Hard Combinatorics Interview Questions
These are the combinatorics questions that separate candidates who know the technique from those who can apply it under pressure.
52 questions, all free to practise.
- 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 →
- Exactly one pairHardProbabilityCombinatoricsView →
- 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 random subsets that overlapHardProbabilityCombinatoricsView →
- Two walks returning togetherHardProbabilityCombinatoricsView →
- Two-color necklacesHardCombinatoricsView →
- When k-to-the-k is a squareHardCombinatoricsBrainteasersView →
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