Brainteasers

Quant brainteasers and interview puzzles

67 classic trading-interview puzzles with progressive hints and full solutions. Type your reasoning and an AI examiner grades it, correct, on the right track, or not yet, the way a real interviewer would probe you. Free, in your browser.

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Trading and quant-research interviews are famous for logic puzzles: they test how you think under uncertainty, not what you have memorized. This desk collects the classics that keep coming up, from one-line warm-ups to the hard ones firms use to separate candidates, each tagged by topic and difficulty.

Every puzzle has hints you can reveal one at a time, so you get unstuck without spoiling the whole answer, and solving without hints pays the most points. When you are signed in, the AI examiner opens a live follow-up: it probes your weakest step ("why does that hold?", "what if n = 100?"), stress-tests correct answers, and closes with an interviewer's summary.

A few classics you will meet

A snail is at the bottom of a 30-foot well. Each day it climbs 3 feet; each night it slides back 2. When does it get out?

Day 28. It nets 1 foot per full day, but on the day it reaches the top it never slides back. After 27 days it is at 27 feet; on day 28 it climbs 3 to 30 and escapes. The trap is counting the last climb like the others.

You have 8 identical-looking balls; one is slightly heavier. Using a balance scale, how many weighings guarantee you find it?

Two. Split into 3, 3, 2. Weigh the two threes: if they balance, the heavy ball is in the pair, one weighing settles it; if not, take the heavier three and weigh one against another. Each weighing has three outcomes, so it carries more information than a yes/no test.

A lily patch doubles in area every day and covers the whole pond on day 48. On what day was it half covered?

Day 47. If it doubles daily, the day before full is exactly half. Exponential growth makes the last step deceptively large, the same intuition that trips people up on compounding and volatility.

The full set spans construction and invariants, probability, game theory, number theory, optimal stopping, symmetry, pure logic, and a few beautiful infinities: the 100 prisoners and 100 boxes, the five pirates, the blue-eyed islanders, Josephus, the secretary problem, the ant on a rubber band, and the colored-hats game, among many others.

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