Brainteasers for IB Interviews: How to Solve Them Every Time

Brainteasers are less common than they used to be, but they still appear – especially at boutiques and in assessment centres. They're not testing whether you're a maths genius. They're testing structured thinking under pressure: can you break a complex problem into manageable steps, state your assumptions clearly, and work logically to an answer?

Category 1: Market Sizing / Estimation

These are the most common type. 'How many golf balls fit in a school bus?', 'What's the market size of the UK umbrella industry?', 'How many piano tuners are there in London?'

Framework: Top-Down vs Bottom-Up

Top-Down: Start with a big number and narrow. UK population = 67m → % who buy umbrellas → frequency → average price = market size.

Bottom-Up: Start small and scale up. Average umbrella shop sells X per day × Y shops in London × Z cities = total.

Always state your assumptions out loud. The interviewer cares more about your process than the answer. Round numbers aggressively – 67 million becomes 70 million, £12.99 becomes £13.

Worked Example: How Many Coffee Cups Are Sold in London Per Day?

London population: ~9 million. Assume 60% are working-age adults who might buy coffee: 5.4 million. Of those, maybe 40% buy at least one coffee out per day: 2.16 million. Many buy 1 coffee, some buy 2. Average 1.3 cups: 2.16m × 1.3 = ~2.8 million cups per day. Add tourists and visitors (maybe another 200–300K): roughly 3 million cups per day.

Category 2: Probability

Common questions involve dice, coins, cards, or simple scenarios.

Key Concepts

Expected Value: Sum of (outcome × probability). If you flip a coin and win £2 on heads, lose £1 on tails, EV = 0.5 × £2 + 0.5 × (-£1) = £0.50.

Conditional Probability: The probability of A given that B has occurred. If you draw two cards without replacement, the second draw's probability depends on the first.

Complementary Probability: Sometimes it's easier to calculate P(not A) and subtract from 1. 'What's the probability of rolling at least one six in four rolls?' = 1 - P(no sixes) = 1 - (5/6)^4 = 51.8%.

Classic Problem: Two Coin Flip Variants

You flip 2 coins. Given that at least one is heads, what's the probability both are heads? The answer is 1/3, not 1/2. The possible outcomes given at least one heads are: HH, HT, TH. Only one of three is HH.

But: if you're told a specific coin is heads (e.g., the left coin), then the only unknown is the right coin, and the probability of both heads is 1/2. The difference between 'at least one' and 'a specific one' is the trap.

Category 3: Logic Puzzles

These test creative problem-solving. Examples: the light switch puzzle, the 100 lockers problem, weighing balls on a balance.

The approach: simplify. Try small cases first. If the problem says '100 lockers', start with 5 and look for a pattern. Work through it systematically and narrate your thinking. Getting stuck is fine – showing you can work through being stuck is the point.

Category 4: Mental Maths

Quick calculations that test speed and accuracy:

Percentages: 15% of 840? = 10% (84) + 5% (42) = 126. Always break percentages into 10% and 5% components.

Division: Divide by 5? Multiply by 2 and divide by 10. 730/5 = 1460/10 = 146.

Multiplication: 23 × 17? = (20 × 17) + (3 × 17) = 340 + 51 = 391. Break one number into round components.

Compounding: Rule of 72: divide 72 by the growth rate to estimate how long it takes to double. At 8% growth, doubling takes ~9 years.

General Tips for All Brainteasers

Think out loud: The interviewer needs to hear your process. Silence is the worst response.

State assumptions: Before you start calculating, say what you're assuming. This shows structured thinking and lets the interviewer guide you if you're off track.

Simplify first: Round numbers. Start with small cases. Don't try to solve the full problem in one step.

Ask clarifying questions: If the problem is ambiguous, ask. 'When you say a school bus, do you mean a standard UK minibus or an American school bus?' This shows attention to detail.

Don't panic if stuck: Say 'Let me think about this for a moment' and work through it methodically. Getting stuck and recovering is better than panicking and guessing.