Combinatorics Interview Questions for Quant Researchers
Quant Researchers get asked combinatorics differently from other quant roles - the emphasis shifts with what the job actually does. This is that slice.
160 questions, 124 of them free to practise right now. The split is 34 easy, 74 medium, 52 hard.
- A coin that branches into a dieEasyCombinatoricsExpected ValueView →
- A divisor of a power of tenEasyProbabilityCombinatoricsView →
- A guest list with a feudEasyCombinatoricsView →
- 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 →
- At least one blue and one greenEasyProbabilityCombinatoricsView →
- Counting 8-bit stringsEasyCombinatoricsView →
- Counting flushesEasyProbabilityCombinatoricsView →
- Counting nines to 1000EasyCombinatoricsBrainteasersView →
- Counting up-down walks to a targetEasyCombinatoricsView →
- Dots on distinct edgesEasyProbabilityCombinatoricsView →
- Even numbers, distinct digitsEasyCombinatoricsView →
- Even-size, non-empty subsetEasyProbabilityCombinatoricsView →
- Finding the number of blue socksEasyProbabilityCombinatoricsView →
- Four dice summing to twentyEasyProbabilityCombinatoricsView →
- Handshakes at four couplesEasyCombinatoricsBrainteasersView →
- Integers that contain a zeroEasyCombinatoricsBrainteasersView →
- Interior crossings of a decagon's diagonalsEasyCombinatoricsView →
- Lattice paths through a checkpointEasyCombinatoricsView →
- MISSISSIPPI with the P's togetherEasyCombinatoricsView →
- Round table with a couple togetherEasyCombinatoricsView →
- The top two cards form a pairEasyProbabilityCombinatoricsView →
- Three cube faces at a cornerEasyProbabilityCombinatoricsView →
- Three distinct dice, no sixEasyProbabilityCombinatoricsView →
- Three-one strings with matching endpointsEasyCombinatoricsView →
- Top three dice summing to eighteenEasyProbabilityCombinatoricsView →
- Two numbers in different groupsEasyProbabilityCombinatoricsView →
- Two ordering constraints at onceEasyProbabilityCombinatoricsView →
- Two primes with an even sumEasyProbabilityCombinatoricsView →
- Units digit of a random productEasyProbabilityCombinatoricsView →
- Ways to reach deuceEasyProbabilityCombinatoricsView →
- Which side holds the heavy weightEasyProbabilityCombinatoricsView →
- 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 →
- Deleting every other number on a circleMediumCombinatoricsBrainteasersView →
- Distinct die labelingsMediumCombinatoricsBrainteasersView →
- Distributing candies with a capMediumCombinatoricsView →
- Eight dice summing to twelveMediumProbabilityCombinatoricsView →
- Emptying the cherry bowlMediumProbabilityCombinatoricsView →
- Exactly two aces in a bridge handMediumProbabilityCombinatoricsView →
- First HH on the tenth tossMediumProbabilityCombinatoricsView →
- Full housesMediumProbabilityCombinatoricsView →
- 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 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 →
- Placing operators among digitsMediumCombinatoricsView →
- Probability of three of a kindMediumProbabilityCombinatoricsView →
- Red faces on a diced cubeMediumCombinatoricsExpected ValueView →
- Regions from ten linesMediumCombinatoricsBrainteasersView →
- 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 third shiny pennyMediumProbabilityCombinatoricsView →
- Three dots on a squareMediumProbabilityCombinatoricsView →
- Three ones in a rowMediumProbabilityCombinatoricsView →
- Three-four-five in Pascal's triangleMediumCombinatoricsBrainteasersView →
- Tiling a stripMediumCombinatoricsView →
- Trailing zeros of 100!MediumCombinatoricsView →
- Units digit of a random powerMediumProbabilityCombinatoricsView →
- Variance of hearts in eight cardsMediumCombinatoricsStatisticsView →
- A rectangle over the shaded rowHardProbabilityCombinatoricsView →
- A weighted sum of binomialsHardCombinatoricsBrainteasersView →
- Average of near-diagonal numbersHardCombinatoricsBrainteasersView →
- Balls into bowls, three eachHardCombinatoricsView →
- 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 →
- Everyone gets one of eachHardProbabilityCombinatoricsView →
- Expected chord intersectionsHardProbabilityCombinatoricsView →
- Expected largest of ten ballsHardCombinatoricsExpected ValueView →
- Filling three bins from a coin flipHardProbabilityCombinatoricsView →
- Head density with no two in a rowHardProbabilityCombinatoricsView →
- How many long cycles?HardProbabilityCombinatoricsView →
- Largest pairwise-coprime subset sumHardCombinatoricsBrainteasersView →
- Locks for a four-of-seven safeHardCombinatoricsBrainteasersView →
- Long cycles in a random permutationHardCombinatoricsExpected ValueView →
- 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 random subsets that overlapHardProbabilityCombinatoricsView →
- Two walks returning togetherHardProbabilityCombinatoricsView →
- Two-color necklacesHardCombinatoricsView →
- When k-to-the-k is a squareHardCombinatoricsBrainteasersView →
- Aces in a seven-card handMediumCombinatoricsExpected Value Premium
- An ace in the handMediumProbabilityCombinatorics Premium
- Climbing stairsMediumCombinatoricsProgramming & DSA Premium
- CompositionsMediumCombinatorics Premium
- Counting straightsMediumProbabilityCombinatorics Premium
- Derangements of four itemsMediumCombinatorics Premium
- Distinct faces in five rollsMediumCombinatoricsExpected Value Premium
- Eight coins, one lightMediumCombinatoricsBrainteasers Premium
- Expected ascents in a shuffleMediumCombinatoricsExpected Value Premium
- Five distinct ranksMediumProbabilityCombinatorics Premium
- Identical balls, no empty boxMediumCombinatorics Premium
- Inversions in a shuffleMediumCombinatoricsExpected Value Premium
- Last two digits of a powerMediumCombinatoricsBrainteasers Premium
- No two heads in a rowMediumProbabilityCombinatorics Premium
- Onto functionsMediumCombinatorics Premium
- Pair at a round tableMediumCombinatorics Premium
- Pairing up six peopleMediumCombinatorics Premium
- Paths on a 4×3 gridMediumCombinatorics Premium
- Position of the first spadeMediumCombinatoricsExpected Value Premium
- Power of three in a factorialMediumCombinatorics Premium
- Spaced onesMediumCombinatorics Premium
- Squares on a chessboardMediumCombinatoricsBrainteasers Premium
- Subsets with no neighborsMediumCombinatorics Premium
- Sum of 10 with three diceMediumProbabilityCombinatorics Premium
- The two black aces, side by sideMediumProbabilityCombinatorics Premium
- Three unlabeled teamsMediumCombinatorics Premium
- A void suit in bridgeHardProbabilityCombinatorics Premium
- Ages from product and sumHardCombinatoricsBrainteasers Premium
- Counting two-pair handsHardProbabilityCombinatorics Premium
- Cycles in a shuffleHardCombinatoricsExpected Value Premium
- Defective stack of coinsHardCombinatoricsBrainteasers Premium
- Exactly one pairHardProbabilityCombinatorics Premium
- Handshakes at a dinner partyHardCombinatoricsBrainteasers Premium
- Last one standingHardCombinatoricsBrainteasers Premium
- Making change in lineHardCombinatoricsStochastic Processes Premium
- Two coprime integersHardProbabilityCombinatorics Premium
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