Brain Teasers Still Asked in IB Interviews (With Full Solutions)

You've drilled your DCF walkthrough and memorized how the three statements link. Then the interviewer leans back and asks, "What's the angle between the hands of a clock at 3:15?"

Brain teasers are less common than they were 15 years ago, but they haven't disappeared. They still show up at boutiques, in some superday rounds, with certain senior bankers who like them, and especially in sales and trading interviews.

This post covers the teasers that still come up, how to solve each one out loud, and a simple framework so you're never caught frozen.

Why Banks Still Ask Brain Teasers

The interviewer usually doesn't care much whether you get the exact answer. They're watching how you think under pressure.

Here's what they're actually testing:

• Structured thinking: Can you break a fuzzy problem into steps?
• Composure: Do you stay calm when you don't immediately know the answer?
• Communication: Can you walk someone through your logic clearly, the way you'd explain a model to a VP?
• Number comfort: Can you do quick math without panicking?

Keep that in mind. A candidate who talks through a logical approach and lands slightly off often beats one who sits in silence and blurts out the right number.

The 4-Step Framework for Any Brain Teaser

Before the examples, lock in this approach:

1. Repeat the question back. It buys you a few seconds and confirms you understood it.
2. Ask a clarifying question if something is ambiguous. "Are we assuming the scale is perfectly accurate?" is fine.
3. Think out loud. Silence is your enemy. Narrate your logic, even the dead ends.
4. Sanity check your answer. Does it make sense? Saying "that seems reasonable because..." shows maturity.

Now let's get into the ones you're most likely to see.

The Classic Logic Teasers

1. The Clock Angle at 3:15

Question: What's the angle between the hour and minute hands at 3:15?

The trap is answering zero. The hour hand doesn't sit still on the 3; it moves as the minutes pass.

• The minute hand at 15 minutes points at the 3, which is 90 degrees from the 12.
• The hour hand moves 30 degrees per hour (360 / 12), which works out to 0.5 degrees per minute.
• At 3:15, the hour hand is at 90 + (15 × 0.5) = 97.5 degrees.

Answer: 7.5 degrees.

2. How Often Do the Clock Hands Overlap?

Question: How many times do the hour and minute hands overlap in a day?

Most people say 24. The real answer is lower, because the hour hand keeps moving forward.

• In 12 hours, the hands overlap 11 times, not 12. The overlap that "should" happen around 11:00 actually happens at 12:00, which is the same as the start of the next cycle.
• So in 24 hours: 22 times.

Bonus point if you mention the overlaps happen roughly every 65 minutes (precisely, every 12/11 hours).

3. The Bat and the Ball

Question: A bat and a ball cost $1.10 together. The bat costs $1.00 more than the ball. How much is the ball?

The gut answer is 10 cents. It's wrong, and interviewers know you'll be tempted.

• Let the ball cost x. The bat costs x + 1.00.
• So x + (x + 1.00) = 1.10, which gives 2x = 0.10.

Answer: 5 cents. Check it: ball $0.05, bat $1.05, total $1.10, difference $1.00. Done.

This one is really a test of whether you slow down before answering.

4. The Lily Pad

Question: A patch of lily pads doubles in size every day. It takes 48 days to cover the whole lake. How long to cover half the lake?

Don't divide by two. Since it doubles daily, the day before it's full, it was half full.

Answer: 47 days.

5. The Two Burning Ropes

Question: You have two ropes. Each takes exactly 60 minutes to burn, but they burn unevenly (half the rope might not take 30 minutes). How do you measure 45 minutes?

The key insight: lighting a rope at both ends makes it burn out in 30 minutes no matter how uneven it is.

• Light Rope A at both ends and Rope B at one end, at the same time.
• Rope A burns out after 30 minutes. At that moment, Rope B has 30 minutes of burn time left.
• Immediately light the other end of Rope B. It now burns out in 15 minutes.

Answer: 30 + 15 = 45 minutes.

6. The Water Jugs

Question: You have a 3-gallon jug and a 5-gallon jug, and unlimited water. How do you measure exactly 4 gallons?

Walk through it step by step:

1. Fill the 5-gallon jug.
2. Pour from it into the 3-gallon jug until full. The 5-gallon jug now has 2 gallons.
3. Empty the 3-gallon jug.
4. Pour the 2 gallons into the 3-gallon jug.
5. Fill the 5-gallon jug again.
6. Pour from the 5 into the 3 until full. The 3-gallon jug only needs 1 more gallon.

Answer: 4 gallons remain in the 5-gallon jug.

7. The Heavy Ball

Question: You have 8 identical-looking balls. One is slightly heavier. Using a balance scale only twice, how do you find it?

The trick is splitting into three groups, not two.

• Put 3 balls on each side, leaving 2 aside.
• If it balances: the heavy ball is one of the 2 you set aside. Weigh them against each other. Done.
• If one side is heavier: take those 3. Weigh 1 against 1. If they balance, it's the third ball. If not, the heavier side wins.

Answer: two weighings always work. (The same logic works with 9 balls: 3 vs 3 vs 3.)

The Math-Flavored Teasers

8. Sum of 1 to 100

Question: What's the sum of every number from 1 to 100?

Pair them up: 1 + 100 = 101, 2 + 99 = 101, and so on. There are 50 pairs.

Answer: 50 × 101 = 5,050.

The general formula is n(n + 1) / 2, which is worth knowing in case they switch the number.

9. Trailing Zeros in 100!

Question: How many zeros are at the end of 100 factorial?

Each trailing zero comes from a 10, which is a 2 × 5. There are way more 2s than 5s, so just count the 5s.

• Multiples of 5 up to 100: 20.
• Multiples of 25 contribute an extra 5 each (25, 50, 75, 100): 4 more.

Answer: 24 trailing zeros.

10. Squares on a Chessboard

Question: How many squares are on a standard 8×8 chessboard?

Not 64. You have to count every size of square.

• 1×1 squares: 64
• 2×2 squares: 49
• 3×3 squares: 36
• ...down to 8×8 squares: 1

That's 1² + 2² + ... + 8².

Answer: 204.

11. The Fair Price of a Dice Game

Question: I roll a fair six-sided die and pay you whatever number comes up in dollars. What would you pay to play?

This is an expected value question, and it's a favorite in S&T interviews.

• Each outcome (1 through 6) has a 1/6 chance.
• Expected value = (1 + 2 + 3 + 4 + 5 + 6) / 6 = 21 / 6 = $3.50.

Answer: up to $3.50 to break even. Strong candidates add that you'd pay a bit less in practice to make a profit or account for risk.

The Market Sizing Question

Technically not a brain teaser, but it often gets lumped in. There's no single right answer, so your structure is everything.

Question: How many cups of coffee are consumed in New York City each day?

Here's how to talk through it, with every number clearly stated as an assumption:

• Population: assume roughly 8 million residents.
• Coffee drinkers: assume about half drink coffee daily, so 4 million people.
• Cups per drinker: assume an average of 1.5 cups per day, so 6 million cups.
• Adjustment: commuters and tourists add more, so you might round up to around 7 million.

The interviewer cares that you segmented the problem logically, stated your assumptions, and did the math cleanly. If they push back on an assumption, adjust calmly instead of defending it to the death.

Don't Skip Mental Math

Quick arithmetic often shows up alongside teasers. A few tricks worth practicing:

• Percentages: 15% of 240? Take 10% (24) plus 5% (12) = 36.
• Multiplying near round numbers: 17 × 23 is (20 − 3)(20 + 3) = 400 − 9 = 391.
• Squaring numbers ending in 5: 35² = 3 × 4 = 12, then add 25, giving 1,225.

These also make you faster on technical questions, like quick IRR or multiple math.

Mistakes That Sink Candidates

• Blurting the first answer. The bat and ball exists to catch exactly this.
• Going silent. The interviewer can't give you credit for thinking they can't hear.
• Refusing to guess. If you're stuck, share a partial approach. It beats nothing.
• Getting flustered when corrected. Taking a hint gracefully is a plus, not a minus.
• Memorizing answers without the logic. Interviewers love tweaking a classic (9 balls instead of 8, 4:20 instead of 3:15). If you only know the answer, you're exposed.

How to Practice in the Next Two Weeks

• Work every problem above out loud, ideally with a friend playing interviewer.
• Then change the inputs. Try the clock at 9:45, or sum 1 to 200, until the method feels automatic.
• Do 5 minutes of mental math daily. Small reps add up fast.
• Run one market sizing question a day, timing yourself to about 3 to 4 minutes.

Brain teasers might be a smaller slice of IB interviews than they once were, but they're also one of the easiest places to stand out. Master the logic behind these classics, keep talking through your thinking, and that "random" question becomes a chance to show exactly how you'd perform on the desk.