Citadel Quant Interview Questions
Citadel and Citadel Securities interviews span probability and statistics, brainteasers, and programming, with a strong emphasis on clear quantitative reasoning for researcher, trader, and engineering roles.
156 questions tagged to Citadel · 21 free to practise now.
- Bond price vs. yieldEasyFinance & DerivativesView →
- Derivative of ln(ln x) at x = eEasyCalculusView →
- Determinant from the spectrumEasyLinear AlgebraView →
- Determinant of a 2×2 (geometry)EasyLinear AlgebraView →
- Hash table average lookupEasyProgramming & DSAView →
- Inverse of a 2×2EasyLinear AlgebraView →
- Maximum subarray sumEasyProgramming & DSAView →
- Minimum of four uniformsEasyExpected ValueStatisticsView →
- Moving averageEasyProgramming & DSAView →
- Precision of the sample meanEasyRandom VariablesStatisticsView →
- Reverse a singly linked listEasyProgramming & DSAView →
- The 68–95–99.7 ruleEasyStatisticsView →
- 25 horses, 5 tracksMediumBrainteasersView →
- All six faces (coupon collector)MediumRandom VariablesExpected ValueView →
- Anagrams of MISSISSIPPIMediumCombinatoricsView →
- Bayes: did it rain?MediumConditional Probability & ExpectationStatisticsView →
- Disease test (Bayes)MediumConditional Probability & ExpectationStatisticsView →
- Monty HallMediumProbabilityConditional Probability & ExpectationView →
- Trailing zeros of 100!MediumCombinatoricsView →
- Variance of a dieMediumRandom VariablesStatisticsView →
- Why divide by n−1?MediumStatisticsView →
- Absorption probability on a lineMediumProbabilityStochastic Processes Premium
- American early exerciseMediumFinance & Derivatives Premium
- At least two sixes in five rollsMediumProbabilityRandom Variables Premium
- Average salary, kept privateMediumBrainteasersStatistics Premium
- Bertrand's boxMediumProbabilityConditional Probability & Expectation Premium
- Brownian motion propertiesMediumStochastic Processes Premium
- Butterfly spread max payoffMediumFinance & Derivatives Premium
- CAPM expected returnMediumStatisticsFinance & Derivatives Premium
- Call option payoffMediumFinance & Derivatives Premium
- Classify critical points of x^3 - 3xMediumCalculus Premium
- Committee with a chairMediumCombinatorics Premium
- CompositionsMediumCombinatorics Premium
- Condition numberMediumLinear Algebra Premium
- Convexity correction signMediumFinance & Derivatives Premium
- Counting straightsMediumProbabilityCombinatorics Premium
- Delta of a callMediumFinance & Derivatives Premium
- Density of a uniform squaredMediumRandom VariablesCalculus Premium
- Detect a cycle in a linked listMediumProgramming & DSA Premium
- Determinant of an orthogonal matrixMediumLinear Algebra Premium
- Dice game, up to three rollsMediumExpected ValueStochastic Processes Premium
- Direction of fastest increaseMediumLinear AlgebraCalculus Premium
- Distinct birthdays representedMediumProbabilityExpected Value Premium
- E[X | X > 0] for a standard normalMediumStatisticsCalculus Premium
- Eigenvalues of a 2×2MediumLinear Algebra Premium
- Eigenvalues of a rotationMediumLinear Algebra Premium
- Expectation as a sum of tailsMediumRandom VariablesExpected Value Premium
- FRA payoff directionMediumFinance & Derivatives Premium
- Fourth moment of a normalMediumProbabilityRandom Variables Premium
- Gambler's ruin (unfair)MediumProbabilityStochastic Processes Premium
- Gap between two uniformsMediumExpected ValueStatistics Premium
- Guess 2/3 of the averageMediumMarket Making & Betting Games Premium
- Heap operationsMediumProgramming & DSA Premium
- Identify the sortMediumProgramming & DSA Premium
- In-place array rotationMediumProgramming & DSA Premium
- Is W(t)³ a martingale?MediumStochastic Processes Premium
- Is the random walk squared a martingale?MediumExpected ValueStochastic Processes Premium
- Joint default rangeMediumProbabilityFinance & Derivatives Premium
- Keeping two apartMediumCombinatorics Premium
- MGF of an exponentialMediumRandom VariablesCalculus Premium
- Markov's boundMediumStatistics Premium
- Maximize xyz on a planeMediumCalculus Premium
- Maximum of x^(1/x)MediumCalculus Premium
- Median of an exponentialMediumRandom VariablesStatistics Premium
- Min and max togetherMediumProgramming & DSA Premium
- Minimum of two exponentialsMediumProbabilityRandom Variables Premium
- Minimum-variance weightsMediumStatisticsFinance & Derivatives Premium
- Modified duration price moveMediumFinance & Derivatives Premium
- Monte Carlo variance reductionMediumFinance & DerivativesProgramming & DSA Premium
- Monty Hall with 100 doorsMediumProbabilityConditional Probability & Expectation Premium
- No two heads in a rowMediumProbabilityCombinatorics Premium
- No-arbitrage call boundsMediumFinance & Derivatives Premium
- Number of runsMediumExpected Value Premium
- Points on a semicircleMediumProbability Premium
- Positive definite matricesMediumLinear Algebra Premium
- Positive semidefinitenessMediumStatisticsLinear Algebra Premium
- Power iterationMediumLinear AlgebraProgramming & DSA Premium
- Pricing a digital optionMediumFinance & Derivatives Premium
- Projecting onto a lineMediumLinear Algebra Premium
- Put-call parityMediumFinance & Derivatives Premium
- Put-call parity: solve for the putMediumFinance & Derivatives Premium
- QR decompositionMediumLinear Algebra Premium
- Quickselect average complexityMediumProgramming & DSA Premium
- Rank–nullityMediumLinear Algebra Premium
- Russian roulette, re-spunMediumProbabilityConditional Probability & Expectation Premium
- Shape of the normalMediumRandom VariablesStatistics Premium
- Short-rate modelsMediumStochastic ProcessesFinance & Derivatives Premium
- Slope of a regression lineMediumStatisticsLinear Algebra Premium
- Spam filterMediumProbabilityConditional Probability & Expectation Premium
- Spectrum of a symmetric matrixMediumStatisticsLinear Algebra Premium
- Stationary distribution of a two-state chainMediumProbabilityStochastic Processes Premium
- Subsets with no neighborsMediumCombinatorics Premium
- Sum of squared standard normalsMediumRandom VariablesStatistics Premium
- The cab problemMediumProbabilityConditional Probability & Expectation Premium
- The probability integral transformMediumRandom VariablesStatistics Premium
- The two-headed coinMediumProbabilityConditional Probability & Expectation Premium
- Two trains and a flyMediumBrainteasers Premium
- Uncorrelated but dependentMediumRandom VariablesStatistics Premium
- Value at RiskMediumStatisticsFinance & Derivatives Premium
- Variance of a difference, correlatedMediumRandom VariablesStatistics Premium
- Variance-minimizing hedgeMediumProbabilityStatistics Premium
- What DV01 measuresMediumFinance & Derivatives Premium
- Which coin produced two heads?MediumProbabilityConditional Probability & Expectation Premium
- Why covariance matrices are PSDMediumStatisticsLinear Algebra Premium
- Will they meet?MediumProbability Premium
- x^4 coefficient of the Maclaurin series of e^xMediumCalculus Premium
- A void suit in bridgeHardProbabilityCombinatorics Premium
- Adverse selection in quotingHardMarket Making & Betting Games Premium
- Ages from product and sumHardCombinatoricsBrainteasers Premium
- Amoeba extinctionHardProbabilityStochastic Processes Premium
- Best-of-seven underdogHardProbabilityRandom Variables Premium
- Blue-eyed islandersHardBrainteasers Premium
- Bluffing frequency in pokerHardProbabilityExpected Value Premium
- Branching process extinction (critical)HardProbabilityStochastic Processes Premium
- Branching process extinction (supercritical)HardProbabilityStochastic Processes Premium
- Connecting noodlesHardProbabilityExpected Value Premium
- Defective stack of coinsHardCombinatoricsBrainteasers Premium
- Drunk man on a bridgeHardExpected ValueStochastic Processes Premium
- Dynamic programming: coin changeHardProgramming & DSA Premium
- Exactly one pairHardProbabilityCombinatorics Premium
- Expected flips for HHHardRandom VariablesExpected Value Premium
- Expected flips for HHHHardExpected ValueStochastic Processes Premium
- Expected flips for HTHHardExpected ValueStochastic Processes Premium
- Expected visits before absorptionHardExpected ValueStochastic Processes Premium
- Finite-difference stabilityHardFinance & DerivativesProgramming & DSA Premium
- First passage of a drifting walkHardExpected ValueStochastic Processes Premium
- First-price auction shadingHardProbabilityExpected Value Premium
- Four heads in a rowHardExpected ValueStochastic Processes Premium
- Gamma and rehedging P&LHardFinance & Derivatives Premium
- Handshakes at a dinner partyHardCombinatoricsBrainteasers Premium
- Hats in a lineHardBrainteasers Premium
- Law of total varianceHardConditional Probability & ExpectationExpected Value Premium
- Max rectangle under a parabolaHardCalculus Premium
- Maximize x + y on the unit circleHardLinear AlgebraCalculus Premium
- Median of a streamHardStatisticsProgramming & DSA Premium
- Order statistics are BetaHardRandom VariablesStatistics Premium
- Par swap rate definitionHardFinance & Derivatives Premium
- Pirate gameHardMarket Making & Betting Games Premium
- Pricing an inverse floaterHardFinance & Derivatives Premium
- Prisoners and the boxesHardProbabilityBrainteasers Premium
- Quadratic variation of Brownian motionHardCalculusStochastic Processes Premium
- Reflection principle for the maximumHardProbabilityStochastic Processes Premium
- Singular values via AᵀAHardLinear Algebra Premium
- Sum of the alternating harmonic seriesHardCalculus Premium
- The all-pay auctionHardProbabilityExpected Value Premium
- The boy born on a TuesdayHardProbabilityConditional Probability & Expectation Premium
- The drunk passengerHardProbabilityConditional Probability & Expectation Premium
- The snow plowHardCalculus Premium
- Three unlabeled teamsHardCombinatorics Premium
- Triangle from three independent sticksHardProbabilityCalculus Premium
- Triangle that swallows the centerHardProbabilityBrainteasers Premium
- Twelve balls, one oddHardBrainteasers Premium
- Two eggs, 100 floorsHardBrainteasers Premium
- Two positive testsHardProbabilityConditional Probability & Expectation Premium
- Volume of revolution of sqrt(x)HardCalculus Premium
- World Series bettingHardExpected ValueStochastic Processes Premium
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