Consulting brain teasers
Whether firms still ask brain teasers, the five-step way to structure one out loud, six classics with the move and script-checked answers, and the mistakes.
Updated October 28, 2026
| Teaser | Kind | The structuring move | Answer |
|---|---|---|---|
| 100 lockers, 100 students; student k toggles every kth locker. How many end open? | Pattern | A locker is toggled once per divisor; only perfect squares have an odd number of divisors | 10 |
| Ten people each shake hands with everyone once. How many handshakes? | Counting | Each pair once: n(n-1)/2 | 45 |
| Same, with 25 people | Counting | Same formula; say it before you compute | 300 |
| How many times do a clock’s hands overlap in 12 hours? | Rate | The minute hand laps the hour hand once every 12/11 hours | 11 |
| Eight balls, one heavier, a balance scale. Fewest weighings to find it? | Logic | Split 3, 3, 2: one weighing narrows to at most 3, a second finds it | 2 |
| Why are manhole covers round? | Open | Name the constraint first (a round cover cannot fall through its hole), then two more reasons, then stop | No single answer |
Do consulting firms still ask brain teasers?
Less than they did, and none of the three largest firms’ interview pages mention them (the pages are quoted in the formats guide). They still appear in some boutique and Big Four rounds, in fit interviews as an icebreaker, and in market sizing disguised as a puzzle. Prepare for them the way you prepare for a sizing question: not by memorizing answers, which the interviewer can tell, but by structuring out loud.
How do I structure a teaser out loud?
- Restate it and name the kind. “So this is a counting problem: every pair shakes once.” Naming the kind tells the interviewer you have seen the shape before, which is allowed.
- Say the constraint or the formula before the number. “Each person shakes nine hands, but that counts every handshake twice.”
- Compute out loud, with a small case first. “For three people it is three handshakes; the formula gives 3 x 2 / 2 = 3, good. For ten: 10 x 9 / 2.”
- Check it. A second method or a sanity bound. “Fewer than 10 x 10 = 100, more than 10.”
- Stop. Give the answer and the one-line reason; do not keep talking.
Three teasers worked
The lockers
Locker k is toggled once for each divisor of k. Most numbers have divisors in pairs (2 and 50 for 100), so an even count, so the locker ends closed. Perfect squares have one unpaired divisor (10 for 100), so an odd count, so open. Perfect squares up to 100: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. Answer: 10. The script toggled all 100 lockers and counted; the reasoning is what you say.
The clock
The minute hand goes around 12 times in 12 hours and the hour hand once, so the minute hand laps it 12 - 1 = 11 times. Candidates who answer 12 forgot that the two laps at 12:00 are the same overlap. Say the subtraction; it is the whole answer.
The balance scale
Split eight balls into three, three and two. Weigh three against three. If they balance, the heavy ball is one of the two left, and one more weighing finds it. If one side is heavier, weigh one of its three against another: a tilt names the ball, a balance names the third. Two weighings. The structuring move is the uneven split; candidates who split four and four need three.
What about open-ended ones?
“Why are manhole covers round” and “how would you move a mountain” have no answer and the interviewer knows it. Give a structure anyway: the one hard constraint first, two secondary reasons, a stop. Thirty seconds, then hand it back. The failure mode is five reasons in a row with no order.
What are the common mistakes?
- Reciting a remembered answer. The interviewer follows up with a variant and the recital ends.
- Silence while computing. Say the formula, then the small case, then the number.
- No check. One bound or one second method, out loud, every time.
- Arguing with the premise. “Nobody shakes hands anymore” is a joke, not a structure.
- Not stopping. Answer, reason, done.
Questions
Do McKinsey, BCG or Bain ask brain teasers?
Their interview pages, quoted in the formats guide, do not mention them. Teasers still appear in some boutique and Big Four rounds and as icebreakers; prepare the structuring move, not the answers.
How should I answer a brain teaser in an interview?
Restate it and name the kind, say the constraint or formula before the number, compute out loud with a small case first, check with a bound or a second method, then stop.
Are the answers on this page checked?
The numeric ones (lockers, handshakes, clock overlaps) were computed in a script in the site’s repository and a test recomputes them. The balance-scale answer is a logic argument on the page.
How does Casepartner help with teasers?
In practice it shows a structure hint naming the kind and the move, never the answer. The computing and the check are yours.