Hard Market Maker Interview Questions
If the standard market maker set feels comfortable, this is the calibration check.
143 questions, 97 of them free to practise right now. The topics that come up most are probability (65), combinatorics (50), brainteasers (40), expected value (33).
- 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 geometric series that sums to a squareHardBrainteasersView →
- A rectangle over the shaded rowHardProbabilityCombinatoricsView →
- A second red ball from the same urnHardProbabilityConditional Probability & ExpectationView →
- A small sub-triangleHardProbabilityRandom VariablesView →
- A three-way race to the first headHardProbabilityRandom VariablesView →
- A triangle of consecutive integersHardBrainteasersView →
- A weighted sum of binomialsHardCombinatoricsBrainteasersView →
- Average of near-diagonal numbersHardCombinatoricsBrainteasersView →
- Balls into bowls, three eachHardCombinatoricsView →
- Cars advancing to the endHardProbabilityExpected ValueView →
- Cats and miceHardBrainteasersView →
- Conditioning a Brownian bridgeHardStochastic ProcessesView →
- Counting fives before a four and a sixHardProbabilityRandom VariablesView →
- Cubes over the terminating denominatorsHardBrainteasersCalculusView →
- Cuts until one orb remainsHardProbabilityExpected ValueView →
- Dealing until kings or a king-and-aceHardCombinatoricsExpected ValueView →
- Digits with distinct pairwise sumsHardCombinatoricsBrainteasersView →
- 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 →
- Everyone gets one of eachHardProbabilityCombinatoricsView →
- Expected arc covering a fixed pointHardProbabilityExpected ValueView →
- Expected chord between two random pointsHardProbabilityExpected ValueView →
- Expected chord intersectionsHardProbabilityCombinatoricsView →
- Expected largest of ten ballsHardCombinatoricsExpected ValueView →
- Expected local maxima in a shuffleHardProbabilityExpected ValueView →
- Filling three bins from a coin flipHardProbabilityCombinatoricsView →
- Guessing cards from a known pileHardProbabilityExpected ValueView →
- HTH before HHTHardProbabilityRandom VariablesView →
- Head density with no two in a rowHardProbabilityCombinatoricsView →
- Hitting zero on a ringHardProbabilityStochastic ProcessesView →
- How many long cycles?HardProbabilityCombinatoricsView →
- Laplace transform of a Brownian exit timeHardStochastic ProcessesView →
- Largest pairwise-coprime subset sumHardCombinatoricsBrainteasersView →
- 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 →
- Measuring two pintsHardBrainteasersView →
- 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 →
- 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 →
- Quadratic variation in mean-squareHardStochastic ProcessesView →
- Reading N(d₂) in Black–ScholesHardFinance & DerivativesView →
- Rolls to a six, given all evenHardConditional Probability & ExpectationExpected ValueView →
- Rotations divisible by 37HardCombinatoricsBrainteasersView →
- 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 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 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 snow plowHardCalculusView →
- The survivor in the circleHardBrainteasersView →
- Three eggs, nine dropsHardCombinatoricsBrainteasersView →
- Three first-heads in non-decreasing orderHardProbabilityRandom VariablesView →
- Triangle with equal side sumsHardCombinatoricsBrainteasersView →
- Twelve balls, one oddHardBrainteasersView →
- Two random segments overlappingHardProbabilityRandom VariablesView →
- Two walks returning togetherHardProbabilityCombinatoricsView →
- Two-color necklacesHardCombinatoricsView →
- Uniforms summing past 1HardRandom VariablesExpected ValueView →
- Variance of an Itô integralHardStochastic ProcessesView →
- 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 →
- A telescoping partial-fraction sumHardCalculus Premium
- A void suit in bridgeHardProbabilityCombinatorics Premium
- Ages from product and sumHardCombinatoricsBrainteasers Premium
- Amoeba extinctionHardProbabilityStochastic Processes Premium
- An arithmetic-geometric seriesHardCalculus Premium
- Bertrand's chordHardProbabilityBrainteasers Premium
- Best-of-seven underdogHardProbabilityRandom Variables Premium
- Blue-eyed islandersHardBrainteasers Premium
- Bluffing frequency in pokerHardProbabilityExpected Value Premium
- Branching process extinction (critical)HardProbabilityStochastic Processes Premium
- Broken-stick triangleHardProbability Premium
- Buffon's needleHardProbabilityCalculus Premium
- Connecting noodlesHardProbabilityExpected Value Premium
- Correlation of min and maxHardProbabilityRandom Variables Premium
- Counting two-pair handsHardProbabilityCombinatorics Premium
- Cycles in a shuffleHardCombinatoricsExpected Value Premium
- Defective stack of coinsHardCombinatoricsBrainteasers Premium
- Deriving the first-price shading factorHardProbabilityExpected Value Premium
- Draws until a smaller valueHardExpected Value Premium
- Drunk man on a bridgeHardExpected ValueStochastic Processes Premium
- Ehrenfest urn stationary distributionHardProbabilityStochastic Processes Premium
- Expected comparisons, from first principlesHardProgramming & DSA Premium
- Expected flips for HHHHardExpected ValueStochastic Processes Premium
- Expected flips for HTHHardExpected ValueStochastic Processes Premium
- Exponential martingale compensatorHardCalculusStochastic Processes Premium
- Four heads in a rowHardExpected ValueStochastic Processes Premium
- Handshakes at a dinner partyHardCombinatoricsBrainteasers Premium
- Hats in a lineHardBrainteasers Premium
- Hats with 100 colorsHardBrainteasers Premium
- Inverse via Cayley–HamiltonHardLinear Algebra Premium
- Laplace's rule of successionHardProbabilityConditional Probability & Expectation Premium
- Last one standingHardCombinatoricsBrainteasers Premium
- Making change in lineHardCombinatoricsStochastic Processes Premium
- Optional stopping between +3 and −5HardExpected ValueStochastic Processes Premium
- Prisoners and the boxesHardProbabilityBrainteasers Premium
- Prisoners and the light switchHardBrainteasers Premium
- Ratio of two normalsHardRandom VariablesStatistics Premium
- Reservoir samplingHardStatisticsProgramming & DSA Premium
- The all-pay auctionHardProbabilityExpected Value Premium
- The racing camelsHardBrainteasers Premium
- The two-envelopes paradoxHardProbabilityConditional Probability & Expectation Premium
- Triangle that swallows the centerHardProbabilityBrainteasers Premium
- Two Newton iterations for a square rootHardCalculusProgramming & DSA Premium
- Two coprime integersHardProbabilityCombinatorics Premium
- Two eggs, 100 floorsHardBrainteasers Premium
- World Series bettingHardExpected ValueStochastic Processes Premium
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