Combinatorics Questions for Market Maker Interviews
A market maker round does not test combinatorics the way a textbook does. This set is the overlap - the combinatorics questions that actually turn up in this format.
123 questions, all free to practise. The split is 18 easy, 55 medium, 50 hard.
- A coin that branches into a dieEasyCombinatoricsExpected ValueView →
- A divisor of a power of tenEasyProbabilityCombinatoricsView →
- A majority of onesEasyCombinatoricsView →
- All four aces before any kingEasyProbabilityCombinatoricsView →
- All the squares on a chessboardEasyCombinatoricsBrainteasersView →
- An odd subset with two small elementsEasyCombinatoricsView →
- Arranging colored balls in a lineEasyCombinatoricsView →
- Counting 8-bit stringsEasyCombinatoricsView →
- Counting nines to 1000EasyCombinatoricsBrainteasersView →
- Counting up-down walks to a targetEasyCombinatoricsView →
- Handshakes at four couplesEasyCombinatoricsBrainteasersView →
- Integers that contain a zeroEasyCombinatoricsBrainteasersView →
- Lattice paths through a checkpointEasyCombinatoricsView →
- Repeated digit on a plateEasyCombinatoricsView →
- The top two cards form a pairEasyProbabilityCombinatoricsView →
- Three cube faces at a cornerEasyProbabilityCombinatoricsView →
- Two primes with an even sumEasyProbabilityCombinatoricsView →
- Units digit of a random productEasyProbabilityCombinatoricsView →
- A prime sum on prime diceMediumProbabilityCombinatoricsView →
- An ace for everyoneMediumProbabilityCombinatoricsView →
- An ace in every pileMediumProbabilityCombinatoricsView →
- Anagrams of LOLLIPOPMediumCombinatoricsView →
- Balanced parenthesesMediumCombinatoricsProgramming & DSAView →
- Boy–girl neighbors in a lineMediumCombinatoricsExpected ValueView →
- Chords that don't crossMediumProbabilityCombinatoricsView →
- Climbing stairsMediumCombinatoricsProgramming & DSAView →
- CompositionsMediumCombinatoricsView →
- Deleting every other number on a circleMediumCombinatoricsBrainteasersView →
- Distinct die labelingsMediumCombinatoricsBrainteasersView →
- Distributing candies with a capMediumCombinatoricsView →
- Emptying the cherry bowlMediumProbabilityCombinatoricsView →
- Exactly two aces in a bridge handMediumProbabilityCombinatoricsView →
- Expected ascents in a shuffleMediumCombinatoricsExpected ValueView →
- First HH on the tenth tossMediumProbabilityCombinatoricsView →
- Inversions in a shuffleMediumCombinatoricsExpected ValueView →
- Keeping two apartMediumCombinatoricsView →
- Lattice paths in 3DMediumCombinatoricsView →
- Median of a list and its squaresMediumCombinatoricsStatisticsView →
- Monotone paths across a gridMediumCombinatoricsView →
- No face card before the two of heartsMediumProbabilityCombinatoricsView →
- No two evens adjacentMediumCombinatoricsView →
- No two heads in a rowMediumProbabilityCombinatoricsView →
- No two neighboring bulbs litMediumProbabilityCombinatoricsView →
- Non-attacking rooksMediumCombinatoricsView →
- Odd multiples of threeMediumCombinatoricsBrainteasersView →
- Odd solutions to a sumMediumCombinatoricsView →
- One card each in casino warMediumProbabilityCombinatoricsView →
- One random subset inside anotherMediumProbabilityCombinatoricsView →
- Onto functionsMediumCombinatoricsView →
- Pair at a round tableMediumCombinatoricsView →
- Pairing up six peopleMediumCombinatoricsView →
- Paths on a 4×3 gridMediumCombinatoricsView →
- Placing operators among digitsMediumCombinatoricsView →
- Power of three in a factorialMediumCombinatoricsView →
- Probability of three of a kindMediumProbabilityCombinatoricsView →
- Red faces on a diced cubeMediumCombinatoricsExpected ValueView →
- Regions from ten linesMediumCombinatoricsBrainteasersView →
- Spaced onesMediumCombinatoricsView →
- Sum of multinomial coefficientsMediumCombinatoricsView →
- Sum of the pandigital numbersMediumCombinatoricsBrainteasersView →
- Summing digits to a millionMediumCombinatoricsBrainteasersView →
- Ten dice, sum divisible by sixMediumProbabilityCombinatoricsView →
- Terms in a multinomial expansionMediumCombinatoricsView →
- The birthday problemMediumProbabilityCombinatoricsView →
- The die that makes sums uniformMediumProbabilityCombinatoricsView →
- The largest unmakeable totalMediumCombinatoricsBrainteasersView →
- The same number of tailsMediumProbabilityCombinatoricsView →
- The two black aces, side by sideMediumProbabilityCombinatoricsView →
- Three ones in a rowMediumProbabilityCombinatoricsView →
- Three unlabeled teamsMediumCombinatoricsView →
- Three-four-five in Pascal's triangleMediumCombinatoricsBrainteasersView →
- Tiling a stripMediumCombinatoricsView →
- Units digit of a random powerMediumProbabilityCombinatoricsView →
- A rectangle over the shaded rowHardProbabilityCombinatoricsView →
- A void suit in bridgeHardProbabilityCombinatoricsView →
- A weighted sum of binomialsHardCombinatoricsBrainteasersView →
- Ages from product and sumHardCombinatoricsBrainteasersView →
- Average of near-diagonal numbersHardCombinatoricsBrainteasersView →
- Balls into bowls, three eachHardCombinatoricsView →
- Counting two-pair handsHardProbabilityCombinatoricsView →
- Cycles in a shuffleHardCombinatoricsExpected ValueView →
- Dealing until kings or a king-and-aceHardCombinatoricsExpected ValueView →
- Defective stack of coinsHardCombinatoricsBrainteasersView →
- Digits with distinct pairwise sumsHardCombinatoricsBrainteasersView →
- Domino tilings of a 3×8 gridHardCombinatoricsView →
- Doors toggled by primesHardCombinatoricsBrainteasersView →
- Everyone gets one of eachHardProbabilityCombinatoricsView →
- Expected chord intersectionsHardProbabilityCombinatoricsView →
- Expected largest of ten ballsHardCombinatoricsExpected ValueView →
- Filling three bins from a coin flipHardProbabilityCombinatoricsView →
- Handshakes at a dinner partyHardCombinatoricsBrainteasersView →
- Head density with no two in a rowHardProbabilityCombinatoricsView →
- Largest pairwise-coprime subset sumHardCombinatoricsBrainteasersView →
- Last one standingHardCombinatoricsBrainteasersView →
- Locks for a four-of-seven safeHardCombinatoricsBrainteasersView →
- Long cycles in a random permutationHardCombinatoricsExpected ValueView →
- Making change in lineHardCombinatoricsStochastic ProcessesView →
- 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 →
- Pairing gloves within oneHardProbabilityCombinatoricsView →
- Pairing with a difference of 1 or 11HardCombinatoricsBrainteasersView →
- Pairs left in the drawerHardCombinatoricsExpected ValueView →
- Rotations divisible by 37HardCombinatoricsBrainteasersView →
- Runs of red and blue marblesHardCombinatoricsExpected ValueView →
- Seven seated in age orderHardProbabilityCombinatoricsView →
- Shuffles to restore the deckHardCombinatoricsBrainteasersView →
- Smallest number with digit product 10000HardCombinatoricsBrainteasersView →
- 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 frog's single leftward hopHardProbabilityCombinatoricsView →
- Three eggs, nine dropsHardCombinatoricsBrainteasersView →
- Triangle with equal side sumsHardCombinatoricsBrainteasersView →
- Two coprime integersHardProbabilityCombinatoricsView →
- Two elements in the long cycleHardProbabilityCombinatoricsView →
- Two walks returning togetherHardProbabilityCombinatoricsView →
- Two-color necklacesHardCombinatoricsView →
- When k-to-the-k is a squareHardCombinatoricsBrainteasersView →
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