Hard Market Maker Interview Questions
If the standard market maker set feels comfortable, this is the calibration check.
143 questions, all free to practise. 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 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 →
- 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 →
- Bluffing frequency in pokerHardProbabilityExpected ValueView →
- Branching process extinction (critical)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 →
- 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 →
- 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 →
- Expected arc covering a fixed pointHardProbabilityExpected ValueView →
- Expected chord between two random pointsHardProbabilityExpected ValueView →
- Expected chord intersectionsHardProbabilityCombinatoricsView →
- Expected comparisons, from first principlesHardProgramming & DSAView →
- 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 →
- 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 →
- 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 →
- Optional stopping between +3 and −5HardExpected ValueStochastic ProcessesView →
- 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 →
- Prisoners and the boxesHardProbabilityBrainteasersView →
- Prisoners and the light switchHardBrainteasersView →
- Quadratic variation in mean-squareHardStochastic ProcessesView →
- Ratio of two normalsHardRandom VariablesStatisticsView →
- Reading N(d₂) in Black–ScholesHardFinance & DerivativesView →
- Reservoir samplingHardStatisticsProgramming & DSAView →
- 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 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 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 that swallows the centerHardProbabilityBrainteasersView →
- Triangle with equal side sumsHardCombinatoricsBrainteasersView →
- Twelve balls, one oddHardBrainteasersView →
- 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 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 →
- World Series bettingHardExpected ValueStochastic ProcessesView →
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