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143 problems across probability, stochastic calculus, options and risk — with worked solutions and spaced-repetition review.
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| # | Problem | Topic | Asked by | Difficulty | |
|---|---|---|---|---|---|
| 01 | Screwy Pirates | Brain Teasers | Jane Street +1 | Hard | |
| 02 | Trailing Zeros in 100! | Brain Teasers | Goldman Sachs +1 | Easy | |
| 03 | Two Eggs, 100 Floors | Brain Teasers | Google +1 | Medium | |
| 04 | Horse Race — Top 3 | Brain Teasers | Google +1 | Medium | |
| 05 | Clock Hands at 3:15 | Brain Teasers | Morgan Stanley +1 | Easy | |
| 06 | Sum 1 to 100 | Brain Teasers | Jane Street +1 | Easy | |
| 07 | 100 Lockers | Brain Teasers | Google +1 | Medium | |
| 08 | Poisoned Wine | Brain Teasers | Google +1 | Medium | |
| 09 | Last Digit of 2^100 | Brain Teasers | Goldman Sachs +1 | Easy | |
| 10 | Mislabeled Jars | Brain Teasers | Jane Street +1 | Medium | |
| 11 | Burning Ropes — 45 Minutes | Brain Teasers | Goldman Sachs +1 | Medium | |
| 12 | 12 Balls, One Odd | Brain Teasers | Citadel +2 | Hard | |
| 13 | Handshakes at a Party | Brain Teasers | Goldman Sachs | Easy | |
| 14 | Bridge Crossing | Brain Teasers | Google +1 | Medium | |
| 15 | Ants on a Triangle | Brain Teasers | Goldman Sachs +1 | Medium | |
| 16 | Water Jugs | Brain Teasers | Medium | ||
| 17 | Three Switches | Brain Teasers | Goldman Sachs +1 | Medium | |
| 18 | Coin Toss — Two Heads | Probability | Jane Street | Easy | |
| 19 | Monty Hall | Probability | Goldman Sachs +1 | Easy | |
| 20 | Roll Until All Six Faces | Probability | Google +1 | Medium | |
| 21 | Birthday Problem | Probability | Goldman Sachs +1 | Medium | |
| 22 | Flips Until First Head | Probability | Optiver +1 | Easy | |
| 23 | Drunk Passenger | Probability | Jane Street +1 | Medium | |
| 24 | Two Dice Sum to 7 | Probability | Optiver +1 | Easy | |
| 25 | Bayes — Disease Test | Probability | Goldman Sachs +1 | Medium | |
| 26 | Broken Stick Triangle | Probability | Jane Street +1 | Medium | |
| 27 | Top Two Aces | Probability | SIG / Susquehanna +1 | Medium | |
| 28 | Hat Check | Probability | Jane Street +1 | Medium | |
| 29 | Two Children | Probability | Goldman Sachs +1 | Easy | |
| 30 | Expected Max of Two Dice | Probability | Optiver +1 | Medium | |
| 31 | Russian Roulette — Spin? | Probability | Jane Street +1 | Medium | |
| 32 | Expected Min of Two Dice | Probability | Optiver +1 | Medium | |
| 33 | Poisson — No Arrivals | Probability | Two Sigma +1 | Medium | |
| 34 | Exponential Survival | Probability | DE Shaw +1 | Medium | |
| 35 | Expected Rolls for a Six | Probability | Optiver +1 | Easy | |
| 36 | At Least One Six | Probability | SIG / Susquehanna +1 | Easy | |
| 37 | Expected Max of Two Uniforms | Probability | Jane Street +1 | Medium | |
| 38 | Flips Until Two Heads in a Row | Stochastic Processes | Jane Street +1 | Medium | |
| 39 | Gambler’s Ruin | Stochastic Processes | Jane Street +1 | Medium | |
| 40 | Expectation of GBM | Stochastic Processes | Goldman Sachs +1 | Hard | |
| 41 | Variance of Brownian Motion | Stochastic Processes | Goldman Sachs +1 | Easy | |
| 42 | Covariance of Brownian Motion | Stochastic Processes | Goldman Sachs +1 | Medium | |
| 43 | Expected Flips for HTH | Stochastic Processes | Jane Street +1 | Hard | |
| 44 | Random Walk Recurrence | Stochastic Processes | Two Sigma +1 | Medium | |
| 45 | Quadratic Variation of BM | Stochastic Processes | Goldman Sachs +1 | Medium | |
| 46 | Random Walk — Expected Steps | Stochastic Processes | Jane Street +1 | Hard | |
| 47 | Expected Running Max of BM | Stochastic Processes | Goldman Sachs +1 | Hard | |
| 48 | Definite Integral of x² | Calculus & Linear Algebra | Goldman Sachs | Easy | |
| 49 | Limit of sin(x)/x | Calculus & Linear Algebra | Goldman Sachs +1 | Easy | |
| 50 | Eigenvalues of a 2×2 | Calculus & Linear Algebra | Goldman Sachs +1 | Medium | |
| 51 | Gaussian Integral | Calculus & Linear Algebra | Goldman Sachs +1 | Medium | |
| 52 | Derivative of xˣ | Calculus & Linear Algebra | Jane Street +1 | Medium | |
| 53 | Maximize x^(1/x) | Calculus & Linear Algebra | Jane Street +1 | Hard | |
| 54 | Geometric Series | Calculus & Linear Algebra | Goldman Sachs | Easy | |
| 55 | Limit of (1+1/n)^n | Calculus & Linear Algebra | Goldman Sachs +1 | Easy | |
| 56 | Integral of x·e^(−x) | Calculus & Linear Algebra | Goldman Sachs +1 | Medium | |
| 57 | L'Hôpital — (eˣ−1)/x | Calculus & Linear Algebra | Goldman Sachs +1 | Easy | |
| 58 | Derivative of ln(x) | Calculus & Linear Algebra | Goldman Sachs | Easy | |
| 59 | Sum of First 10 Squares | Calculus & Linear Algebra | Jane Street +1 | Easy | |
| 60 | Trace = Sum of Eigenvalues | Calculus & Linear Algebra | Two Sigma +1 | Easy | |
| 61 | Determinant = Product of Eigenvalues | Calculus & Linear Algebra | Two Sigma +1 | Easy | |
| 62 | Integrate x·eˣ | Calculus & Linear Algebra | Goldman Sachs +1 | Medium | |
| 63 | Approximate cos(0.1) | Calculus & Linear Algebra | Jane Street +1 | Easy | |
| 64 | Two SumLeetCode | Algorithms & Numerical | Google +1 | Easy | |
| 65 | Product of Array Except SelfLeetCode | Algorithms & Numerical | Two Sigma +1 | Medium | |
| 66 | Trapping Rain WaterLeetCode | Algorithms & Numerical | Jane Street +1 | Hard | |
| 67 | Kth Largest ElementLeetCode | Algorithms & Numerical | Two Sigma +1 | Medium | |
| 68 | Sliding Window MaximumLeetCode | Algorithms & Numerical | HRT +1 | Hard | |
| 69 | Maximum Subarray (Kadane)LeetCode | Algorithms & Numerical | Two Sigma +1 | Medium | |
| 70 | Random Pick with WeightLeetCode | Algorithms & Numerical | Citadel +1 | Medium | |
| 71 | Shuffle an Array (Fisher-Yates)LeetCode | Algorithms & Numerical | Two Sigma +1 | Medium | |
| 72 | Best Time to Buy and Sell StockLeetCode | Algorithms & Numerical | Two Sigma +1 | Medium | |
| 73 | Monte Carlo — Estimate π | Algorithms & Numerical | Goldman Sachs +1 | Easy | |
| 74 | Newton’s Method for √2 | Algorithms & Numerical | Goldman Sachs +1 | Easy | |
| 75 | Rand10() from Rand7()LeetCode | Algorithms & Numerical | Jane Street +1 | Medium | |
| 76 | Coin Change (DP)LeetCode | Algorithms & Numerical | Google +1 | Medium | |
| 77 | Median of Two Sorted ArraysLeetCode | Algorithms & Numerical | Google +1 | Hard | |
| 78 | Online Stock SpanLeetCode | Algorithms & Numerical | Citadel Securities +1 | Medium | |
| 79 | Time-Based Key-Value StoreLeetCode | Algorithms & Numerical | Two Sigma +1 | Medium | |
| 80 | Best Time to Buy and Sell Stock IILeetCode | Algorithms & Numerical | Optiver +1 | Medium | |
| 81 | Gas StationLeetCode | Algorithms & Numerical | Jane Street +1 | Medium | |
| 82 | Jump GameLeetCode | Algorithms & Numerical | Google +1 | Medium | |
| 83 | Nim GameLeetCode | Algorithms & Numerical | Jane Street +1 | Easy | |
| 84 | Predict the WinnerLeetCode | Algorithms & Numerical | Jane Street +1 | Medium | |
| 85 | LRU CacheLeetCode | Algorithms & Numerical | Two Sigma +1 | Medium | |
| 86 | Longest Increasing SubsequenceLeetCode | Algorithms & Numerical | Two Sigma +1 | Medium | |
| 87 | Find Median from Data StreamLeetCode | Algorithms & Numerical | Two Sigma +1 | Hard | |
| 88 | Course ScheduleLeetCode | Algorithms & Numerical | Google +1 | Medium | |
| 89 | Number of IslandsLeetCode | Algorithms & Numerical | Google +1 | Medium | |
| 90 | Put-Call Parity | Finance | Goldman Sachs +1 | Easy | |
| 91 | Black-Scholes ATM Call | Finance | Goldman Sachs +1 | Medium | |
| 92 | Risk-Neutral Probability | Finance | Goldman Sachs +1 | Medium | |
| 93 | Zero-Coupon Bond Price | Finance | Goldman Sachs +1 | Easy | |
| 94 | Futures Fair Value | Finance | Goldman Sachs +1 | Easy | |
| 95 | Duration & Price Sensitivity | Finance | Goldman Sachs +2 | Easy | |
| 96 | Perpetuity Value | Finance | Goldman Sachs +1 | Easy | |
| 97 | Rule of 72 | Finance | Goldman Sachs +1 | Easy | |
| 98 | Gordon Growth Model | Finance | Goldman Sachs +1 | Medium | |
| 99 | Implied Forward Rate | Finance | J.P. Morgan +1 | Medium | |
| 100 | Coupon Equals Yield | Finance | Goldman Sachs +1 | Easy | |
| 101 | Current Yield | Finance | Barclays +1 | Easy | |
| 102 | Forward Price with a Dividend Yield | Finance | J.P. Morgan +1 | Medium | |
| 103 | FX Forward by Interest Parity | Finance | Goldman Sachs +1 | Medium | |
| 104 | Duration and a Rate Move | Finance | PIMCO +1 | Easy | |
| 105 | Present Value of an Annuity | Finance | Morgan Stanley +1 | Medium | |
| 106 | Real Rate of Return | Finance | PIMCO +1 | Easy | |
| 107 | Delta of an ATM Call | Options & Greeks | Optiver +1 | Easy | |
| 108 | Delta of a Forward | Options & Greeks | Optiver +1 | Easy | |
| 109 | Gamma Near Expiry | Options & Greeks | Optiver +1 | Medium | |
| 110 | Most Negative Put Delta | Options & Greeks | Goldman Sachs +1 | Easy | |
| 111 | Sign of Theta | Options & Greeks | Optiver +1 | Medium | |
| 112 | Sign & Peak of Vega | Options & Greeks | Optiver +1 | Easy | |
| 113 | Delta Hedging | Options & Greeks | Optiver +1 | Easy | |
| 114 | Early Exercise of a Call | Options & Greeks | Goldman Sachs +1 | Medium | |
| 115 | Delta of an ATM Straddle | Options & Greeks | Optiver +2 | Medium | |
| 116 | How Dear Can a Call Be? | Options & Greeks | Jane Street +1 | Easy | |
| 117 | Value of a Box Spread | Options & Greeks | Optiver +1 | Medium | |
| 118 | Find the Put from Parity | Options & Greeks | Goldman Sachs +1 | Easy | |
| 119 | Delta of a Deep ITM Call | Options & Greeks | IMC Trading +1 | Easy | |
| 120 | Worst Case with a Protective Put | Options & Greeks | Barclays +1 | Medium | |
| 121 | Straddle Breakeven | Options & Greeks | SIG / Susquehanna +1 | Easy | |
| 122 | Covered Call Max Profit | Options & Greeks | Morgan Stanley +1 | Easy | |
| 123 | Sharpe Ratio | Portfolio & Risk | Goldman Sachs +1 | Easy | |
| 124 | Two-Asset Portfolio Volatility | Portfolio & Risk | Goldman Sachs +1 | Medium | |
| 125 | Value at Risk (Normal) | Portfolio & Risk | Goldman Sachs +2 | Medium | |
| 126 | CVaR / Expected Shortfall | Portfolio & Risk | AQR Capital +1 | Medium | |
| 127 | Diversification & Sharpe | Portfolio & Risk | AQR Capital +1 | Medium | |
| 128 | Maximum Drawdown | Portfolio & Risk | Citadel +2 | Medium | |
| 129 | Kelly Criterion | Portfolio & Risk | Citadel +1 | Medium | |
| 130 | VaR Time Scaling | Portfolio & Risk | Goldman Sachs +1 | Medium | |
| 131 | Minimum-Variance Weight | Portfolio & Risk | AQR Capital +1 | Medium | |
| 132 | Portfolio Beta | Portfolio & Risk | Goldman Sachs +1 | Easy | |
| 133 | Annualizing Sharpe | Portfolio & Risk | Two Sigma +1 | Medium | |
| 134 | Correlation of X and X² | Statistics | Two Sigma +1 | Medium | |
| 135 | Variance of Uniform(0,1) | Statistics | Goldman Sachs +1 | Easy | |
| 136 | OLS Slope | Statistics | Two Sigma +1 | Easy | |
| 137 | Variance of a Sum | Statistics | Goldman Sachs +1 | Easy | |
| 138 | Central Limit Theorem | Statistics | Goldman Sachs +1 | Easy | |
| 139 | MLE of a Coin | Statistics | Two Sigma +1 | Easy | |
| 140 | Covariance of a Linear Transform | Statistics | Goldman Sachs +1 | Medium | |
| 141 | Range of Correlation | Statistics | Goldman Sachs +1 | Easy | |
| 142 | Variance of a Scaled Variable | Statistics | Goldman Sachs | Easy | |
| 143 | Variance of the Sample Mean | Statistics | Two Sigma +1 | Medium |