: First weigh 3 balls vs 3 balls. If the scale balances, the heavy ball is in the two not weighed – weigh those to find which one is heavier. If one side is heavier, then the heavy ball is among those 3; weigh two of them – if one is heavier, that’s the heavy ball, if they balance then the one left out is the heavy one.
26. Question: The king has 10 bags of gold coins. One entire bag has fake coins that are 0.9 oz each instead of 1.0 oz. The king can use a very precise scale only once. How can he identify which bag has the fake coins with a single weighing?
Answer: Weigh a specific selection of coins from each bag all at once.
Explanation: Take a different number of coins from each bag (1 from Bag 1, 2 from Bag 2, …, 10 from Bag 10) and weigh them together. If all coins were real, the total would weigh 55.0 ounces (1+2+…+10 coins). If the total is, say, 54.8 oz (0.2 oz short), then Bag 2 has the fakes (0.2 corresponds to 2 fake coins). In general, the number of tenths of an ounce under 55.0 indicates which bag is fake.
Pattern Recognition
27. Question: What is the next number in this sequence: 2, 4, 8, 16, 32, …?
Answer: 64.
Explanation: It’s a doubling sequence (powers of 2). Each term is multiplied by 2 to get the next. So after 32 comes 64 (since 32×2 = 64). This one is straightforward, sometimes they’ll throw an easy pattern to see if you don’t overthink under pressure.
28. Question: What comes next in this sequence: 8, 5, 4, 9, 1, 7, …?
Answer: 6 (six).
Explanation: The sequence is not mathematical but alphabetical – it’s the numbers 0 through 9 listed by the spelling of their names in English. “Eight” (8), “five” (5), “four” (4), “nine” (9), “one” (1), “seven” (7), … The next in alphabetical order would be “six” (6). This tests lateral pattern recognition; it’s more about how you interpret the sequence than compute it.
29. Question: What is the next term in this sequence: 1, 11, 21, 1211, 111221, …?
Answer: 312211.
Explanation: This is the “look-and-say” sequence, where each term describes the previous term’s digits. Starting from 1: “11” reads as “one 1”; “21” reads as “two 1s”; “1211” reads as “one 2, one 1”; and “111221” reads as “three 1s, two 2s, one 1” – so the next term is “312211.”
30. Question: What occurs once in a minute, twice in a moment, but never in a thousand years?
Answer: The letter “M”.
Explanation: The riddle is talking about letters, not time. The word minute has one “M” in it, moment has two, and thousand years has none. Interviewers might throw in a quick word puzzle like this just to see if you can shift gears into abstract thinking. The answer jumps out once you think beyond the literal meaning of the words.
Closing: Will Brain Teasers Make or Break You?
After all this, you might be wondering: Are brain teasers the be-all and end-all of my interview? The answer is no! They’re just one piece of the puzzle (pun intended).
Banks care about your financial knowledge, technical skills, “fit,” and more.
But brain teasers can be that curveball that distinguishes candidates who handle the unexpected with poise.
The takeaway is: They’re not looking for perfect, they’re looking for poise under pressure.
Nail that, and you’ll show them you’re the kind of person they want when things get unpredictable.