Brain Teaser Academy
Six levels, from intuition to interview
A graded ladder of quantitative brain teasers. Each problem is self-contained and ships with progressive hints, a full worked solution, the interview angle a desk actually probes, an expected solving time, and an independent difficulty rating.
264 problems published · difficulty rated ●○○○○ (warm-up) to ●●●●● (expert)
The Ladder
L1 · Basic probability intuition
Sample spaces, counting, complements, symmetry, and independence — the reflexes every desk screen assumes you already have.
L2 · Conditional probability
Bayes' theorem, base rates, and updating on evidence — where intuition fails most reliably and interviewers probe hardest.
L3 · Expectations
Linearity, the tail-sum formula, first-step analysis, and waiting times — the workhorses behind every expected-value desk question.
L4 · Random walks
Gambler's ruin, hitting probabilities, recurrence, and the reflection principle — the discrete scaffolding under Brownian motion and barrier pricing.
L5 · Markov chains
Stationary distributions, hitting times, recurrence, and ergodicity — the state-machine reasoning behind regime models and queueing.
L6 · Interview classics
The famous trading-floor and quant-screen puzzles — strategy, encoding, optimal stopping, and game-theoretic backward induction.
L7 · Combinatorics & counting
Permutations, combinations, stars & bars, inclusion–exclusion, Catalan numbers, and pigeonhole — the counting machinery behind every probability.
L8 · Statistics & estimation
MLE, bias and variance, the CLT, correlation structure, and sampling error — the estimation toolkit hedge-fund and quant-research interviews lean on.
L9 · Game theory & optimal stopping
Secretary problems, the Kelly criterion, auctions, mixed strategies, and strategic paradoxes — the decision-and-strategy puzzles trading desks favour.
L10 · Mental math & market-making
Fermi estimation, fast arithmetic, expected-value games, and making two-sided markets — the trading-floor reflexes that prop and market-making firms screen for.
The Academy aims to be the most complete brain-teaser bank for quant interviews — probability, expectation, stochastic processes, plus combinatorics, statistics, game theory, and trading-floor estimation. New problems are appended to each level as they clear review; start the ladder from Level 1, or jump to the topic you want to drill.