Trading and quant
Brain teasers: a method, not luck
A six-step approach for puzzles under pressure, with worked classics: clock angles, handshakes, lockers, two eggs and burning ropes.
What's being tested
How you think under pressure. A structured approach, said out loud, earns credit even before you reach the answer.
The method
- 1
Restate and clarify
Check the rules. Puzzles often turn on one detail.
- 2
Try small cases
Two people, three lockers, one egg. Patterns appear quickly.
- 3
Look for structure
Symmetry, pairing, something that never changes (an invariant).
- 4
Work backwards
Start from the end state and ask what must happen just before it.
- 5
Think out loud
The interviewer can only give credit, or a hint, for what they hear.
- 6
Check
Test the answer on a small or extreme case before you commit.
Worked classics
Worked example · Clock angle
Checked by codeWhat is the angle between the hands of a clock at 3:15?
Show the working
- 1.The minute hand is at 90°.
- 2.The hour hand moves 0.5° a minute: 90° + 15 × 0.5° = 97.5°.
Answer7.5°.
Worked example · Handshakes
Checked by codeTen people each shake hands with everyone else once. How many handshakes?
Show the working
- 1.Each person shakes 9 hands, but that counts each handshake twice.
- 2.10 × 9 ÷ 2 = 45. Small check: 3 people make 3 handshakes.
Answer45.
Worked example · 100 lockers
Checked by code100 closed lockers. Student 1 toggles every locker, student 2 every second one, and so on up to student 100. How many are open at the end?
Show the working
- 1.Locker n is toggled once for each divisor of n.
- 2.Divisors come in pairs, except for perfect squares, so only squares are toggled an odd number of times.
- 3.There are 10 squares up to 100.
Answer10 (lockers 1, 4, 9, …, 100).
Worked example · Two eggs, 100 floors
Checked by codeWith two eggs, find the highest floor an egg survives from, out of 100, with the fewest drops in the worst case.
Show the working
- 1.If you allow d drops, drop the first egg from floor d, then d − 1 floors higher, then d − 2, and so on, so the second egg never needs more than the drops left.
- 2.That covers d + (d − 1) + … + 1 = d(d + 1)/2 floors.
- 3.13 drops cover 91 floors, too few; 14 cover 105.
Answer14 drops.
Worked example · Burning ropes
Checked by codeTwo ropes each take 60 minutes to burn, but unevenly. How do you measure 45 minutes?
Show the working
- 1.Light rope A at both ends and rope B at one end. A burns out after 30 minutes, whatever its shape.
- 2.Then light B's other end: its remaining 30 minutes of burning now takes 15.
Answer30 + 15 = 45 minutes.
Common mistakes
Common mistakes
- Going silent. Say what you're trying, even if it doesn't work.
- Blurting a guess with no reasoning behind it.
- Skipping small cases, which usually reveal the pattern.
- Giving up. If you're stuck, say what you'd try next.
Trading and quant