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.
指南以英文編寫，與面試語言一致。
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
例題 · Clock angle
經程式驗證What is the angle between the hands of a clock at 3:15?
查看解題過程
- 1.The minute hand is at 90°.
- 2.The hour hand moves 0.5° a minute: 90° + 15 × 0.5° = 97.5°.
答案7.5°.
例題 · Handshakes
經程式驗證Ten people each shake hands with everyone else once. How many handshakes?
查看解題過程
- 1.Each person shakes 9 hands, but that counts each handshake twice.
- 2.10 × 9 ÷ 2 = 45. Small check: 3 people make 3 handshakes.
答案45.
例題 · 100 lockers
經程式驗證100 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?
查看解題過程
- 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.
答案10 (lockers 1, 4, 9, …, 100).
例題 · Two eggs, 100 floors
經程式驗證With two eggs, find the highest floor an egg survives from, out of 100, with the fewest drops in the worst case.
查看解題過程
- 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.
答案14 drops.
例題 · Burning ropes
經程式驗證Two ropes each take 60 minutes to burn, but unevenly. How do you measure 45 minutes?
查看解題過程
- 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.
答案30 + 15 = 45 minutes.
Common mistakes
常見錯誤
- 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