Your problem set
Problems
188 problems across probability, stochastic calculus, options and risk — with worked solutions. Rate each one and star the ones you want to keep.
Solved
0/188
Mastery
0%
Sign in to track what you’ve solved, rate each problem and keep a list of the ones to revisit.
Get started free188 / 188
| # | Problem | Topic | Asked by | Acceptance | Difficulty | |
|---|---|---|---|---|---|---|
| 01 | Screwy Pirates | Brain Teasers | Jane Street +1 | 51% | Hard | |
| 02 | Trailing Zeros in 100! | Brain Teasers | Goldman Sachs +1 | 52% | Easy | |
| 03 | Two Eggs, 100 Floors | Brain Teasers | Google +1 | 31% | Medium | |
| 04 | Horse Race — Top 3 | Brain Teasers | Google +1 | 42% | Medium | |
| 05 | Clock Hands at 3:15 | Brain Teasers | Morgan Stanley +1 | 58% | Easy | |
| 06 | Sum 1 to 100 | Brain Teasers | Jane Street +1 | 72% | Easy | |
| 07 | 100 Lockers | Brain Teasers | Google +1 | 62% | Medium | |
| 08 | Poisoned Wine | Brain Teasers | Google +1 | 35% | Medium | |
| 09 | Last Digit of 2^100 | Brain Teasers | Goldman Sachs +1 | 60% | Easy | |
| 10 | Mislabeled Jars | Brain Teasers | Jane Street +1 | 59% | Medium | |
| 11 | Burning Ropes — 45 Minutes | Brain Teasers | Goldman Sachs +1 | 76% | Medium | |
| 12 | 12 Balls, One Odd | Brain Teasers | Citadel +2 | 45% | Hard | |
| 13 | Handshakes at a Party | Brain Teasers | Goldman Sachs | 67% | Easy | |
| 14 | Bridge Crossing | Brain Teasers | Google +1 | 49% | Medium | |
| 15 | Ants on a Triangle | Brain Teasers | Goldman Sachs +1 | 84% | Medium | |
| 16 | Water Jugs | Brain Teasers | 74% | Medium | ||
| 17 | Three Switches | Brain Teasers | Goldman Sachs +1 | 70% | Medium | |
| 18 | The Camel and the Bananas | Brain Teasers | Jane Street +1 | 40% | Hard | |
| 19 | The Blue-Eyed Islanders | Brain Teasers | Jane Street +1 | 40% | Hard | |
| 20 | The Mutilated Chessboard | Brain Teasers | Google +1 | 67% | Medium | |
| 21 | Coin Toss — Two Heads | Probability | Jane Street | 53% | Easy | |
| 22 | Monty Hall | Probability | Goldman Sachs +1 | 56% | Easy | |
| 23 | Roll Until All Six Faces | Probability | Google +1 | 41% | Medium | |
| 24 | Birthday Problem | Probability | Goldman Sachs +1 | 52% | Medium | |
| 25 | Flips Until First Head | Probability | Optiver +1 | 69% | Easy | |
| 26 | Drunk Passenger | Probability | Jane Street +1 | 55% | Medium | |
| 27 | Two Dice Sum to 7 | Probability | Optiver +1 | 85% | Easy | |
| 28 | Bayes — Disease Test | Probability | Goldman Sachs +1 | 55% | Medium | |
| 29 | Broken Stick Triangle | Probability | Jane Street +1 | 43% | Medium | |
| 30 | Top Two Aces | Probability | SIG / Susquehanna +1 | 63% | Medium | |
| 31 | Hat Check | Probability | Jane Street +1 | 72% | Medium | |
| 32 | Two Children | Probability | Goldman Sachs +1 | 66% | Easy | |
| 33 | Expected Max of Two Dice | Probability | Optiver +1 | 41% | Medium | |
| 34 | Russian Roulette — Spin? | Probability | Jane Street +1 | 62% | Medium | |
| 35 | Expected Min of Two Dice | Probability | Optiver +1 | 71% | Medium | |
| 36 | Poisson — No Arrivals | Probability | Two Sigma +1 | 69% | Medium | |
| 37 | Exponential Survival | Probability | DE Shaw +1 | 52% | Medium | |
| 38 | Expected Rolls for a Six | Probability | Optiver +1 | 79% | Easy | |
| 39 | At Least One Six | Probability | SIG / Susquehanna +1 | 60% | Easy | |
| 40 | Expected Max of Two Uniforms | Probability | Jane Street +1 | 51% | Medium | |
| 41 | The Tuesday Boy | Probability | Jane Street +1 | 44% | Hard | |
| 42 | The 100 Prisoners Problem | Probability | Jane Street +1 | 45% | Hard | |
| 43 | The Shorter Piece | Probability | Optiver +1 | 52% | Medium | |
| 44 | The Secretary Problem | Probability | Jane Street +1 | 44% | Medium | |
| 45 | Galileo’s Three Dice | Probability | Optiver +1 | 58% | Medium | |
| 46 | Flips Until Two Heads in a Row | Stochastic Processes | Jane Street +1 | 44% | Medium | |
| 47 | Gambler’s Ruin | Stochastic Processes | Jane Street +1 | 72% | Medium | |
| 48 | Expectation of GBM | Stochastic Processes | Goldman Sachs +1 | 59% | Hard | |
| 49 | Variance of Brownian Motion | Stochastic Processes | Goldman Sachs +1 | 69% | Easy | |
| 50 | Covariance of Brownian Motion | Stochastic Processes | Goldman Sachs +1 | 65% | Medium | |
| 51 | Expected Flips for HTH | Stochastic Processes | Jane Street +1 | 45% | Hard | |
| 52 | Random Walk Recurrence | Stochastic Processes | Two Sigma +1 | 69% | Medium | |
| 53 | Quadratic Variation of BM | Stochastic Processes | Goldman Sachs +1 | 66% | Medium | |
| 54 | Random Walk — Expected Steps | Stochastic Processes | Jane Street +1 | 57% | Hard | |
| 55 | Expected Running Max of BM | Stochastic Processes | Goldman Sachs +1 | 54% | Hard | |
| 56 | The Ballot Problem | Stochastic Processes | Jane Street +1 | 47% | Hard | |
| 57 | Hitting 3 Before 0 | Stochastic Processes | Citadel +1 | 77% | Medium | |
| 58 | Two Poisson Streams | Stochastic Processes | Jump Trading +1 | 70% | Medium | |
| 59 | How Long Until Ruin or Riches | Stochastic Processes | Optiver +1 | 57% | Medium | |
| 60 | Half-Life of Mean Reversion | Stochastic Processes | AQR Capital +1 | 64% | Medium | |
| 61 | Reflection Principle for the Maximum | Stochastic Processes | Citadel +1 | 50% | Hard | |
| 62 | Definite Integral of x² | Calculus & Linear Algebra | Goldman Sachs | 78% | Easy | |
| 63 | Limit of sin(x)/x | Calculus & Linear Algebra | Goldman Sachs +1 | 91% | Easy | |
| 64 | Eigenvalues of a 2×2 | Calculus & Linear Algebra | Goldman Sachs +1 | 80% | Medium | |
| 65 | Gaussian Integral | Calculus & Linear Algebra | Goldman Sachs +1 | 43% | Medium | |
| 66 | Derivative of xˣ | Calculus & Linear Algebra | Jane Street +1 | 83% | Medium | |
| 67 | Maximize x^(1/x) | Calculus & Linear Algebra | Jane Street +1 | 51% | Hard | |
| 68 | Geometric Series | Calculus & Linear Algebra | Goldman Sachs | 86% | Easy | |
| 69 | Limit of (1+1/n)^n | Calculus & Linear Algebra | Goldman Sachs +1 | 55% | Easy | |
| 70 | Integral of x·e^(−x) | Calculus & Linear Algebra | Goldman Sachs +1 | 74% | Medium | |
| 71 | L'Hôpital — (eˣ−1)/x | Calculus & Linear Algebra | Goldman Sachs +1 | 84% | Easy | |
| 72 | Derivative of ln(x) | Calculus & Linear Algebra | Goldman Sachs | 85% | Easy | |
| 73 | Sum of First 10 Squares | Calculus & Linear Algebra | Jane Street +1 | 87% | Easy | |
| 74 | Trace = Sum of Eigenvalues | Calculus & Linear Algebra | Two Sigma +1 | 82% | Easy | |
| 75 | Determinant = Product of Eigenvalues | Calculus & Linear Algebra | Two Sigma +1 | 71% | Easy | |
| 76 | Integrate x·eˣ | Calculus & Linear Algebra | Goldman Sachs +1 | 73% | Medium | |
| 77 | Approximate cos(0.1) | Calculus & Linear Algebra | Jane Street +1 | 84% | Easy | |
| 78 | Two SumLeetCode | Algorithms & Numerical | Google +1 | — | Easy | |
| 79 | Product of Array Except SelfLeetCode | Algorithms & Numerical | Two Sigma +1 | — | Medium | |
| 80 | Trapping Rain WaterLeetCode | Algorithms & Numerical | Jane Street +1 | — | Hard | |
| 81 | Kth Largest ElementLeetCode | Algorithms & Numerical | Two Sigma +1 | — | Medium | |
| 82 | Sliding Window MaximumLeetCode | Algorithms & Numerical | HRT +1 | — | Hard | |
| 83 | Maximum Subarray (Kadane)LeetCode | Algorithms & Numerical | Two Sigma +1 | — | Medium | |
| 84 | Random Pick with WeightLeetCode | Algorithms & Numerical | Citadel +1 | — | Medium | |
| 85 | Shuffle an Array (Fisher-Yates)LeetCode | Algorithms & Numerical | Two Sigma +1 | — | Medium | |
| 86 | Best Time to Buy and Sell StockLeetCode | Algorithms & Numerical | Two Sigma +1 | — | Medium | |
| 87 | Monte Carlo — Estimate π | Algorithms & Numerical | Goldman Sachs +1 | 65% | Easy | |
| 88 | Newton’s Method for √2 | Algorithms & Numerical | Goldman Sachs +1 | 79% | Easy | |
| 89 | Rand10() from Rand7()LeetCode | Algorithms & Numerical | Jane Street +1 | — | Medium | |
| 90 | Coin Change (DP)LeetCode | Algorithms & Numerical | Google +1 | — | Medium | |
| 91 | Median of Two Sorted ArraysLeetCode | Algorithms & Numerical | Google +1 | — | Hard | |
| 92 | Online Stock SpanLeetCode | Algorithms & Numerical | Citadel Securities +1 | — | Medium | |
| 93 | Time-Based Key-Value StoreLeetCode | Algorithms & Numerical | Two Sigma +1 | — | Medium | |
| 94 | Best Time to Buy and Sell Stock IILeetCode | Algorithms & Numerical | Optiver +1 | — | Medium | |
| 95 | Gas StationLeetCode | Algorithms & Numerical | Jane Street +1 | — | Medium | |
| 96 | Jump GameLeetCode | Algorithms & Numerical | Google +1 | — | Medium | |
| 97 | Nim GameLeetCode | Algorithms & Numerical | Jane Street +1 | — | Easy | |
| 98 | Predict the WinnerLeetCode | Algorithms & Numerical | Jane Street +1 | — | Medium | |
| 99 | LRU CacheLeetCode | Algorithms & Numerical | Two Sigma +1 | — | Medium | |
| 100 | Longest Increasing SubsequenceLeetCode | Algorithms & Numerical | Two Sigma +1 | — | Medium | |
| 101 | Find Median from Data StreamLeetCode | Algorithms & Numerical | Two Sigma +1 | — | Hard | |
| 102 | Course ScheduleLeetCode | Algorithms & Numerical | Google +1 | — | Medium | |
| 103 | Number of IslandsLeetCode | Algorithms & Numerical | Google +1 | — | Medium | |
| 104 | Put-Call Parity | Finance | Goldman Sachs +1 | 66% | Easy | |
| 105 | Black-Scholes ATM Call | Finance | Goldman Sachs +1 | 72% | Medium | |
| 106 | Risk-Neutral Probability | Finance | Goldman Sachs +1 | 81% | Medium | |
| 107 | Zero-Coupon Bond Price | Finance | Goldman Sachs +1 | 63% | Easy | |
| 108 | Futures Fair Value | Finance | Goldman Sachs +1 | 63% | Easy | |
| 109 | Duration & Price Sensitivity | Finance | Goldman Sachs +2 | 72% | Easy | |
| 110 | Perpetuity Value | Finance | Goldman Sachs +1 | 61% | Easy | |
| 111 | Rule of 72 | Finance | Goldman Sachs +1 | 71% | Easy | |
| 112 | Gordon Growth Model | Finance | Goldman Sachs +1 | 62% | Medium | |
| 113 | Implied Forward Rate | Finance | J.P. Morgan +1 | 65% | Medium | |
| 114 | Coupon Equals Yield | Finance | Goldman Sachs +1 | 64% | Easy | |
| 115 | Current Yield | Finance | Barclays +1 | 64% | Easy | |
| 116 | Forward Price with a Dividend Yield | Finance | J.P. Morgan +1 | 65% | Medium | |
| 117 | FX Forward by Interest Parity | Finance | Goldman Sachs +1 | 65% | Medium | |
| 118 | Duration and a Rate Move | Finance | PIMCO +1 | 49% | Easy | |
| 119 | Present Value of an Annuity | Finance | Morgan Stanley +1 | 56% | Medium | |
| 120 | Real Rate of Return | Finance | PIMCO +1 | 62% | Easy | |
| 121 | Delta of an ATM Call | Options & Greeks | Optiver +1 | 61% | Easy | |
| 122 | Delta of a Forward | Options & Greeks | Optiver +1 | 73% | Easy | |
| 123 | Gamma Near Expiry | Options & Greeks | Optiver +1 | 66% | Medium | |
| 124 | Most Negative Put Delta | Options & Greeks | Goldman Sachs +1 | 66% | Easy | |
| 125 | Sign of Theta | Options & Greeks | Optiver +1 | 71% | Medium | |
| 126 | Sign & Peak of Vega | Options & Greeks | Optiver +1 | 74% | Easy | |
| 127 | Delta Hedging | Options & Greeks | Optiver +1 | 76% | Easy | |
| 128 | Early Exercise of a Call | Options & Greeks | Goldman Sachs +1 | 71% | Medium | |
| 129 | Delta of an ATM Straddle | Options & Greeks | Optiver +2 | 73% | Medium | |
| 130 | How Dear Can a Call Be? | Options & Greeks | Jane Street +1 | 76% | Easy | |
| 131 | Value of a Box Spread | Options & Greeks | Optiver +1 | 69% | Medium | |
| 132 | Find the Put from Parity | Options & Greeks | Goldman Sachs +1 | 58% | Easy | |
| 133 | Delta of a Deep ITM Call | Options & Greeks | IMC Trading +1 | 74% | Easy | |
| 134 | Worst Case with a Protective Put | Options & Greeks | Barclays +1 | 69% | Medium | |
| 135 | Straddle Breakeven | Options & Greeks | SIG / Susquehanna +1 | 74% | Easy | |
| 136 | Covered Call Max Profit | Options & Greeks | Morgan Stanley +1 | 72% | Easy | |
| 137 | Make a Market on Two Dice | Market Making & Games | Optiver +1 | 87% | Easy | |
| 138 | Fair Value of a Loaded Die | Market Making & Games | Optiver +1 | 68% | Medium | |
| 139 | Roll, Keep or Re-roll | Market Making & Games | Jane Street +1 | 45% | Medium | |
| 140 | The Red–Black Card Game | Market Making & Games | Jane Street +1 | 39% | Hard | |
| 141 | Two Bookmakers, One Arbitrage | Market Making & Games | SIG / Susquehanna +1 | 55% | Medium | |
| 142 | The Bookmaker’s Edge | Market Making & Games | SIG / Susquehanna +1 | 54% | Medium | |
| 143 | Odds to Probability | Market Making & Games | Flow Traders +1 | 39% | Easy | |
| 144 | Quoting Against Informed Flow | Market Making & Games | Citadel Securities +1 | 46% | Hard | |
| 145 | Kelly with 2-to-1 Odds | Market Making & Games | SIG / Susquehanna +1 | 40% | Medium | |
| 146 | Two-Thirds of the Average | Market Making & Games | Jane Street +1 | 65% | Medium | |
| 147 | Shading a First-Price Bid | Market Making & Games | Jane Street +1 | 55% | Hard | |
| 148 | Triangular FX Arbitrage | Market Making & Games | Flow Traders +1 | 68% | Easy | |
| 149 | The St. Petersburg Game | Market Making & Games | Jane Street +1 | 62% | Medium | |
| 150 | Piano Tuners in Chicago | Market Making & Games | Optiver +1 | 65% | Easy | |
| 151 | Skewing Off an Inventory | Market Making & Games | Optiver +1 | 76% | Easy | |
| 152 | The Two-Envelope Paradox | Market Making & Games | Jane Street | 51% | Hard | |
| 153 | The House Edge in European Roulette | Market Making & Games | SIG / Susquehanna +1 | 52% | Easy | |
| 154 | The Doubling “System” | Market Making & Games | SIG / Susquehanna +1 | 59% | Medium | |
| 155 | Sharpe Ratio | Portfolio & Risk | Goldman Sachs +1 | 83% | Easy | |
| 156 | Two-Asset Portfolio Volatility | Portfolio & Risk | Goldman Sachs +1 | 44% | Medium | |
| 157 | Value at Risk (Normal) | Portfolio & Risk | Goldman Sachs +2 | 54% | Medium | |
| 158 | CVaR / Expected Shortfall | Portfolio & Risk | AQR Capital +1 | 52% | Medium | |
| 159 | Diversification & Sharpe | Portfolio & Risk | AQR Capital +1 | 52% | Medium | |
| 160 | Maximum Drawdown | Portfolio & Risk | Citadel +2 | 52% | Medium | |
| 161 | Kelly Criterion | Portfolio & Risk | Citadel +1 | 59% | Medium | |
| 162 | VaR Time Scaling | Portfolio & Risk | Goldman Sachs +1 | 52% | Medium | |
| 163 | Minimum-Variance Weight | Portfolio & Risk | AQR Capital +1 | 52% | Medium | |
| 164 | Portfolio Beta | Portfolio & Risk | Goldman Sachs +1 | 86% | Easy | |
| 165 | Annualizing Sharpe | Portfolio & Risk | Two Sigma +1 | 52% | Medium | |
| 166 | The Diversification Floor | Portfolio & Risk | BlackRock +1 | 52% | Medium | |
| 167 | Minimum-Variance Hedge Ratio | Portfolio & Risk | Goldman Sachs +1 | 52% | Medium | |
| 168 | Two-Asset Risk Parity | Portfolio & Risk | AQR Capital +1 | 52% | Medium | |
| 169 | Information Ratio | Portfolio & Risk | BlackRock +1 | 76% | Easy | |
| 170 | Beta of a Portfolio | Portfolio & Risk | J.P. Morgan +1 | 76% | Easy | |
| 171 | Sortino Ratio | Portfolio & Risk | Man Group +1 | 76% | Easy | |
| 172 | Correlation of X and X² | Statistics | Two Sigma +1 | 74% | Medium | |
| 173 | Variance of Uniform(0,1) | Statistics | Goldman Sachs +1 | 71% | Easy | |
| 174 | OLS Slope | Statistics | Two Sigma +1 | 90% | Easy | |
| 175 | Variance of a Sum | Statistics | Goldman Sachs +1 | 63% | Easy | |
| 176 | Central Limit Theorem | Statistics | Goldman Sachs +1 | 74% | Easy | |
| 177 | MLE of a Coin | Statistics | Two Sigma +1 | 85% | Easy | |
| 178 | Covariance of a Linear Transform | Statistics | Goldman Sachs +1 | 74% | Medium | |
| 179 | Range of Correlation | Statistics | Goldman Sachs +1 | 85% | Easy | |
| 180 | Variance of a Scaled Variable | Statistics | Goldman Sachs | 84% | Easy | |
| 181 | Variance of the Sample Mean | Statistics | Two Sigma +1 | 63% | Medium | |
| 182 | The German Tank Problem | Statistics | Two Sigma +1 | 69% | Medium | |
| 183 | Width of a 95% Confidence Interval | Statistics | Goldman Sachs +1 | 45% | Easy | |
| 184 | From Correlation to R² | Statistics | Two Sigma +1 | 60% | Easy | |
| 185 | Correlation of X with X + Y | Statistics | Jane Street +1 | 57% | Medium | |
| 186 | Median of an Exponential | Statistics | DE Shaw +1 | 64% | Medium | |
| 187 | A One-Sample z-Statistic | Statistics | Morgan Stanley +1 | 75% | Easy | |
| 188 | Simpson’s Paradox | Statistics | Two Sigma +1 | 69% | Medium |