Hard Quant Researcher Interview Questions
Everything asked of quant researchers, filtered to the hard end - useful for calibrating where you actually are.
171 questions, all free to practise. The topics that come up most are probability (76), combinatorics (52), brainteasers (40), expected value (39).
- A 12 before two 7sHardProbabilityStochastic ProcessesView →
- A Fibonacci power sumHardBrainteasersView →
- A coin thick enough to land on its sideHardProbabilityBrainteasersView →
- A flea's shortest escape across a boxHardBrainteasersCalculusView →
- A function minus its derivativeHardCalculusView →
- A geometric series that sums to a squareHardBrainteasersView →
- A half-plane, given positiveHardProbabilityRandom VariablesView →
- A rectangle over the shaded rowHardProbabilityCombinatoricsView →
- A second red ball from the same urnHardProbabilityConditional Probability & ExpectationView →
- A small sub-triangleHardProbabilityRandom VariablesView →
- A telescoping partial-fraction sumHardCalculusView →
- A three-way race to the first headHardProbabilityRandom VariablesView →
- A triangle of consecutive integersHardBrainteasersView →
- A void suit in bridgeHardProbabilityCombinatoricsView →
- A weighted sum of binomialsHardCombinatoricsBrainteasersView →
- Absorption in naive floating-point summationHardCalculusProgramming & DSAView →
- Ages from product and sumHardCombinatoricsBrainteasersView →
- Amoeba extinctionHardProbabilityStochastic ProcessesView →
- An arithmetic-geometric seriesHardCalculusView →
- Average of near-diagonal numbersHardCombinatoricsBrainteasersView →
- Balls into bowls, three eachHardCombinatoricsView →
- Bertrand's chordHardProbabilityBrainteasersView →
- Best-of-seven underdogHardProbabilityRandom VariablesView →
- Blue-eyed islandersHardBrainteasersView →
- Branching process extinction (critical)HardProbabilityStochastic ProcessesView →
- Branching process extinction (supercritical)HardProbabilityStochastic ProcessesView →
- Broken-stick triangleHardProbabilityView →
- Buffon's needleHardProbabilityCalculusView →
- Cars advancing to the endHardProbabilityExpected ValueView →
- Cats and miceHardBrainteasersView →
- Conditioning a Brownian bridgeHardStochastic ProcessesView →
- Connecting noodlesHardProbabilityExpected ValueView →
- Correlation of min and maxHardProbabilityRandom VariablesView →
- Counting fives before a four and a sixHardProbabilityRandom VariablesView →
- Counting two-pair handsHardProbabilityCombinatoricsView →
- Covariance of X with Y squaredHardRandom VariablesStatisticsView →
- Covariance with a lognormal childHardConditional Probability & ExpectationRandom VariablesView →
- Cubes over the terminating denominatorsHardBrainteasersCalculusView →
- Cuts until one orb remainsHardProbabilityExpected ValueView →
- Cycles in a shuffleHardCombinatoricsExpected ValueView →
- Dealing until kings or a king-and-aceHardCombinatoricsExpected ValueView →
- Defective stack of coinsHardCombinatoricsBrainteasersView →
- Deriving the first-price shading factorHardProbabilityExpected ValueView →
- Digits with distinct pairwise sumsHardCombinatoricsBrainteasersView →
- Distinct toys from seven boxesHardProbabilityExpected ValueView →
- Domino tilings of a 3×8 gridHardCombinatoricsView →
- Doors toggled by primesHardCombinatoricsBrainteasersView →
- Draws to beat a hidden uniformHardRandom VariablesExpected ValueView →
- Draws to pass a log thresholdHardProbabilityRandom VariablesView →
- Draws to pass twoHardProbabilityRandom VariablesView →
- Draws until a smaller valueHardExpected ValueView →
- Drunk man on a bridgeHardExpected ValueStochastic ProcessesView →
- Ehrenfest urn stationary distributionHardProbabilityStochastic ProcessesView →
- Everyone gets one of eachHardProbabilityCombinatoricsView →
- Exactly one pairHardProbabilityCombinatoricsView →
- Expected arc covering a fixed pointHardProbabilityExpected ValueView →
- Expected chord between two random pointsHardProbabilityExpected ValueView →
- Expected chord intersectionsHardProbabilityCombinatoricsView →
- Expected comparisons, from first principlesHardProgramming & DSAView →
- Expected duration of a fair walkHardExpected ValueStochastic ProcessesView →
- Expected flips for HHHHardExpected ValueStochastic ProcessesView →
- Expected flips for HTHHardExpected ValueStochastic ProcessesView →
- Expected largest of ten ballsHardCombinatoricsExpected ValueView →
- Expected local maxima in a shuffleHardProbabilityExpected ValueView →
- Expected revisits of the start stateHardExpected ValueStochastic ProcessesView →
- Exponential martingale compensatorHardCalculusStochastic ProcessesView →
- Filling three bins from a coin flipHardProbabilityCombinatoricsView →
- Four heads in a rowHardExpected ValueStochastic ProcessesView →
- Guessing cards from a known pileHardProbabilityExpected ValueView →
- HTH before HHTHardProbabilityRandom VariablesView →
- Handshakes at a dinner partyHardCombinatoricsBrainteasersView →
- Hats in a lineHardBrainteasersView →
- Hats with 100 colorsHardBrainteasersView →
- Head density with no two in a rowHardProbabilityCombinatoricsView →
- Hitting zero on a ringHardProbabilityStochastic ProcessesView →
- Inverse via Cayley–HamiltonHardLinear AlgebraView →
- Laplace transform of a Brownian exit timeHardStochastic ProcessesView →
- Laplace's rule of successionHardProbabilityConditional Probability & ExpectationView →
- Largest pairwise-coprime subset sumHardCombinatoricsBrainteasersView →
- Last one standingHardCombinatoricsBrainteasersView →
- Locks for a four-of-seven safeHardCombinatoricsBrainteasersView →
- Long cycles in a random permutationHardCombinatoricsExpected ValueView →
- Loops from tying noodlesHardProbabilityExpected ValueView →
- Making a power of Brownian motion a martingaleHardStochastic ProcessesView →
- Making change in lineHardCombinatoricsStochastic ProcessesView →
- Mean of a mean-reverting processHardStochastic ProcessesFinance & DerivativesView →
- Measuring two pintsHardBrainteasersView →
- Median of a streamHardStatisticsProgramming & DSAView →
- Minimum coins where greedy failsHardProgramming & DSAView →
- More coins, more heads?HardProbabilityCombinatoricsView →
- No two samples too closeHardProbabilityCombinatoricsView →
- Odd sums on a 3×3 gridHardProbabilityCombinatoricsView →
- One of each face before the two of heartsHardProbabilityCombinatoricsView →
- Only seven left unchosenHardProbabilityCombinatoricsView →
- Optional stopping between +3 and −5HardExpected ValueStochastic ProcessesView →
- Order statistics are BetaHardRandom VariablesStatisticsView →
- Overshoot past oneHardProbabilityRandom VariablesView →
- Pairing gloves within oneHardProbabilityCombinatoricsView →
- Pairing with a difference of 1 or 11HardCombinatoricsBrainteasersView →
- Pairs left in the drawerHardCombinatoricsExpected ValueView →
- Penalty kicks with a shifting rateHardProbabilityRandom VariablesView →
- Pirate gameHardMarket Making & Betting GamesView →
- Pricing an inverse floaterHardFinance & DerivativesView →
- Prisoners and the boxesHardProbabilityBrainteasersView →
- Prisoners and the light switchHardBrainteasersView →
- Quadratic variation in mean-squareHardStochastic ProcessesView →
- Quadratic variation of a scaled Itô integralHardCalculusStochastic ProcessesView →
- Range beats the midpointHardProbabilityRandom VariablesView →
- Ratio of two normalsHardRandom VariablesStatisticsView →
- Reading N(d₂) in Black–ScholesHardFinance & DerivativesView →
- Reflected paths ending below the levelHardProbabilityStochastic ProcessesView →
- Reflecting wall first-passage timeHardExpected ValueStochastic ProcessesView →
- Repainting balls to one colorHardExpected ValueStochastic ProcessesView →
- Reservoir samplingHardStatisticsProgramming & DSAView →
- Rolling until two rolls are closeHardProbabilityExpected ValueView →
- Rolls to a six, given all evenHardConditional Probability & ExpectationExpected ValueView →
- Rotations divisible by 37HardCombinatoricsBrainteasersView →
- Rounds to see all faces with two diceHardProbabilityExpected ValueView →
- Runs of red and blue marblesHardCombinatoricsExpected ValueView →
- Second moment of a Gaussian-kernel stochastic integralHardCalculusStochastic ProcessesView →
- Seven seated in age orderHardProbabilityCombinatoricsView →
- Shortest of three piecesHardProbabilityRandom VariablesView →
- Shuffles to restore the deckHardCombinatoricsBrainteasersView →
- Six pieces, none past a halfHardProbabilityRandom VariablesView →
- Smallest card sharing a boxHardProbabilityExpected ValueView →
- Smallest number with digit product 10000HardCombinatoricsBrainteasersView →
- Smallest possible MGF valueHardRandom VariablesStatisticsView →
- Spread of a lognormal raised to the fourthHardRandom VariablesStatisticsView →
- Spread of a multinomial count gapHardRandom VariablesStatisticsView →
- Subsets with one consecutive pairHardCombinatoricsView →
- Sum of repeating decimalsHardCombinatoricsBrainteasersView →
- Sums of fours and fivesHardCombinatoricsBrainteasersView →
- Ten prime digits with a set productHardCombinatoricsView →
- The all-pay auctionHardProbabilityExpected ValueView →
- The boy born on a TuesdayHardProbabilityConditional Probability & ExpectationView →
- The decreasing run of uniformsHardRandom VariablesExpected ValueView →
- The drunk passengerHardProbabilityConditional Probability & ExpectationView →
- The frog's single leftward hopHardProbabilityCombinatoricsView →
- The leap-frog's favorite landing spotHardProbabilityStochastic ProcessesView →
- The number with no new digitsHardBrainteasersView →
- The racing camelsHardBrainteasersView →
- The reroll advantage in a die duelHardProbabilityMarket Making & Betting GamesView →
- The snow plowHardCalculusView →
- The survivor in the circleHardBrainteasersView →
- The two-envelopes paradoxHardProbabilityConditional Probability & ExpectationView →
- Three eggs, nine dropsHardCombinatoricsBrainteasersView →
- Three first-heads in non-decreasing orderHardProbabilityRandom VariablesView →
- Triangle from three independent sticksHardProbabilityCalculusView →
- Triangle that swallows the centerHardProbabilityBrainteasersView →
- Triangle with equal side sumsHardCombinatoricsBrainteasersView →
- Twelve balls, one oddHardBrainteasersView →
- Two Brownian values, both positiveHardProbabilityStochastic ProcessesView →
- Two Newton iterations for a square rootHardCalculusProgramming & DSAView →
- Two coprime integersHardProbabilityCombinatoricsView →
- Two eggs, 100 floorsHardBrainteasersView →
- Two elements in the long cycleHardProbabilityCombinatoricsView →
- Two random segments overlappingHardProbabilityRandom VariablesView →
- Two random subsets that overlapHardProbabilityCombinatoricsView →
- Two walks returning togetherHardProbabilityCombinatoricsView →
- Two-color necklacesHardCombinatoricsView →
- Uniforms summing past 1HardRandom VariablesExpected ValueView →
- Variance of an Itô integralHardStochastic ProcessesView →
- Variance of the exponential of a gammaHardRandom VariablesStatisticsView →
- Variance under random parametersHardRandom VariablesStatisticsView →
- Weighings for the odd beanHardBrainteasersView →
- When a power of the process is a submartingaleHardProbabilityStochastic ProcessesView →
- When a uniform ratio rounds to a squareHardProbabilityRandom VariablesView →
- When k-to-the-k is a squareHardCombinatoricsBrainteasersView →
- When the extremes sum above oneHardProbabilityRandom VariablesView →
- Will the three-legged table stand?HardProbabilityView →
- World Series bettingHardExpected ValueStochastic ProcessesView →
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