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673 problems across eight parts. Filter by topic and difficulty, or search the statements.
673 problems
| # | Problem | Topic | Difficulty | Access | |
|---|---|---|---|---|---|
| 22.9 | Costly Uniform SamplingThresholds for Continuous Draws | Games and Decisions | Medium | ||
| 15.8 | Extinction of a Bacterial Colony+1Branching Processes | Random Processes | Medium | Free | |
| 6.3 | Deuce in TennisWhich Comes First? | Probability | Easy | ||
| 31.21 | Linear Diophantine ParametrisationModular Arithmetic | Brainteasers and Pure Mathematics | Easy | ||
| 7.9 | Glass Bridge Line PositionBinomial and Geometric | Probability | Medium | ||
| 32.9 | Repunit Decimals with xy = x + yAlgebraic Tricks | Brainteasers and Pure Mathematics | Easy | ||
| 33.2 | The Sliding LadderCalculus | Brainteasers and Pure Mathematics | Easy | ||
| 13.12 | Longest of Three PiecesUniform Order Statistics and Spacings | Expectation and Variance | Medium | ||
| 21.2 | Reroll Unless the Sum Hits SevenKeep, Switch or Reroll Once | Games and Decisions | Medium | ||
| 9.9 | No Piece Longer Than HalfBroken Sticks | Probability | Medium | ||
| 11.10 | Consecutive Rolls Differing by OneWaiting for Patterns | Expectation and Variance | Medium | ||
| 1.12 | Triangles With Prime DifferencesArrangements and Selections | Counting | Hard | ||
| 13.14 | Waiting to Beat the First Value+2Records and Monotone Runs | Expectation and Variance | Easy | Free | |
| 7.30 | Relabelled Die for a Uniform SumSums of Dice and Generating Functions | Probability | Medium | ||
| 14.1 | Product of Heads and TailsVariance of Counts | Expectation and Variance | Easy | Free | |
| 3.27 | No Two Adjacent Bulbs LitDice, Coins, Urns and Seats | Probability | Medium | ||
| 3.33 | Product of Two Dice Divisible by SixComplements and 'At Least One' | Probability | Easy | ||
| 26.7 | Short Call Vega as Spot FallsGreeks and Their Relationships | Finance and Derivatives | Easy | ||
| 21.3 | Stay or Switch UrnsKeep, Switch or Reroll Once | Games and Decisions | Medium | ||
| 9.1 | Conditional Region in the Unit SquareRegions in the Unit Square | Probability | Easy | Free | |
| 5.2 | Random Number of Die RollsThe Law of Total Probability | Probability | Easy | ||
| 5.14 | Predicting the Next FlipWhich Coin Was It? | Probability | Easy | ||
| 3.34 | Both Special Marbles AppearComplements and 'At Least One' | Probability | Easy | ||
| 31.8 | Arithmetic Progression with Prime ProductDivisibility and Primes | Brainteasers and Pure Mathematics | Easy | ||
| 29.3 | Two-Jug Water MeasuringMeasuring | Brainteasers and Pure Mathematics | Medium | ||
| 23.19 | Counting Auction EquilibriaMixed Strategies and Equilibria | Games and Decisions | Hard | ||
| 10.35 | Tying Noodle EndsCycles and Loops | Expectation and Variance | Medium | ||
| 10.30 | Cards Between First Two and First AcePositions in a Shuffled Deck | Expectation and Variance | Hard | ||
| 14.5 | Correlation Under Affine MapsCovariance and Correlation Calculations | Expectation and Variance | Easy | Free | |
| 3.17 | Restoring a House NumberDice, Coins, Urns and Seats | Probability | Medium | ||
| 10.7 | Paying Per Door OpenedFair Prices from the Definition | Expectation and Variance | Easy | ||
| 13.1 | Expected Maximum of Two Dice+1Maxima and Minima of Dice and Cards | Expectation and Variance | Easy | Free | |
| 21.18 | Options on Dice ProductsBetting, Bidding and Market Making | Games and Decisions | Easy | ||
| 3.9 | Girls Joining a Circle of BoysDice, Coins, Urns and Seats | Probability | Medium | ||
| 7.5 | Return to Start With Uneven StepsBinomial and Geometric | Probability | Easy | ||
| 18.7 | Log-Price Dynamics of GBM+3Ito's Lemma | Random Processes | Easy | Free | |
| 13.7 | Highest of Four CardsMaxima and Minima of Dice and Cards | Expectation and Variance | Medium | ||
| 14.30 | Infinite Expected Wait to WinMoments and Generating Functions | Expectation and Variance | Easy | ||
| 1.13 | Allocating Identical Units+6Stars and Bars | Counting | Easy | Free | |
| 31.24 | Cyclic Shifts Divisible by 37Modular Arithmetic | Brainteasers and Pure Mathematics | Easy | ||
| 32.13 | Ferry PassengersAlgebraic Tricks | Brainteasers and Pure Mathematics | Easy | ||
| 32.1 | Balancing FruitsAlgebraic Tricks | Brainteasers and Pure Mathematics | Easy | Free | |
| 23.7 | Pirates Dividing GoldBackward Induction and Winning Positions | Games and Decisions | Medium | ||
| 32.19 | When a² + ab + b² Is a SquareAlgebraic Tricks | Brainteasers and Pure Mathematics | Easy | ||
| 32.38 | Fly Between Two CarsRates, Work and Motion | Brainteasers and Pure Mathematics | Easy | ||
| 9.11 | Triangle Containing the Centre+1Points on a Circle | Probability | Medium | Free | |
| 3.5 | Each Player Gets One of Each RankCards and Poker Hands | Probability | Medium | ||
| 24.4 | Stock Against an Even-Money Bet+2Betting Odds and Dutch Books | Finance and Derivatives | Easy | Free | |
| 32.4 | Product of Four Consecutive Integers Plus OneAlgebraic Tricks | Brainteasers and Pure Mathematics | Easy | ||
| 31.7 | Smallest Multiple of 77 Above a BoundDivisibility and Primes | Brainteasers and Pure Mathematics | Easy | ||
| 16.12 | Stopping When Heads First LeadPaths, Reflection and First Returns | Random Processes | Hard | ||
| 32.34 | Chained Race MarginsRates, Work and Motion | Brainteasers and Pure Mathematics | Easy | ||
| 4.10 | Parking Spots and Random ArrivalsRelative Order of Exchangeable Values | Probability | Hard | ||
| 21.8 | Maximising a Product With One RerollKeep, Switch or Reroll Once | Games and Decisions | Medium | ||
| 21.9 | Thirty-Sided Against Twenty-Sided DieKeep, Switch or Reroll Once | Games and Decisions | Hard | ||
| 8.14 | CLT for a Sum of ExponentialsThe Normal Distribution | Probability | Easy | ||
| 12.19 | Arc Containing a Fixed PointThe Inspection Paradox | Expectation and Variance | Medium | ||
| 24.1 | Borrow Low, Lend HighInterest Rates and Currencies | Finance and Derivatives | Easy | Free | |
| 31.1 | Four Integers from Pair ProductsDivisibility and Primes | Brainteasers and Pure Mathematics | Easy | Free | |
| 21.6 | Choosing a Threshold BetKeep, Switch or Reroll Once | Games and Decisions | Easy | ||
| 30.14 | Deleting Every Other NumberRecursion and Induction | Brainteasers and Pure Mathematics | Medium | ||
| 10.33 | Cycles of a Random Permutation+1Cycles and Loops | Expectation and Variance | Medium | Free | |
| 24.3 | Triangular Currency ArbitrageInterest Rates and Currencies | Finance and Derivatives | Easy | ||
| 8.4 | Uniform Exceeds a ProductSums, Products and Ratios of Uniforms | Probability | Easy | ||
| 3.30 | Distinct Win Totals in a Round RobinDice, Coins, Urns and Seats | Probability | Medium | ||
| 31.6 | Adults at a ConcertDivisibility and Primes | Brainteasers and Pure Mathematics | Medium | ||
| 34.7 | South, East, NorthGeometry and Spatial Reasoning | Brainteasers and Pure Mathematics | Medium | ||
| 4.32 | Die Rolls Forming a Multiple of EightParity and Divisibility of Random Sums | Probability | Easy | ||
| 16.18 | Exponential Martingale of a Walk+1Martingales and Optional Stopping | Random Processes | Easy | Free | |
| 12.17 | Uniform Angle Given Its SineConditioning on Sums and Symmetric Functions | Expectation and Variance | Easy | ||
| 30.10 | Most Coins Without Change for a DollarPigeonhole and Extremal Principles | Brainteasers and Pure Mathematics | Medium | ||
| 9.2 | Cuts on Opposite HalvesRegions in the Unit Square | Probability | Easy | ||
| 25.5 | Replicating an Absolute-Value Payoff+4Static Replication | Finance and Derivatives | Medium | Free | |
| 4.2 | Strictly Increasing Dice RollsRelative Order of Exchangeable Values | Probability | Easy | ||
| 2.31 | Sorted by One Bubble-Sort PassRecursions | Counting | Medium | ||
| 14.21 | Smallest MGF Value Given AnotherBounds on Moments and Correlations | Expectation and Variance | Medium | ||
| 3.40 | Rolling Until a RepeatComplements and 'At Least One' | Probability | Easy | ||
| 12.15 | Gaussian Share of a SumConditioning on Sums and Symmetric Functions | Expectation and Variance | Easy | Free | |
| 28.1 | Finding a Heavier CoinWeighings | Brainteasers and Pure Mathematics | Easy | Free | |
| 13.10 | Shorter Piece of a Broken StickUniform Order Statistics and Spacings | Expectation and Variance | Easy | ||
| 10.23 | Urn Recolouring Black to RedIndicator Variables | Expectation and Variance | Easy | ||
| 11.21 | Uniforms Summing Past a ThresholdStopping Rules and Wald's Identity | Expectation and Variance | Medium | ||
| 29.9 | Toasting Three at a TimeScheduling and Clever Constructions | Brainteasers and Pure Mathematics | Easy | Free | |
| 23.17 | Secret Redraw GameMixed Strategies and Equilibria | Games and Decisions | Medium | ||
| 19.1 | Maximum Likelihood for a BinomialEstimators | Statistics and Regression | Easy | Free | |
| 31.33 | Distinct Pairwise Digit SumsDigit Puzzles | Brainteasers and Pure Mathematics | Medium | ||
| 32.29 | Egyptian Fraction RepresentationAlgebraic Tricks | Brainteasers and Pure Mathematics | Medium | ||
| 7.4 | Top Three of Five DiceBinomial and Geometric | Probability | Easy | ||
| 27.8 | Decoding Colour CodesDeduction Puzzles | Brainteasers and Pure Mathematics | Easy | ||
| 8.16 | Aiming at Two Tiny TargetsThe Normal Distribution | Probability | Medium | ||
| 14.2 | Correlation of Multinomial CountsVariance of Counts | Expectation and Variance | Medium | ||
| 32.31 | Combined Work Rates+4Rates, Work and Motion | Brainteasers and Pure Mathematics | Easy | Free | |
| 33.12 | High Derivative from Taylor CoefficientsSequences, Series and Estimation | Brainteasers and Pure Mathematics | Easy | ||
| 5.17 | The Added BabyConditioning Paradoxes | Probability | Easy | ||
| 31.11 | Random Divisor Divisible by a NumberDivisibility and Primes | Brainteasers and Pure Mathematics | Easy | ||
| 5.1 | Transfer Between Urns Then Draw+1The Law of Total Probability | Probability | Easy | Free | |
| 4.34 | Even Gaps Between Matching BlocksParity and Divisibility of Random Sums | Probability | Medium | ||
| 22.2 | Unlimited Costly RerollsStop or Roll Again? | Games and Decisions | Medium | ||
| 32.17 | Missing Pairwise ProductAlgebraic Tricks | Brainteasers and Pure Mathematics | Easy | ||
| 7.17 | One Geometric Four Times AnotherBinomial and Geometric | Probability | Medium | ||
| 31.29 | Least Multiple of 15 in 0s and 1sDigit Puzzles | Brainteasers and Pure Mathematics | Easy | ||
| 32.32 | Speed With and Against a CurrentRates, Work and Motion | Brainteasers and Pure Mathematics | Easy | ||
| 13.17 | Dart Distance From the Centre+1Expected Lengths and Distances | Expectation and Variance | Easy | Free | |
| 31.22 | Missing Digit by Casting Out NinesModular Arithmetic | Brainteasers and Pure Mathematics | Medium | ||
| 21.1 | Reroll a Die Once+8Keep, Switch or Reroll Once | Games and Decisions | Easy | Free | |
| 18.6 | Laplace Transform of an Exit TimeHitting Times and the Reflection Principle | Random Processes | Hard | ||
| 10.18 | Local Maxima of a PermutationIndicator Variables | Expectation and Variance | Easy | ||
| 32.7 | The Value of iiAlgebraic Tricks | Brainteasers and Pure Mathematics | Easy | ||
| 33.15 | Sum over Terminating DecimalsSequences, Series and Estimation | Brainteasers and Pure Mathematics | Easy | ||
| 25.9 | Calendar Spread ArbitrageNo-Arbitrage Bounds | Finance and Derivatives | Easy | ||
| 27.5 | Snail Climbing OutDeduction Puzzles | Brainteasers and Pure Mathematics | Easy | ||
| 32.37 | Two Burning CandlesRates, Work and Motion | Brainteasers and Pure Mathematics | Easy | ||
| 2.4 | Squares on a ChessboardBijections and Double Counting | Counting | Easy | ||
| 30.15 | Josephus ProblemRecursion and Induction | Brainteasers and Pure Mathematics | Medium | ||
| 32.12 | Sheep StealersAlgebraic Tricks | Brainteasers and Pure Mathematics | Easy | ||
| 26.8 | Largest Gamma Among At-the-Money OptionsGreeks and Their Relationships | Finance and Derivatives | Medium | ||
| 1.14 | Multisets and Non-Decreasing CodesStars and Bars | Counting | Easy | ||
| 12.13 | Highest Roll Before a FourConditioning on How It Ended | Expectation and Variance | Medium | ||
| 30.5 | Particles Falling Off a LineInvariants and Symmetry Arguments | Brainteasers and Pure Mathematics | Medium | ||
| 8.9 | Sums of Uniforms Below OneSums, Products and Ratios of Uniforms | Probability | Medium | ||
| 20.7 | Sample Size for a Significant SlopeR-Squared, Data Transformations and Pitfalls | Statistics and Regression | Medium | ||
| 6.9 | Checker Reaching a Top CornerSmall Absorbing Chains | Probability | Easy | Free | |
| 2.28 | Pairs Differing by 1 or 11Recursions | Counting | Hard | ||
| 25.10 | Upper Bound on a Put SpreadNo-Arbitrage Bounds | Finance and Derivatives | Easy | ||
| 13.5 | Smallest Card in the Box of 100Maxima and Minima of Dice and Cards | Expectation and Variance | Medium | ||
| 2.25 | No Two Consecutive HeadsRecursions | Counting | Medium | ||
| 5.8 | The Flippant JurorThe Law of Total Probability | Probability | Easy | ||
| 14.27 | Poisson Factorial MomentMoments and Generating Functions | Expectation and Variance | Medium | ||
| 14.20 | Frechet Bound on UnionBounds on Moments and Correlations | Expectation and Variance | Easy | ||
| 2.13 | Locks for a Majority SafeBijections and Double Counting | Counting | Medium | ||
| 4.35 | Odd Row and Column Sums in a GridParity and Divisibility of Random Sums | Probability | Medium | ||
| 29.5 | Fox, Chicken and GrainCrossings and Transport | Brainteasers and Pure Mathematics | Easy | Free | |
| 26.1 | Two-Step Tree for a Squared Payoff+3Binomial Trees and Risk-Neutral Pricing | Finance and Derivatives | Easy | Free | |
| 12.7 | Normal With Random ParametersThe Tower Property | Expectation and Variance | Easy | ||
| 29.7 | Bridge and LanternCrossings and Transport | Brainteasers and Pure Mathematics | Medium | ||
| 33.14 | Series via a Uniform ExpectationSequences, Series and Estimation | Brainteasers and Pure Mathematics | Easy | ||
| 23.5 | Halving a Card StackBackward Induction and Winning Positions | Games and Decisions | Medium | ||
| 23.14 | Choosing Die SizesMixed Strategies and Equilibria | Games and Decisions | Medium | ||
| 1.3 | Teams With a Restricted MemberArrangements and Selections | Counting | Easy | ||
| 22.7 | Take and RollStop or Roll Again? | Games and Decisions | Medium | ||
| 10.20 | Complete Four-Circuits in a Random GraphIndicator Variables | Expectation and Variance | Easy | ||
| 16.6 | Expected Duration of Fair RuinGambler's Ruin | Random Processes | Easy | ||
| 34.6 | Consecutive Sides and HeightGeometry and Spatial Reasoning | Brainteasers and Pure Mathematics | Medium | ||
| 29.12 | Blind Split of CoinsScheduling and Clever Constructions | Brainteasers and Pure Mathematics | Medium | ||
| 31.32 | Move the Last Digit, Multiply by 4Digit Puzzles | Brainteasers and Pure Mathematics | Medium | ||
| 32.3 | Alternating Sum of SquaresAlgebraic Tricks | Brainteasers and Pure Mathematics | Easy | ||
| 24.7 | Minimum-Variance Hedge Ratio+3Portfolio Variance | Finance and Derivatives | Easy | Free | |
| 11.19 | Two Cars AdvancingFirst-Step Equations for Expectations | Expectation and Variance | Medium | ||
| 13.6 | Expected Maximum Without ReplacementMaxima and Minima of Dice and Cards | Expectation and Variance | Medium | ||
| 6.8 | HHT Before HTT+1Pattern Races | Probability | Medium | Free | |
| 10.32 | Halving Large LoavesPositions in a Shuffled Deck | Expectation and Variance | Hard | ||
| 33.5 | Steinmetz SolidCalculus | Brainteasers and Pure Mathematics | Medium | ||
| 3.38 | A Ball Drawn by EveryoneComplements and 'At Least One' | Probability | Hard | ||
| 11.8 | Waiting for HTHWaiting for Patterns | Expectation and Variance | Easy | ||
| 32.20 | Median of Numbers and Their SquaresAlgebraic Tricks | Brainteasers and Pure Mathematics | Medium | ||
| 15.7 | Reflecting Walk at a BarrierLong-Run Behaviour | Random Processes | Medium | ||
| 11.7 | HT: A Pattern Without OverlapWaiting for Patterns | Expectation and Variance | Easy | ||
| 4.16 | First Matching Socks on WednesdaySymmetry in a Shuffled Deck | Probability | Medium | ||
| 8.8 | Uniform Plus Exponential Exceeds OneSums, Products and Ratios of Uniforms | Probability | Easy | ||
| 14.12 | Covariance of Complementary VariablesCovariance and Correlation Calculations | Expectation and Variance | Easy | ||
| 29.4 | Beer Barrel MeasuringMeasuring | Brainteasers and Pure Mathematics | Medium | ||
| 13.9 | Order Statistic Given ExtremesUniform Order Statistics and Spacings | Expectation and Variance | Easy | ||
| 31.2 | When Planets RealignDivisibility and Primes | Brainteasers and Pure Mathematics | Easy | ||
| 24.6 | Binary Contracts with Two WinnersBetting Odds and Dutch Books | Finance and Derivatives | Medium | ||
| 4.21 | Equal Head CountsIngenious Symmetries and Couplings | Probability | Easy | ||
| 14.18 | Ranking Second Moments of DiceCovariance and Correlation Calculations | Expectation and Variance | Medium | ||
| 7.22 | One Ace in Each HandSampling Without Replacement | Probability | Easy | ||
| 30.12 | Largest Coprime Subset SumPigeonhole and Extremal Principles | Brainteasers and Pure Mathematics | Medium | ||
| 12.6 | Mean From a Joint DensityThe Tower Property | Expectation and Variance | Easy | ||
| 22.8 | Three Cards of Unknown OffsetThresholds for Continuous Draws | Games and Decisions | Medium | Free | |
| 32.41 | Courier Along a Marching ArmyRates, Work and Motion | Brainteasers and Pure Mathematics | Medium | ||
| 8.26 | Minimum Plus Maximum Exceeds OneOrder Statistics | Probability | Medium | Free | |
| 5.15 | Given At Least One Head+2Conditioning Paradoxes | Probability | Easy | Free | |
| 14.11 | Variance of a ProductCovariance and Correlation Calculations | Expectation and Variance | Easy | ||
| 25.4 | Put-Call Parity ArbitragePut-Call Parity | Finance and Derivatives | Easy | ||
| 4.27 | Dice Sum Divisible by Six+3Parity and Divisibility of Random Sums | Probability | Easy | Free | |
| 18.9 | Itô Isometry with a Gaussian MGFIto Integrals and the Isometry | Random Processes | Medium | ||
| 7.29 | Blue Pair Beats Red PairSums of Dice and Generating Functions | Probability | Easy | ||
| 3.24 | Loaded Die and a Sum of SevenDice, Coins, Urns and Seats | Probability | Easy | ||
| 1.10 | Distinct Sums of PairingsArrangements and Selections | Counting | Medium | ||
| 5.3 | Coin With a Random BiasThe Law of Total Probability | Probability | Easy | ||
| 14.19 | Largest Variance on an IntervalBounds on Moments and Correlations | Expectation and Variance | Easy | Free | |
| 9.6 | One Cut and a Fixed Third SideBroken Sticks | Probability | Easy | Free | |
| 7.32 | Die Whose Single and Double Rolls AgreeSums of Dice and Generating Functions | Probability | Medium | ||
| 23.15 | Marble LotteryMixed Strategies and Equilibria | Games and Decisions | Medium | ||
| 31.23 | Cubes Ending in 11Modular Arithmetic | Brainteasers and Pure Mathematics | Easy | ||
| 11.9 | A Two or Two OnesWaiting for Patterns | Expectation and Variance | Easy | ||
| 28.10 | Two-Egg DropAdversarial Search | Brainteasers and Pure Mathematics | Medium | ||
| 33.13 | Leading Coefficient of a Power SumSequences, Series and Estimation | Brainteasers and Pure Mathematics | Easy | ||
| 2.1 | Counting From the ComplementsBijections and Double Counting | Counting | Easy | Free | |
| 22.1 | Up to Two RerollsStop or Roll Again? | Games and Decisions | Easy | Free | |
| 2.23 | Climbing Stairs One or Two at a Time+3Recursions | Counting | Easy | Free | |
| 31.20 | Frobenius Coin ProblemModular Arithmetic | Brainteasers and Pure Mathematics | Easy | ||
| 7.14 | Fives Before the First SixBinomial and Geometric | Probability | Easy | ||
| 9.15 | Darts in Concentric RingsDiscs, Spheres and Darts | Probability | Easy | ||
| 30.11 | The Taxman GamePigeonhole and Extremal Principles | Brainteasers and Pure Mathematics | Medium | ||
| 30.6 | Socks for a Matching PairPigeonhole and Extremal Principles | Brainteasers and Pure Mathematics | Easy | Free | |
| 3.14 | Sock Drawer With Probability One HalfDice, Coins, Urns and Seats | Probability | Easy | ||
| 28.3 | Light Bulb and Four SwitchesEncoding and Group Testing | Brainteasers and Pure Mathematics | Medium | Free | |
| 32.42 | The Potato ParadoxPercentages, Mixtures and Growth | Brainteasers and Pure Mathematics | Easy | Free | |
| 1.25 | Avoiding Four-Term ProgressionsComplements and Inclusion-Exclusion | Counting | Medium | ||
| 9.8 | Triangle From Three Uniform LengthsBroken Sticks | Probability | Medium | ||
| 8.25 | Maximum of Exponentials Near ln nOrder Statistics | Probability | Easy | ||
| 16.4 | Fair Gambler's Ruin+1Gambler's Ruin | Random Processes | Easy | Free | |
| 8.20 | One Bulb Outlasting Ten in SequenceExponential Variables and Races | Probability | Medium | ||
| 31.26 | Period of the Over-Under ShuffleModular Arithmetic | Brainteasers and Pure Mathematics | Medium | ||
| 18.11 | Quadratic Variation in L²Ito Integrals and the Isometry | Random Processes | Medium | ||
| 32.45 | Alternating Up and Down MovesPercentages, Mixtures and Growth | Brainteasers and Pure Mathematics | Easy | Free | |
| 25.3 | Call Price from Put-Call Parity+3Put-Call Parity | Finance and Derivatives | Easy | Free | |
| 8.27 | Guessing the Rank of a Revealed ValueOrder Statistics | Probability | Medium | ||
| 33.11 | Fibonacci Decimal SeriesSequences, Series and Estimation | Brainteasers and Pure Mathematics | Easy | ||
| 5.10 | Random Wiring Forms One LoopThe Law of Total Probability | Probability | Medium | ||
| 4.4 | Higher Card Than the DealerRelative Order of Exchangeable Values | Probability | Easy | ||
| 2.5 | Rectangles on a Chessboard+2Bijections and Double Counting | Counting | Easy | Free | |
| 7.26 | Every Value but One ChosenOccupancy | Probability | Medium | Free | |
| 10.24 | Non-Overlapping Blocks in Black RunsIndicator Variables | Expectation and Variance | Hard | ||
| 2.19 | Ticket Queue With No ChangeLattice Paths, Reflection and Catalan Numbers | Counting | Medium | ||
| 8.1 | Ratio of Two Uniforms in a Band+2Sums, Products and Ratios of Uniforms | Probability | Easy | Free | |
| 1.8 | All B's Before the First OArrangements and Selections | Counting | Medium | ||
| 23.4 | Removing Powers of TwoBackward Induction and Winning Positions | Games and Decisions | Medium | ||
| 3.35 | Range of Three Dice Equals FourComplements and 'At Least One' | Probability | Medium | ||
| 5.13 | Which Coin Was Drawn?+2Which Coin Was It? | Probability | Easy | Free | |
| 25.6 | Binary Strangle from Binary CallsStatic Replication | Finance and Derivatives | Easy | ||
| 25.2 | Call on a Uniform PricePayoffs and Strategies | Finance and Derivatives | Easy | ||
| 10.6 | Roulette With Side BetFair Prices from the Definition | Expectation and Variance | Easy | ||
| 27.4 | Fenceposts and GunshotsDeduction Puzzles | Brainteasers and Pure Mathematics | Easy | Free | |
| 18.1 | Variance of a Sum of Brownian ValuesGaussian Structure | Random Processes | Easy | Free | |
| 6.11 | Passing a Ball Around a CircleSmall Absorbing Chains | Probability | Medium | ||
| 7.6 | Random Subset PairsBinomial and Geometric | Probability | Easy | ||
| 6.1 | Alternating Until First Success+5Taking Turns | Probability | Easy | Free | |
| 18.12 | Killing the Drift+3Martingales from Ito's Lemma | Random Processes | Easy | Free | |
| 7.1 | Conditioning on Past Coin FlipsBinomial and Geometric | Probability | Easy | Free | |
| 32.39 | Three Cars PassingRates, Work and Motion | Brainteasers and Pure Mathematics | Medium | ||
| 10.29 | Cards Until the First Ace+4Positions in a Shuffled Deck | Expectation and Variance | Easy | Free | |
| 2.14 | Lattice Paths Across a Grid+4Lattice Paths, Reflection and Catalan Numbers | Counting | Easy | Free | |
| 32.28 | Geometric Progression Summing to a SquareAlgebraic Tricks | Brainteasers and Pure Mathematics | Medium | ||
| 2.27 | Density of Heads Without HHRecursions | Counting | Hard | ||
| 2.11 | Magic Triangle Side SumsBijections and Double Counting | Counting | Hard | ||
| 21.13 | How Many Searchers to HireHow Many to Buy? | Games and Decisions | Easy | Free | |
| 13.3 | Median of Three DiceMaxima and Minima of Dice and Cards | Expectation and Variance | Easy | ||
| 3.25 | A Run of Exactly Three HeadsDice, Coins, Urns and Seats | Probability | Easy | ||
| 3.39 | The Birthday ProblemComplements and 'At Least One' | Probability | Easy | ||
| 30.1 | Red and Black Pairs+1Invariants and Symmetry Arguments | Brainteasers and Pure Mathematics | Easy | Free | |
| 10.9 | Red Faces of Painted CubesIndicator Variables | Expectation and Variance | Easy | Free | |
| 24.5 | Three-Horse Dutch BookBetting Odds and Dutch Books | Finance and Derivatives | Easy | ||
| 24.2 | Pricing a Forward ContractInterest Rates and Currencies | Finance and Derivatives | Easy | ||
| 9.7 | Broken Stick TriangleBroken Sticks | Probability | Medium | ||
| 11.4 | Two Dice per RoundThe Coupon Collector | Expectation and Variance | Medium | ||
| 7.31 | Loaded Dice With a Uniform SumSums of Dice and Generating Functions | Probability | Medium | ||
| 6.13 | Escaping on a Triangular LatticeSmall Absorbing Chains | Probability | Medium | ||
| 4.22 | Winner-Stays TournamentIngenious Symmetries and Couplings | Probability | Medium | ||
| 2.8 | Sum of Multinomial CoefficientsBijections and Double Counting | Counting | Easy | ||
| 23.9 | Coprime Picking GameBackward Induction and Winning Positions | Games and Decisions | Hard | ||
| 11.1 | Coupon Collector+4The Coupon Collector | Expectation and Variance | Easy | Free | |
| 11.14 | Paid Until the Dice TieFirst-Step Equations for Expectations | Expectation and Variance | Easy | ||
| 6.7 | Two Wins in a RowWhich Comes First? | Probability | Medium | ||
| 32.5 | Sum of Three Cubes Is a CubeAlgebraic Tricks | Brainteasers and Pure Mathematics | Easy | ||
| 22.3 | Accumulate or BustStop or Roll Again? | Games and Decisions | Easy | ||
| 16.14 | Return Before Leaving a SquareWalks on Cycles and Lattices | Random Processes | Medium | ||
| 10.16 | Runs in Coin TossesIndicator Variables | Expectation and Variance | Easy | ||
| 7.20 | Most Likely Draw of the Fifth KingSampling Without Replacement | Probability | Medium | ||
| 31.25 | Period of a Perfect Riffle ShuffleModular Arithmetic | Brainteasers and Pure Mathematics | Medium | ||
| 29.13 | Fastest Spread of InfectionScheduling and Clever Constructions | Brainteasers and Pure Mathematics | Easy | ||
| 3.2 | Exactly Two Aces DealtCards and Poker Hands | Probability | Easy | ||
| 25.11 | Butterfly ArbitrageNo-Arbitrage Bounds | Finance and Derivatives | Easy | ||
| 13.4 | Dice Sum Over the Smaller DieMaxima and Minima of Dice and Cards | Expectation and Variance | Medium | ||
| 5.21 | Monty Hall+3Conditioning Paradoxes | Probability | Easy | Free | |
| 33.17 | Concatenating 21000 and 51000Sequences, Series and Estimation | Brainteasers and Pure Mathematics | Medium | ||
| 16.8 | Winning Exactly Once Before RuinPaths, Reflection and First Returns | Random Processes | Medium | Free | |
| 31.34 | Dates with All Digits DistinctDigit Puzzles | Brainteasers and Pure Mathematics | Medium | ||
| 20.4 | Duplicating the DataR-Squared, Data Transformations and Pitfalls | Statistics and Regression | Easy | ||
| 14.15 | Uncorrelated but Dependent CoordinatesCovariance and Correlation Calculations | Expectation and Variance | Easy | ||
| 16.2 | Expected Hitting Time of a LevelHitting Probabilities and Times | Random Processes | Medium | ||
| 10.19 | Intact Pairs of SocksIndicator Variables | Expectation and Variance | Easy | ||
| 10.8 | Expected Sum of Bills DrawnIndicator Variables | Expectation and Variance | Easy | Free | |
| 27.10 | Hilbert's HotelDeduction Puzzles | Brainteasers and Pure Mathematics | Medium | ||
| 23.3 | Coins on a Round TableBackward Induction and Winning Positions | Games and Decisions | Easy | ||
| 33.6 | Solving f − f′ = PolynomialCalculus | Brainteasers and Pure Mathematics | Easy | ||
| 10.4 | Chuck-a-Luck Expected PayoffFair Prices from the Definition | Expectation and Variance | Easy | ||
| 1.17 | Digit Sum 19 Below a MillionStars and Bars | Counting | Medium | ||
| 33.7 | Limit of n∫dx/(1 + xn)Calculus | Brainteasers and Pure Mathematics | Medium | ||
| 2.9 | Binomial Coefficients With Odd IndicesBijections and Double Counting | Counting | Medium | ||
| 5.5 | King Back in the CornerThe Law of Total Probability | Probability | Easy | ||
| 29.8 | Camel and BananasCrossings and Transport | Brainteasers and Pure Mathematics | Medium | ||
| 25.8 | American Versus European CallNo-Arbitrage Bounds | Finance and Derivatives | Easy | Free | |
| 27.9 | Cheryl's BirthdayDeduction Puzzles | Brainteasers and Pure Mathematics | Medium | ||
| 11.3 | Removing Matching PairsThe Coupon Collector | Expectation and Variance | Easy | ||
| 31.12 | 100 Lockers and Toggled LightsDivisibility and Primes | Brainteasers and Pure Mathematics | Easy | Free | |
| 18.4 | Brownian Exit ProbabilityHitting Times and the Reflection Principle | Random Processes | Easy | Free | |
| 30.7 | Pirates Aiming CannonsPigeonhole and Extremal Principles | Brainteasers and Pure Mathematics | Easy | ||
| 31.3 | Regular Polygons with Integer AnglesDivisibility and Primes | Brainteasers and Pure Mathematics | Easy | ||
| 26.5 | Straddle Delta via Parity+4Greeks and Their Relationships | Finance and Derivatives | Easy | Free | |
| 33.19 | Idempotent Matrix SpectrumLinear Algebra | Brainteasers and Pure Mathematics | Easy | ||
| 4.36 | Even Sum Before First SixParity and Divisibility of Random Sums | Probability | Easy | ||
| 8.7 | Geometric Mean of UniformsSums, Products and Ratios of Uniforms | Probability | Easy | ||
| 32.6 | Square as a Difference of CubesAlgebraic Tricks | Brainteasers and Pure Mathematics | Easy | ||
| 31.4 | When kk Is a SquareDivisibility and Primes | Brainteasers and Pure Mathematics | Easy | ||
| 13.13 | Nearest Neighbour on a CircleUniform Order Statistics and Spacings | Expectation and Variance | Easy | ||
| 18.10 | Variance of the Integral of WIto Integrals and the Isometry | Random Processes | Medium | ||
| 16.11 | Two Walks That Stay OrderedPaths, Reflection and First Returns | Random Processes | Hard | ||
| 10.3 | Accumulate, Cash Out or BustFair Prices from the Definition | Expectation and Variance | Easy | ||
| 10.17 | Runs in a Shuffled DeckIndicator Variables | Expectation and Variance | Easy | ||
| 12.18 | Bus Wait With Random DelaysThe Inspection Paradox | Expectation and Variance | Medium | Free | |
| 4.31 | Odd Units Digit of a ProductParity and Divisibility of Random Sums | Probability | Easy | ||
| 4.3 | Conditional Order of UniformsRelative Order of Exchangeable Values | Probability | Easy | ||
| 4.7 | Minimum Roll Before the First FiveRelative Order of Exchangeable Values | Probability | Medium | ||
| 28.7 | Guessing a Number by HalvingAdversarial Search | Brainteasers and Pure Mathematics | Easy | Free | |
| 4.20 | n+1 Coins Versus n CoinsIngenious Symmetries and Couplings | Probability | Medium | ||
| 10.21 | Adjacent Heads with Shrinking ProbabilitiesIndicator Variables | Expectation and Variance | Easy | ||
| 10.36 | Pruning a Random TreeCycles and Loops | Expectation and Variance | Medium | ||
| 10.25 | Crossings of Random ChordsIndicator Variables | Expectation and Variance | Medium | ||
| 2.10 | Weighted Hockey-Stick SumBijections and Double Counting | Counting | Medium | ||
| 14.4 | Variance of Fixed PointsVariance of Counts | Expectation and Variance | Medium | ||
| 33.9 | Fibonacci Sums in TriplesSequences, Series and Estimation | Brainteasers and Pure Mathematics | Easy | ||
| 20.6 | Bounds on Joint R-SquaredR-Squared, Data Transformations and Pitfalls | Statistics and Regression | Medium | ||
| 3.36 | Tower With Exactly Two ColoursComplements and 'At Least One' | Probability | Medium | ||
| 32.25 | Ages Hidden in Power YearsAlgebraic Tricks | Brainteasers and Pure Mathematics | Medium | ||
| 8.22 | Gladiators With Fixed StrengthsExponential Variables and Races | Probability | Hard | ||
| 33.21 | Matrix Powers by DiagonalisationLinear Algebra | Brainteasers and Pure Mathematics | Easy | ||
| 32.18 | Pascal Entries in Ratio 3:4:5Algebraic Tricks | Brainteasers and Pure Mathematics | Easy | ||
| 3.29 | Exactly One Leftward HopDice, Coins, Urns and Seats | Probability | Medium | ||
| 5.11 | Last Cherry EatenThe Law of Total Probability | Probability | Hard | ||
| 23.1 | Race to FiftyBackward Induction and Winning Positions | Games and Decisions | Easy | Free | |
| 8.2 | Ceiling of a Ratio Is a SquareSums, Products and Ratios of Uniforms | Probability | Medium | ||
| 4.5 | All Odd Faces Before Any EvenRelative Order of Exchangeable Values | Probability | Easy | ||
| 32.22 | Hundred FowlsAlgebraic Tricks | Brainteasers and Pure Mathematics | Easy | ||
| 5.6 | Chip Drawn After Even DrawsThe Law of Total Probability | Probability | Easy | ||
| 12.3 | Unequal Dice Payout GameThe Tower Property | Expectation and Variance | Medium | ||
| 3.12 | One Random Subset Inside AnotherDice, Coins, Urns and Seats | Probability | Easy | ||
| 4.23 | Fair Match Between Dice SumsIngenious Symmetries and Couplings | Probability | Medium | ||
| 7.15 | Fives Before Both a 4 and a 6Binomial and Geometric | Probability | Medium | ||
| 19.5 | German Tank ProblemEstimators | Statistics and Regression | Medium | ||
| 28.2 | Twelve Coins, Heavier or LighterWeighings | Brainteasers and Pure Mathematics | Hard | ||
| 32.40 | Ships Meeting MidwayRates, Work and Motion | Brainteasers and Pure Mathematics | Medium | ||
| 25.1 | Maximum Profit of a Covered CallPayoffs and Strategies | Finance and Derivatives | Easy | Free | |
| 14.3 | Variance of Clubs in a HandVariance of Counts | Expectation and Variance | Easy | ||
| 2.7 | Sum of All Pandigital NumbersBijections and Double Counting | Counting | Medium | ||
| 19.2 | Capture-RecaptureEstimators | Statistics and Regression | Easy | ||
| 11.2 | Replacing Red Orbs with BlueThe Coupon Collector | Expectation and Variance | Easy | ||
| 4.1 | Cards Drawn in Increasing Order+1Relative Order of Exchangeable Values | Probability | Easy | Free | |
| 7.24 | Mode of a PoissonThe Poisson Distribution | Probability | Easy | ||
| 22.6 | Stop Before a Red CardStop or Roll Again? | Games and Decisions | Medium | ||
| 4.29 | Even Sum of Random PrimesParity and Divisibility of Random Sums | Probability | Easy | ||
| 22.4 | Cash Out Before a SixStop or Roll Again? | Games and Decisions | Hard | ||
| 5.22 | Russian Roulette: Spin or NotConditioning Paradoxes | Probability | Easy | ||
| 7.12 | Maximum of Geometric CountsBinomial and Geometric | Probability | Easy | ||
| 1.1 | Boys and Girls AlternatingArrangements and Selections | Counting | Easy | Free | |
| 8.23 | Maximum of Uniforms in an Interval+2Order Statistics | Probability | Easy | Free | |
| 8.19 | Maxima of Scaled ExponentialsExponential Variables and Races | Probability | Medium | ||
| 5.9 | Most Likely Final RollThe Law of Total Probability | Probability | Medium | ||
| 7.11 | Memorylessness of the GeometricBinomial and Geometric | Probability | Easy | ||
| 3.37 | At Least One Couple PairedComplements and 'At Least One' | Probability | Medium | ||
| 10.22 | Expected Number of RecordsIndicator Variables | Expectation and Variance | Easy | ||
| 3.15 | Matching Pair From Three SocksDice, Coins, Urns and Seats | Probability | Easy | ||
| 9.14 | Coin Inside a Square+1Discs, Spheres and Darts | Probability | Easy | Free | |
| 10.13 | Digits Equal to EightIndicator Variables | Expectation and Variance | Easy | ||
| 15.6 | Noisy Relay of a MessageLong-Run Behaviour | Random Processes | Medium | ||
| 10.31 | Two Kings or a King and an AcePositions in a Shuffled Deck | Expectation and Variance | Hard | ||
| 12.16 | Normal Given the Squared RadiusConditioning on Sums and Symmetric Functions | Expectation and Variance | Easy | ||
| 8.21 | Racing Poisson Arrival CountsExponential Variables and Races | Probability | Medium | ||
| 2.3 | Shooting Targets in ColumnsBijections and Double Counting | Counting | Easy | ||
| 12.12 | Mossel's Dice ParadoxConditioning on How It Ended | Expectation and Variance | Hard | ||
| 10.15 | Couples Seated TogetherIndicator Variables | Expectation and Variance | Easy | ||
| 28.8 | Matching Keys to LocksAdversarial Search | Brainteasers and Pure Mathematics | Easy | ||
| 7.18 | Ordering Three Geometric WaitsBinomial and Geometric | Probability | Medium | ||
| 9.17 | Random Point on a SnowmanDiscs, Spheres and Darts | Probability | Easy | ||
| 30.16 | Doubling Stacks Working BackwardRecursion and Induction | Brainteasers and Pure Mathematics | Medium | ||
| 2.15 | Two Walkers Meeting on GridLattice Paths, Reflection and Catalan Numbers | Counting | Medium | ||
| 10.11 | Random Number of Ones and NinesIndicator Variables | Expectation and Variance | Medium | ||
| 5.16 | Small Dice Sum Given Two EvensConditioning Paradoxes | Probability | Easy | ||
| 8.18 | First Bid Above a ThresholdExponential Variables and Races | Probability | Easy | ||
| 1.5 | Palindromic Anagrams of MISSISSIPPIArrangements and Selections | Counting | Easy | ||
| 1.15 | Sums Bounded by an InequalityStars and Bars | Counting | Easy | ||
| 11.22 | Uniforms Summing Past TwoStopping Rules and Wald's Identity | Expectation and Variance | Hard | ||
| 4.33 | Parity of Paired ProductsParity and Divisibility of Random Sums | Probability | Easy | ||
| 8.12 | Normal Half-Plane by SymmetryThe Normal Distribution | Probability | Easy | Free | |
| 32.14 | Paying for Shared LoavesAlgebraic Tricks | Brainteasers and Pure Mathematics | Easy | ||
| 24.8 | Tangency Portfolio of Two AssetsPortfolio Variance | Finance and Derivatives | Medium | ||
| 15.4 | Proportions in an Infinite LineLong-Run Behaviour | Random Processes | Easy | Free | |
| 32.10 | Bhaskara's Swarm of BeesAlgebraic Tricks | Brainteasers and Pure Mathematics | Easy | ||
| 32.15 | Weights from Pairwise SumsAlgebraic Tricks | Brainteasers and Pure Mathematics | Easy | ||
| 3.8 | Seated in Age Order Around a TableDice, Coins, Urns and Seats | Probability | Easy | ||
| 14.26 | Mean Absolute Value of a NormalMoments and Generating Functions | Expectation and Variance | Easy | ||
| 1.22 | Codes With a Repeated DigitComplements and Inclusion-Exclusion | Counting | Medium | ||
| 16.9 | First Return to a TiePaths, Reflection and First Returns | Random Processes | Hard | ||
| 31.10 | Trailing Zeros of a FactorialDivisibility and Primes | Brainteasers and Pure Mathematics | Easy | ||
| 21.17 | Kelly Bet SizingBetting, Bidding and Market Making | Games and Decisions | Easy | ||
| 16.10 | Ruin at an Exact TimePaths, Reflection and First Returns | Random Processes | Hard | ||
| 19.6 | Error Rates of a Binomial Test+1Hypothesis Tests and Sample Sizes | Statistics and Regression | Easy | Free | |
| 32.23 | De Morgan's Square YearAlgebraic Tricks | Brainteasers and Pure Mathematics | Easy | ||
| 16.17 | Peierls Bound for PercolationWalks on Cycles and Lattices | Random Processes | Medium | ||
| 5.20 | Rolled Painted Cube Shows RedConditioning Paradoxes | Probability | Easy | ||
| 28.6 | Prisoners and the GlassEncoding and Group Testing | Brainteasers and Pure Mathematics | Medium | ||
| 11.6 | Runs of Consecutive Successes+1Waiting for Patterns | Expectation and Variance | Easy | Free | |
| 2.21 | Two Kinds of BracketsLattice Paths, Reflection and Catalan Numbers | Counting | Medium | ||
| 32.33 | Average Speed Is a Harmonic MeanRates, Work and Motion | Brainteasers and Pure Mathematics | Easy | ||
| 4.18 | Top Two Seeds Meet in the Final+2Ingenious Symmetries and Couplings | Probability | Easy | Free | |
| 9.20 | Thick Coin Landing on Its EdgeDiscs, Spheres and Darts | Probability | Medium | ||
| 26.6 | Delta as an Exercise ProbabilityGreeks and Their Relationships | Finance and Derivatives | Easy | ||
| 3.41 | Free Sundae Birthday LineComplements and 'At Least One' | Probability | Medium | ||
| 21.11 | Place or TakeKeep, Switch or Reroll Once | Games and Decisions | Hard | ||
| 32.36 | When the Clock Hands MeetRates, Work and Motion | Brainteasers and Pure Mathematics | Easy | Free | |
| 23.2 | Rook to the CornerBackward Induction and Winning Positions | Games and Decisions | Easy | ||
| 4.17 | Next Ball Given a Colour ImbalanceSymmetry in a Shuffled Deck | Probability | Medium | ||
| 1.23 | Strings Without Repeated NeighboursComplements and Inclusion-Exclusion | Counting | Medium | ||
| 5.12 | Diagnostic Test Base Rate+2Bayes' Rule and Base Rates | Probability | Easy | Free | |
| 3.11 | Max Equals Min Around ZeroDice, Coins, Urns and Seats | Probability | Easy | ||
| 9.18 | Second Dart Farther OutDiscs, Spheres and Darts | Probability | Medium | ||
| 19.7 | Type II Error of a z-TestHypothesis Tests and Sample Sizes | Statistics and Regression | Medium | ||
| 4.12 | Exchangeable Draws Without ReplacementSymmetry in a Shuffled Deck | Probability | Easy | ||
| 23.10 | Rock-Paper-Scissors Without RockMixed Strategies and Equilibria | Games and Decisions | Easy | Free | |
| 16.7 | Visits to a Level Before RuinGambler's Ruin | Random Processes | Hard | ||
| 21.5 | Choosing a Number Against a Random OneKeep, Switch or Reroll Once | Games and Decisions | Medium | ||
| 7.33 | Random Sum Is a Perfect SquareSums of Dice and Generating Functions | Probability | Hard | ||
| 10.26 | Knowing a Neighbour at a Round TableIndicator Variables | Expectation and Variance | Medium | ||
| 1.2 | No Two Evens AdjacentArrangements and Selections | Counting | Easy | ||
| 5.7 | Single Roll Against Best of TwoThe Law of Total Probability | Probability | Easy | ||
| 4.28 | Parity of Biased Bernoulli SumsParity and Divisibility of Random Sums | Probability | Medium | ||
| 32.27 | Boys and Girls Exchanging GiftsAlgebraic Tricks | Brainteasers and Pure Mathematics | Medium | ||
| 12.10 | Rolling Until the Sum Is Not SevenConditioning on How It Ended | Expectation and Variance | Easy | Free | |
| 2.2 | Staircase With Hops of Any SizeBijections and Double Counting | Counting | Easy | ||
| 23.16 | Matching Integers GameMixed Strategies and Equilibria | Games and Decisions | Medium | ||
| 27.7 | Rock-Paper-Scissors TalliesDeduction Puzzles | Brainteasers and Pure Mathematics | Easy | ||
| 2.29 | Domino Tilings of a 3×n BoardRecursions | Counting | Hard | ||
| 13.18 | Expected Chord LengthExpected Lengths and Distances | Expectation and Variance | Medium | ||
| 33.18 | Eigenvalues of a Matrix FunctionLinear Algebra | Brainteasers and Pure Mathematics | Easy | Free | |
| 1.20 | Integers Containing a ZeroComplements and Inclusion-Exclusion | Counting | Easy | Free | |
| 6.12 | Chopping Heads Off a DragonSmall Absorbing Chains | Probability | Medium | ||
| 23.18 | Noisy DuelMixed Strategies and Equilibria | Games and Decisions | Medium | ||
| 8.3 | Same Dyadic IntervalSums, Products and Ratios of Uniforms | Probability | Easy | ||
| 11.15 | Roll Until a New ValueFirst-Step Equations for Expectations | Expectation and Variance | Easy | ||
| 9.3 | Origin Between Two PointsRegions in the Unit Square | Probability | Easy | ||
| 32.43 | Doubling Lily PadsPercentages, Mixtures and Growth | Brainteasers and Pure Mathematics | Easy | ||
| 3.28 | Monochromatic Rectangles in a DodecagonDice, Coins, Urns and Seats | Probability | Medium | ||
| 7.23 | Rescaling a Poisson Time WindowThe Poisson Distribution | Probability | Easy | Free | |
| 21.10 | Guessing Card ColoursKeep, Switch or Reroll Once | Games and Decisions | Medium | ||
| 4.9 | One Random Interval Inside AnotherRelative Order of Exchangeable Values | Probability | Hard | ||
| 8.13 | Budget for Two Normal PricesThe Normal Distribution | Probability | Easy | ||
| 5.4 | Die With One Face LoweredThe Law of Total Probability | Probability | Easy | ||
| 14.14 | Limit of Halving Nested IntervalsCovariance and Correlation Calculations | Expectation and Variance | Medium | ||
| 33.4 | Maximal Spherical Zone AreaCalculus | Brainteasers and Pure Mathematics | Medium | ||
| 3.20 | Ants Moving on a TriangleDice, Coins, Urns and Seats | Probability | Easy | ||
| 1.9 | Heights Descending OutwardArrangements and Selections | Counting | Easy | ||
| 7.3 | First Flip Leads at the EndBinomial and Geometric | Probability | Medium | ||
| 17.3 | Thinned and Merged Client StreamsArrivals, Thinning and Superposition | Random Processes | Easy | ||
| 10.34 | Cycles Longer Than HalfCycles and Loops | Expectation and Variance | Medium | ||
| 4.19 | Coins Flipped Until All Heads or GoneIngenious Symmetries and Couplings | Probability | Easy | ||
| 15.1 | Two-State Chain Return TimeHitting and Return Times | Random Processes | Easy | Free | |
| 16.15 | Last Vertex Visited on a CycleWalks on Cycles and Lattices | Random Processes | Medium | ||
| 11.13 | Trapped MinerFirst-Step Equations for Expectations | Expectation and Variance | Easy | ||
| 7.16 | Tie Versus Win for Geometric WaitsBinomial and Geometric | Probability | Easy | ||
| 19.8 | Sample Size for a ProportionHypothesis Tests and Sample Sizes | Statistics and Regression | Easy | ||
| 31.31 | The Cyclic Number 142857Digit Puzzles | Brainteasers and Pure Mathematics | Easy | ||
| 11.20 | Running Sum Hits a Multiple of Six+1Stopping Rules and Wald's Identity | Expectation and Variance | Easy | Free | |
| 32.35 | Angle Between Clock HandsRates, Work and Motion | Brainteasers and Pure Mathematics | Easy | ||
| 32.8 | Infinite Nested RadicalAlgebraic Tricks | Brainteasers and Pure Mathematics | Easy | ||
| 32.46 | Repeated Dilution of WinePercentages, Mixtures and Growth | Brainteasers and Pure Mathematics | Easy | ||
| 10.10 | Replacing the Lowest CardIndicator Variables | Expectation and Variance | Easy | ||
| 3.6 | Choosing the Safest Full HouseCards and Poker Hands | Probability | Hard | ||
| 3.32 | How Many Trials for ConfidenceComplements and 'At Least One' | Probability | Easy | ||
| 32.24 | Age a Fraction of the Birth YearAlgebraic Tricks | Brainteasers and Pure Mathematics | Easy | ||
| 15.2 | Random Walk on a CubeHitting and Return Times | Random Processes | Medium | ||
| 21.16 | Accepting a Doubled BetBetting, Bidding and Market Making | Games and Decisions | Easy | ||
| 26.2 | At-the-Money Call Approximation+2Black-Scholes Rules of Thumb | Finance and Derivatives | Easy | Free | |
| 33.3 | πe Versus eπCalculus | Brainteasers and Pure Mathematics | Easy | ||
| 31.15 | Most Balanced FactorisationDivisibility and Primes | Brainteasers and Pure Mathematics | Medium | ||
| 32.21 | Coins Not Uniquely DeterminedAlgebraic Tricks | Brainteasers and Pure Mathematics | Easy | ||
| 33.1 | Derivative of (ln x)xCalculus | Brainteasers and Pure Mathematics | Easy | Free | |
| 33.22 | Solvability and RankLinear Algebra | Brainteasers and Pure Mathematics | Easy | ||
| 14.9 | Perfectly Correlated Sum and DifferenceCovariance and Correlation Calculations | Expectation and Variance | Medium | ||
| 20.1 | Reverse Regression Slope+1OLS Mechanics | Statistics and Regression | Easy | Free | |
| 23.6 | Tigers and SheepBackward Induction and Winning Positions | Games and Decisions | Medium | ||
| 9.19 | Two Points on a Square's BoundaryDiscs, Spheres and Darts | Probability | Medium | ||
| 14.24 | Mean of the Exponential MartingaleMoments and Generating Functions | Expectation and Variance | Easy | Free | |
| 3.13 | Rerolling the Same Dice ValuesDice, Coins, Urns and Seats | Probability | Easy | ||
| 3.1 | Four of a Kind and Poker Hands+5Cards and Poker Hands | Probability | Easy | Free | |
| 10.5 | St Petersburg ParadoxFair Prices from the Definition | Expectation and Variance | Easy | ||
| 2.16 | Unit-Step Sequences to a TargetLattice Paths, Reflection and Catalan Numbers | Counting | Easy | ||
| 1.6 | Anagrams With Matching EndsArrangements and Selections | Counting | Easy | ||
| 11.5 | LCM of Rolls Exceeding 2000The Coupon Collector | Expectation and Variance | Hard | ||
| 3.18 | Random Weights on a BalanceDice, Coins, Urns and Seats | Probability | Medium | ||
| 6.4 | Length of a First-to-Three RaceWhich Comes First? | Probability | Easy | ||
| 2.26 | Subsets With One Consecutive PairRecursions | Counting | Hard | ||
| 33.10 | Propagated Fibonacci ErrorSequences, Series and Estimation | Brainteasers and Pure Mathematics | Easy | ||
| 4.8 | Five Random Intervals Sharing a PointRelative Order of Exchangeable Values | Probability | Hard | ||
| 26.4 | Option Price from the GreeksBlack-Scholes Rules of Thumb | Finance and Derivatives | Easy | ||
| 21.7 | Discarding Cards Before AveragingKeep, Switch or Reroll Once | Games and Decisions | Medium | ||
| 15.5 | Doubly Stochastic ChainsLong-Run Behaviour | Random Processes | Easy | ||
| 31.19 | Remainder One Less Than DivisorModular Arithmetic | Brainteasers and Pure Mathematics | Easy | ||
| 29.2 | Burning RopesMeasuring | Brainteasers and Pure Mathematics | Easy | ||
| 18.2 | Conditioning a Brownian BridgeGaussian Structure | Random Processes | Medium | ||
| 32.30 | Nine Children and the Father's AgeAlgebraic Tricks | Brainteasers and Pure Mathematics | Medium | ||
| 23.12 | Two Below WinsMixed Strategies and Equilibria | Games and Decisions | Medium | ||
| 4.13 | Card After the First AceSymmetry in a Shuffled Deck | Probability | Medium | ||
| 31.16 | Bikes and SpokesDivisibility and Primes | Brainteasers and Pure Mathematics | Medium | ||
| 1.4 | Prime Digits With Fixed ProductArrangements and Selections | Counting | Easy | ||
| 10.14 | Expected Fixed PointsIndicator Variables | Expectation and Variance | Easy | ||
| 21.4 | Guess Higher or LowerKeep, Switch or Reroll Once | Games and Decisions | Medium | ||
| 31.30 | Smallest Number with Given Digit ProductDigit Puzzles | Brainteasers and Pure Mathematics | Easy | ||
| 32.2 | Power Sums from Sum and ProductAlgebraic Tricks | Brainteasers and Pure Mathematics | Easy | ||
| 13.11 | Last of Four Exponential BulbsUniform Order Statistics and Spacings | Expectation and Variance | Easy | ||
| 1.7 | Scheduling Repeated AppointmentsArrangements and Selections | Counting | Easy | ||
| 30.4 | Ants on a String+1Invariants and Symmetry Arguments | Brainteasers and Pure Mathematics | Easy | Free | |
| 14.7 | Decorrelating by a Regression CoefficientCovariance and Correlation Calculations | Expectation and Variance | Easy | ||
| 14.29 | Covariance of Infinite-Mean VariablesMoments and Generating Functions | Expectation and Variance | Medium | ||
| 23.11 | Distance Game on an IntervalMixed Strategies and Equilibria | Games and Decisions | Medium | ||
| 7.28 | Sum Seven With a Weighted DieSums of Dice and Generating Functions | Probability | Easy | Free | |
| 7.8 | Choosing p for Exactly Two Heads in a RowBinomial and Geometric | Probability | Medium | ||
| 3.7 | Two Birds Side by SideDice, Coins, Urns and Seats | Probability | Easy | Free | |
| 4.26 | Strength-Conserving Gladiator DuelsIngenious Symmetries and Couplings | Probability | Hard | ||
| 12.9 | Lognormal With Exponential VarianceThe Tower Property | Expectation and Variance | Medium | ||
| 4.6 | Last Queen Before Last KingRelative Order of Exchangeable Values | Probability | Medium | ||
| 7.27 | Geometric Number of BallsOccupancy | Probability | Medium | ||
| 18.8 | Variance by the Itô Isometry+2Ito Integrals and the Isometry | Random Processes | Easy | Free | |
| 9.10 | Shortest Piece of a Broken StickBroken Sticks | Probability | Medium | ||
| 2.22 | Non-Crossing Chord PairingsLattice Paths, Reflection and Catalan Numbers | Counting | Medium | ||
| 33.20 | Spectrum of Identity Plus All-OnesLinear Algebra | Brainteasers and Pure Mathematics | Easy | ||
| 26.3 | Call with Infinite MaturityBlack-Scholes Rules of Thumb | Finance and Derivatives | Medium | ||
| 7.21 | Big or Small Deck for the First AceSampling Without Replacement | Probability | Medium | ||
| 13.15 | Length of a Monotone RunRecords and Monotone Runs | Expectation and Variance | Medium | ||
| 10.28 | Elevator Stops+4Distinct Values | Expectation and Variance | Easy | Free | |
| 4.14 | Which Colour Runs Out LastSymmetry in a Shuffled Deck | Probability | Medium | ||
| 12.1 | Die Size Set by a Die+1The Tower Property | Expectation and Variance | Easy | Free | |
| 9.4 | Window Catching a Light ChangeRegions in the Unit Square | Probability | Easy | ||
| 23.13 | Choosing Coin BiasesMixed Strategies and Equilibria | Games and Decisions | Easy | ||
| 1.18 | Dice Totals by Stars and BarsStars and Bars | Counting | Easy | ||
| 8.10 | Random Quadratic With No Real RootsSums, Products and Ratios of Uniforms | Probability | Easy | ||
| 4.24 | The Airplane SeatIngenious Symmetries and Couplings | Probability | Medium | ||
| 8.24 | Median of Three UniformsOrder Statistics | Probability | Easy | ||
| 4.11 | Marked Cards Before the Joker+3Symmetry in a Shuffled Deck | Probability | Easy | Free | |
| 25.12 | Arbitrage Across an Options ChainNo-Arbitrage Bounds | Finance and Derivatives | Medium | ||
| 11.11 | Forgetful Bottles of BeerWaiting for Patterns | Expectation and Variance | Medium | ||
| 6.2 | One Total Before Another+3Which Comes First? | Probability | Easy | Free | |
| 29.11 | Double-Padlock ExchangeScheduling and Clever Constructions | Brainteasers and Pure Mathematics | Easy | ||
| 7.7 | Bear Catching Three FishBinomial and Geometric | Probability | Easy | ||
| 27.1 | One Question for Liar and Truth-TellerTruth-Tellers and Liars | Brainteasers and Pure Mathematics | Medium | Free | |
| 2.34 | Labelling a DieCounting Under Symmetry | Counting | Easy | ||
| 31.9 | Up 20% or Down 20%Divisibility and Primes | Brainteasers and Pure Mathematics | Easy | ||
| 8.15 | Wedges of the Standard Bivariate NormalThe Normal Distribution | Probability | Medium | ||
| 2.20 | Ballot ProblemLattice Paths, Reflection and Catalan Numbers | Counting | Medium | ||
| 22.5 | Drawing From a Biased UrnStop or Roll Again? | Games and Decisions | Medium | ||
| 19.3 | Monte Carlo Estimate of PiEstimators | Statistics and Regression | Easy | ||
| 31.27 | Digit Product Equal to HalfDigit Puzzles | Brainteasers and Pure Mathematics | Easy | Free | |
| 5.18 | Bertrand's BoxConditioning Paradoxes | Probability | Easy | ||
| 8.5 | Product of Two Uniforms Above a HalfSums, Products and Ratios of Uniforms | Probability | Easy | ||
| 2.17 | Reaching 4-4 in a Deuce GameLattice Paths, Reflection and Catalan Numbers | Counting | Easy | ||
| 26.10 | Delta Decay Near ExpiryHedging and Approximations | Finance and Derivatives | Medium | ||
| 10.27 | Random Plane Through an OctahedronIndicator Variables | Expectation and Variance | Medium | ||
| 21.19 | Winner's CurseBetting, Bidding and Market Making | Games and Decisions | Medium | ||
| 1.16 | Numbers With Digit Sum 9Stars and Bars | Counting | Easy | ||
| 16.16 | Expected Squared DisplacementWalks on Cycles and Lattices | Random Processes | Easy | ||
| 6.6 | Alternating Race to Two HeadsWhich Comes First? | Probability | Medium | ||
| 3.19 | Random Tic-Tac-Toe LineDice, Coins, Urns and Seats | Probability | Easy | ||
| 30.2 | Wine and Water GlassesInvariants and Symmetry Arguments | Brainteasers and Pure Mathematics | Easy | ||
| 3.31 | De Méré's Problem+1Complements and 'At Least One' | Probability | Easy | Free | |
| 9.12 | All Points in a SemicirclePoints on a Circle | Probability | Medium | ||
| 14.23 | Range of a Third CorrelationBounds on Moments and Correlations | Expectation and Variance | Medium | ||
| 32.26 | Dollars and Cents SwappedAlgebraic Tricks | Brainteasers and Pure Mathematics | Medium | ||
| 11.12 | Simulating a One-Third Event+1First-Step Equations for Expectations | Expectation and Variance | Easy | Free | |
| 29.6 | Soldiers and Two ChildrenCrossings and Transport | Brainteasers and Pure Mathematics | Medium | ||
| 17.2 | No Heads in a Poisson Number of FlipsArrivals, Thinning and Superposition | Random Processes | Easy | ||
| 21.14 | Paying for More Uniform DrawsHow Many to Buy? | Games and Decisions | Medium | ||
| 34.5 | Incircle of an Isosceles TriangleGeometry and Spatial Reasoning | Brainteasers and Pure Mathematics | Easy | ||
| 2.12 | Lines in 3D Tic-Tac-ToeBijections and Double Counting | Counting | Medium | ||
| 29.10 | Fewest Bills for Every AmountScheduling and Clever Constructions | Brainteasers and Pure Mathematics | Easy | ||
| 32.44 | Estimating Compound InterestPercentages, Mixtures and Growth | Brainteasers and Pure Mathematics | Easy | ||
| 31.5 | Smallest Square-Valued Question BankDivisibility and Primes | Brainteasers and Pure Mathematics | Easy | ||
| 1.11 | Medals With TiesArrangements and Selections | Counting | Medium | ||
| 28.5 | One Yes/No Question BoundEncoding and Group Testing | Brainteasers and Pure Mathematics | Medium | ||
| 12.2 | Peeled Die SumThe Tower Property | Expectation and Variance | Easy | ||
| 20.3 | Simpson's ParadoxR-Squared, Data Transformations and Pitfalls | Statistics and Regression | Easy | Free | |
| 32.11 | Sharing a Fixed AllowanceAlgebraic Tricks | Brainteasers and Pure Mathematics | Easy | ||
| 17.4 | Long Gaps Until the First WomanArrivals, Thinning and Superposition | Random Processes | Medium | ||
| 14.25 | Skewness of a Symmetric DensityMoments and Generating Functions | Expectation and Variance | Easy | ||
| 13.8 | Piece Marked by a DotUniform Order Statistics and Spacings | Expectation and Variance | Easy | Free | |
| 25.7 | Vanilla Put from Binary PutsStatic Replication | Finance and Derivatives | Medium | ||
| 7.13 | Flip Until a Repeat: Even LengthBinomial and Geometric | Probability | Easy | ||
| 12.8 | Uniform on a Random IntervalThe Tower Property | Expectation and Variance | Easy | ||
| 30.8 | Forcing a Heavy RowPigeonhole and Extremal Principles | Brainteasers and Pure Mathematics | Medium | ||
| 26.9 | Delta-Gamma Price EstimateHedging and Approximations | Finance and Derivatives | Easy | Free | |
| 31.14 | Factoring by Algebraic IdentityDivisibility and Primes | Brainteasers and Pure Mathematics | Medium | ||
| 34.3 | Minimum Cuts for a CubeGeometry and Spatial Reasoning | Brainteasers and Pure Mathematics | Easy | ||
| 16.5 | Huygens' Gambler's RuinGambler's Ruin | Random Processes | Medium | ||
| 2.18 | Paths Not Crossing the DiagonalLattice Paths, Reflection and Catalan Numbers | Counting | Medium | ||
| 14.10 | Correlation of Overlapping SumsCovariance and Correlation Calculations | Expectation and Variance | Easy | ||
| 31.18 | Large Powers Modulo nModular Arithmetic | Brainteasers and Pure Mathematics | Easy | ||
| 32.16 | Five Numbers from Ten Pair SumsAlgebraic Tricks | Brainteasers and Pure Mathematics | Medium | ||
| 20.5 | Rescaling the DataR-Squared, Data Transformations and Pitfalls | Statistics and Regression | Easy | ||
| 14.6 | Correlation From Standard DeviationsCovariance and Correlation Calculations | Expectation and Variance | Easy | ||
| 33.8 | Golden Ratio as a Fibonacci Limit+1Sequences, Series and Estimation | Brainteasers and Pure Mathematics | Easy | Free | |
| 20.2 | OLS as Maximum LikelihoodOLS Mechanics | Statistics and Regression | Medium | ||
| 11.18 | Turn One, Flip OneFirst-Step Equations for Expectations | Expectation and Variance | Medium | ||
| 3.10 | Dice Sum At Least ProductDice, Coins, Urns and Seats | Probability | Easy | ||
| 1.21 | Starts With 1 or Ends With 00Complements and Inclusion-Exclusion | Counting | Easy | ||
| 3.23 | Each Face Exactly Six TimesDice, Coins, Urns and Seats | Probability | Easy | ||
| 15.3 | Flipping Identity Matrix EntriesHitting and Return Times | Random Processes | Medium | ||
| 6.5 | Two Fives Before a Four and a SixWhich Comes First? | Probability | Medium | ||
| 17.1 | Covariance of Poisson CountsArrivals, Thinning and Superposition | Random Processes | Easy | Free | |
| 10.2 | Multiplier That Keeps Value ConstantFair Prices from the Definition | Expectation and Variance | Easy | ||
| 31.17 | Units Digit of a PowerModular Arithmetic | Brainteasers and Pure Mathematics | Easy | Free | |
| 2.32 | Seating Four at a Round TableCounting Under Symmetry | Counting | Easy | Free | |
| 11.16 | Turning Coins Over in PairsFirst-Step Equations for Expectations | Expectation and Variance | Easy | ||
| 3.4 | Another Pair from a Depleted DeckCards and Poker Hands | Probability | Medium | ||
| 9.16 | Point in the Lower Part of a ConeDiscs, Spheres and Darts | Probability | Easy | ||
| 4.30 | Prime Sum of Prime DiceParity and Divisibility of Random Sums | Probability | Easy | ||
| 19.4 | Beta-Binomial Posterior MeanEstimators | Statistics and Regression | Easy | ||
| 16.3 | Variance of a Hitting TimeHitting Probabilities and Times | Random Processes | Medium | ||
| 3.26 | Four Dogs in a Row at a Round TableDice, Coins, Urns and Seats | Probability | Medium | ||
| 18.3 | Brownian Orthant ProbabilityGaussian Structure | Random Processes | Medium | ||
| 22.10 | Continuous BlackjackThresholds for Continuous Draws | Games and Decisions | Hard | ||
| 29.1 | Hourglasses for Nine MinutesMeasuring | Brainteasers and Pure Mathematics | Easy | Free | |
| 26.11 | Sticky-Delta Volatility SmileHedging and Approximations | Finance and Derivatives | Medium | ||
| 30.9 | Maximum Product PartitionPigeonhole and Extremal Principles | Brainteasers and Pure Mathematics | Medium | ||
| 14.28 | Beta Parameters From MomentsMoments and Generating Functions | Expectation and Variance | Medium | ||
| 12.14 | Trapped Miner Given Door CountConditioning on How It Ended | Expectation and Variance | Medium | ||
| 14.22 | Minimum Common CorrelationBounds on Moments and Correlations | Expectation and Variance | Medium | ||
| 4.25 | Pólya's Urn Free ThrowsIngenious Symmetries and Couplings | Probability | Medium | ||
| 2.30 | Pairing Gloves With Close LabelsRecursions | Counting | Medium | ||
| 18.5 | Running Maximum Is PositiveHitting Times and the Reflection Principle | Random Processes | Medium | ||
| 8.11 | Random Cubic With a Root in (0,1)Sums, Products and Ratios of Uniforms | Probability | Medium | ||
| 13.2 | Expected Minimum of Three DiceMaxima and Minima of Dice and Cards | Expectation and Variance | Easy | ||
| 16.19 | Powers of a Product MartingaleMartingales and Optional Stopping | Random Processes | Medium | ||
| 8.6 | Density of a Product of UniformsSums, Products and Ratios of Uniforms | Probability | Medium | ||
| 30.13 | Tower of HanoiRecursion and Induction | Brainteasers and Pure Mathematics | Easy | Free | |
| 21.15 | Market on a DifferenceBetting, Bidding and Market Making | Games and Decisions | Easy | Free | |
| 2.24 | Lazy Caterer's LinesRecursions | Counting | Easy | ||
| 14.8 | Sum and Difference With Equal VariancesCovariance and Correlation Calculations | Expectation and Variance | Easy | ||
| 9.13 | Random Arcs That Avoid Each OtherPoints on a Circle | Probability | Medium | ||
| 34.2 | Ant on a CubeGeometry and Spatial Reasoning | Brainteasers and Pure Mathematics | Easy | ||
| 14.16 | Variance of a Coordinate on the SphereCovariance and Correlation Calculations | Expectation and Variance | Easy | ||
| 18.13 | Mean of the Vasicek Rate+1Mean-Reverting SDEs | Random Processes | Medium | Free | |
| 28.9 | Twenty-Five HorsesAdversarial Search | Brainteasers and Pure Mathematics | Medium | ||
| 7.25 | Fixed Points Poisson LimitThe Poisson Distribution | Probability | Easy | ||
| 3.42 | Waiting for Adjacent BirthdaysComplements and 'At Least One' | Probability | Hard | ||
| 31.28 | Ages from the Grandmother's DigitsDigit Puzzles | Brainteasers and Pure Mathematics | Easy | ||
| 3.21 | Four Chords Forming a QuadrilateralDice, Coins, Urns and Seats | Probability | Easy | ||
| 31.13 | Prime JanitorsDivisibility and Primes | Brainteasers and Pure Mathematics | Medium | ||
| 34.1 | The Degenerate Triangle GardenGeometry and Spatial Reasoning | Brainteasers and Pure Mathematics | Easy | Free | |
| 23.8 | Kayles With Ten CardsBackward Induction and Winning Positions | Games and Decisions | Hard | ||
| 12.5 | Nested Random Dice SumsThe Tower Property | Expectation and Variance | Easy | ||
| 5.19 | Painted Cube Showing Five Blank FacesConditioning Paradoxes | Probability | Medium | ||
| 13.16 | Expected Final Maximum Of Increasing RunRecords and Monotone Runs | Expectation and Variance | Hard | ||
| 7.19 | Last Green Ball on a Given Draw+1Sampling Without Replacement | Probability | Easy | Free | |
| 3.16 | Matching Colours in Two HalvesDice, Coins, Urns and Seats | Probability | Medium | ||
| 10.1 | Stopping at the First BoyFair Prices from the Definition | Expectation and Variance | Easy | Free | |
| 33.16 | Number of Digits of 100!Sequences, Series and Estimation | Brainteasers and Pure Mathematics | Medium | ||
| 6.10 | Frog Landing on kSmall Absorbing Chains | Probability | Medium | ||
| 27.2 | Hundred Self-Referential StatementsTruth-Tellers and Liars | Brainteasers and Pure Mathematics | Medium | ||
| 3.22 | Three Colours Meeting at a CornerDice, Coins, Urns and Seats | Probability | Easy | ||
| 2.6 | Digit Sum From 1 to a MillionBijections and Double Counting | Counting | Medium | ||
| 16.1 | Probability of Ever Reaching a Level+3Hitting Probabilities and Times | Random Processes | Medium | Free | |
| 14.13 | Deviation From the Sample MeanCovariance and Correlation Calculations | Expectation and Variance | Medium | ||
| 11.17 | Re-flipping Pairs of TailsFirst-Step Equations for Expectations | Expectation and Variance | Medium | ||
| 12.11 | Geometric Times Given Who Finished FirstConditioning on How It Ended | Expectation and Variance | Medium | ||
| 21.12 | Splitting Balls Between Two UrnsKeep, Switch or Reroll Once | Games and Decisions | Easy | Free | |
| 27.6 | Mislabelled Fruit BagsDeduction Puzzles | Brainteasers and Pure Mathematics | Easy | ||
| 1.24 | Dice Hitting Every TotalComplements and Inclusion-Exclusion | Counting | Hard | ||
| 14.17 | Determinant of a Random Antisymmetric MatrixCovariance and Correlation Calculations | Expectation and Variance | Easy | ||
| 30.3 | Even Row and Column SumsInvariants and Symmetry Arguments | Brainteasers and Pure Mathematics | Easy | ||
| 2.33 | Two-Colour Bracelets Up to RotationCounting Under Symmetry | Counting | Medium | ||
| 4.15 | First Colour Exhausted Among ThreeSymmetry in a Shuffled Deck | Probability | Medium | ||
| 27.3 | Finding an Honest AgentTruth-Tellers and Liars | Brainteasers and Pure Mathematics | Hard | ||
| 9.5 | Meeting Problem+1Regions in the Unit Square | Probability | Easy | Free | |
| 12.4 | Thinned Poisson EggsThe Tower Property | Expectation and Variance | Easy | ||
| 28.4 | Poisoned Wine and Binary TastersEncoding and Group Testing | Brainteasers and Pure Mathematics | Medium | ||
| 7.2 | Independent Gender EventsBinomial and Geometric | Probability | Easy | ||
| 1.19 | Two-Colour Balls in Full BowlsStars and Bars | Counting | Medium | ||
| 34.4 | Shadow of a CubeGeometry and Spatial Reasoning | Brainteasers and Pure Mathematics | Medium | ||
| 16.13 | Vertical or Horizontal Side FirstWalks on Cycles and Lattices | Random Processes | Medium | Free | |
| 10.12 | Ratio of Partial SumsIndicator Variables | Expectation and Variance | Easy | ||
| 3.3 | Probability of a StraightCards and Poker Hands | Probability | Easy | ||
| 8.17 | Exponential Race After Scaling+1Exponential Variables and Races | Probability | Easy | Free | |
| 7.10 | Recovering a Geometric ParameterBinomial and Geometric | Probability | Easy | ||
| No problems match these filters. | |||||