Firm-Style Puzzles
Multi-step problems in the style of Jane Street, Optiver, IMC, and Citadel. Each requires creative insight — not just formulas.
15
Total puzzles
0
Solved
6
Hard / Very Hard
15
Remaining
15 puzzles · 0 solved
The 100 Prisoners Problem
HardProbability25–35 minJane StreetOptiverIMC
PermutationsCyclesStrategyCombinatorics
Broken Stick: Triangle Probability
MediumGeometric Probability10–15 minJane StreetGoldman SachsGeneral
Geometric ProbabilityTriangle InequalityUniform Distribution
Amoeba Colony: Extinction Probability
HardBranching Processes20–30 minJane StreetTwo Sigma
Branching ProcessGenerating FunctionsFixed PointRecursion
Records in a Random Permutation
MediumCombinatorics10–15 minJane StreetCitadelHRT
Indicator VariablesSymmetryHarmonic NumbersLinearity of Expectation
Derangements: The Hat-Check Problem
MediumCombinatorics10–15 minJane StreetGoldman SachsGeneral
Inclusion-ExclusionDerangementsIndicator VariablesLimit Theorems
The Ballot Problem
HardCombinatorics20–30 minJane StreetIMCOptiver
Reflection PrincipleBallot ProblemPathsCycle Lemma
Kelly Criterion: Optimal Bet Sizing
MediumBet Sizing15–20 minJane StreetOptiverIMCCitadelDE Shaw
Kelly CriterionExpected LogGeometric GrowthRisk Management
Sequential Bayesian Testing
MediumBayesian15–20 minJane StreetTwo SigmaDE ShawAQR
Bayes' TheoremBase Rate FallacySequential UpdatingMedical Testing
Order Statistics: Uniform Distribution
MediumOrder Statistics15–20 minJane StreetCitadelIMCOptiver
Order StatisticsExpected ValueUniform DistributionMarket Making
Expected Position of the Last Ace
MediumCombinatorics10–15 minJane StreetGoldman SachsOptiver
Expected ValueSymmetryOrder StatisticsCards
The Inspection Paradox
MediumProbability20–25 minTwo SigmaDE ShawAQRWinton
Length-Biased SamplingExponential DistributionSampling BiasBacktesting
Random Walk Recurrence: Pólya's Theorem
HardRandom Walks25–35 minJane StreetOptiverTwo Sigma
Random WalkRecurrenceTransienceGreen's FunctionHarmonic Analysis
Generalized Coupon Collector Problem
MediumProbability15–20 minJane StreetCitadelOptiver
Geometric DistributionHarmonic NumbersExpected ValueIndependence
Martingale Optional Stopping Theorem
HardMartingales25–35 minJane StreetTwo SigmaCitadel
MartingaleOptional StoppingGambler's RuinStopping Time
Bertrand's Paradox: Model Specification
HardModeling20–30 minJane StreetDE ShawTwo Sigma
Geometric ProbabilityModel SpecificationInvarianceParadox