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Two Sigma Interview Questions
Problems
41
Topics
8
Hard
6
Two Sigma is a systematic hedge fund whose interviews stress probability, statistics, programming and applied machine learning. Below are 41 quant interview questions of the kind asked at Two Sigma, spanning Brain Teasers, Probability, Stochastic Processes, Calculus & Linear Algebra, Algorithms & Numerical, Market Making & Games, Portfolio & Risk, Statistics. Each comes with a full worked solution — sign in to check your answers and track your progress.
Brain Teasers 4Probability 4Stochastic Processes 4Calculus & Linear Algebra 5Algorithms & Numerical 13Portfolio & Risk 3Statistics 7
442%Medium762%Medium1245%Hard1940%Hard2341%Medium2855%Medium3669%Medium4245%Hard5065%Medium5269%Medium5366%Medium5457%Hard6543%Medium7074%Medium7387%Easy7482%Easy7571%Easy79Medium81Medium83Medium84Medium85Medium86Medium8765%Easy91Hard93Medium99Medium100Medium101Hard103Medium14962%Medium15852%Medium16052%Medium16552%Medium17274%Medium17490%Easy17785%Easy18163%Medium18269%Medium18460%Easy18869%Medium
Horse Race — Top 3
Brain TeasersGoogleTwo Sigma
100 Lockers
Brain TeasersGoogleTwo Sigma
12 Balls, One Odd
Brain TeasersCitadelJane StreetTwo Sigma
The Blue-Eyed Islanders
Brain TeasersJane StreetTwo Sigma
Roll Until All Six Faces
ProbabilityGoogleTwo Sigma
Bayes — Disease Test
ProbabilityGoldman SachsTwo Sigma
Poisson — No Arrivals
ProbabilityTwo SigmaJump Trading
The 100 Prisoners Problem
ProbabilityJane StreetTwo Sigma
Covariance of Brownian Motion
Stochastic ProcessesGoldman SachsTwo Sigma
Random Walk Recurrence
Stochastic ProcessesTwo SigmaDE Shaw
Quadratic Variation of BM
Stochastic ProcessesGoldman SachsTwo Sigma
Random Walk — Expected Steps
Stochastic ProcessesJane StreetTwo Sigma
Gaussian Integral
Calculus & Linear AlgebraGoldman SachsTwo Sigma
Integral of x·e^(−x)
Calculus & Linear AlgebraGoldman SachsTwo Sigma
Sum of First 10 Squares
Calculus & Linear AlgebraJane StreetTwo Sigma
Trace = Sum of Eigenvalues
Calculus & Linear AlgebraTwo SigmaGoldman Sachs
Determinant = Product of Eigenvalues
Calculus & Linear AlgebraTwo SigmaDE Shaw
Product of Array Except SelfLeetCode
Algorithms & NumericalTwo SigmaHRT
Kth Largest ElementLeetCode
Algorithms & NumericalTwo SigmaDE Shaw
Maximum Subarray (Kadane)LeetCode
Algorithms & NumericalTwo SigmaDE Shaw
Random Pick with WeightLeetCode
Algorithms & NumericalCitadelTwo Sigma
Shuffle an Array (Fisher-Yates)LeetCode
Algorithms & NumericalTwo SigmaDE Shaw
Best Time to Buy and Sell StockLeetCode
Algorithms & NumericalTwo SigmaDE Shaw
Monte Carlo — Estimate π
Algorithms & NumericalGoldman SachsTwo Sigma
Median of Two Sorted ArraysLeetCode
Algorithms & NumericalGoogleTwo Sigma
Time-Based Key-Value StoreLeetCode
Algorithms & NumericalTwo SigmaJump Trading
LRU CacheLeetCode
Algorithms & NumericalTwo SigmaHRT
Longest Increasing SubsequenceLeetCode
Algorithms & NumericalTwo SigmaDE Shaw
Find Median from Data StreamLeetCode
Algorithms & NumericalTwo SigmaCitadel
Number of IslandsLeetCode
Algorithms & NumericalGoogleTwo Sigma
The St. Petersburg Game
Market Making & GamesJane StreetTwo Sigma
CVaR / Expected Shortfall
Portfolio & RiskAQR CapitalTwo Sigma
Maximum Drawdown
Portfolio & RiskCitadelTwo SigmaMan Group
Annualizing Sharpe
Portfolio & RiskTwo SigmaAQR Capital
Correlation of X and X²
StatisticsTwo SigmaDE Shaw
OLS Slope
StatisticsTwo SigmaAQR Capital
MLE of a Coin
StatisticsTwo SigmaDE Shaw
Variance of the Sample Mean
StatisticsTwo SigmaDE Shaw
The German Tank Problem
StatisticsTwo SigmaDE Shaw
From Correlation to R²
StatisticsTwo SigmaAQR Capital
Simpson’s Paradox
StatisticsTwo SigmaCitadel
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