Hudson River Trading Interview Questions
The real Hudson River Trading quant-interview problems candidates report — expected value, probability and coding — each with a full worked solution.
Inside the Hudson River Trading interview
Hudson River Trading is a high-frequency market maker whose edge is low-latency execution, hiring algorithm developers and quants. Its interviews emphasize fast, correct algorithmic coding, sharp probability and expectation, and the statistics needed to model price behavior.
What they test
The largest blocks are expectation (20) and probability (17) — games, hitting times, conditional reasoning, and distribution puzzles — paired with a heavy algorithmic coding presence (15) where speed and correctness both matter. A real statistics core (14) covers estimators, variance, and inference, and a distinctive market-microstructure (7) and stochastic-process (5) strand ties the puzzles back to order books and price paths.
The recurring shapes
Expectation problems typically collapse to conditioning on the first event and solving a fixed point; probability rewards a clean sample space and Bayes' rule. The microstructure and stochastic-process items model fills, adverse selection, and random walks, and the coding questions favor a tight one-pass or streaming solution where the latency-conscious data structure is part of the answer.
How to approach
Get to a correct, low-latency solution fast — narrate the streaming or sliding-window invariant and the time/space complexity before coding. For probability and expectation, exploit symmetry and linearity and verify on small cases; for the statistics and microstructure questions, reason from first principles about estimators and order-flow rather than quoting formulas.
This set skews hard (51) with a medium body (41) and 15 easy warm-ups, reflecting HFT's bar on both algorithmic speed and probabilistic depth, so train coding fluency and probability together.
Hudson River Trading expected value questions (20)
- Expected Number of Chord Intersections Inside a Circle
- Expected Sum of Rolls in the Coupon Collector Problem
- Expected Crossing Handshakes in a Circle
- Expected Number of Uniforms to Exceed One
- Expected Draws to First Ace
- Expected People Passed Before Seeing Someone Taller
- Expected Steps Between Circle Intersections
- Expected Number of Color Runs in a 4-Card Sequence
- Expected Runs in a Card Deck
- Identifying the Expert Among Random Voters
- Gambler's Ruin With Poorer-Player Advantage
- Waiting Time to Patterns HTH and HHH
- Expected Same-Group Handshakes in a Circle
- Expected Sum Until Rolling a 1
- Expected Waiting Time to Beat the First Observation
- Expected Loss From Stale Quotes Under Compound Poisson Jumps
- Fourth Moment of a Normal Distribution
- Expected Hitting Time of a Birth-Death Chain
- Expected Tosses for Three Consecutive Heads
- Order Statistics of Exponential Clocks
Hudson River Trading probability questions (17)
- Gambler's Ruin on a Fair Coin
- Even vs Odd Heads and Coin Fairness
- More Heads With One Extra Coin
- Probability a Broken Stick Triangle Is Acute
- Dice Sum vs. Coin Flip Count
- Does an Even Number of Heads Indicate a Fair Coin?
- Hidden Face of a Painted Cube
- The Other Ball in the Box
- Dice Sum vs. Coin Heads: Which is More Likely?
- Probability of More Heads Than Tails With Odd Flips
- Gaussian Wedge Probability
- Posterior Update from a Trade Followed by Silence
- Probability of Y > 3X for Independent Normals
- Posterior Probability of a Double-Headed Coin
- Gaussian Half-Space Probability
- Probability of Age-Ordered Circular Seating
- Probability of a Red Top Face on a Painted Cube
Hudson River Trading coding questions (15)
- Second Largest with Minimum Comparisons
- Finding the Median of a Trillion-Element Dataset
- Sorting a K-Sorted Array
- Streaming Quantile Approximation with T-Digest
- 2D Peak Finding in a Matrix
- K Disjoint Maximum-Sum Subarrays
- K-th Smallest Element of Two Sorted Arrays
- Maximum Subarray Sum With One Deletion
- Online Mean, Variance, and Covariance with Exponential Decay
- Range Minimum Query via Sparse Table
- Weighted Interval Scheduling
- Convex Hull via Monotone Chain
- Sorting Algorithms: Speed, In-Place, and Structural Assumptions
- Hotter/Colder Guessing Game
- Rooted Forest Construction and Preorder Traversal
Hudson River Trading statistics questions (14)
- Hypothesis Test for M&M Color Identification
- MLE for Uniform Distribution
- Bayesian Coin: Posterior, Predictive, and Betting Decision
- Hypothesis Test for M&M Blue Proportion
- Hypothesis Test for M&M Color Identification
- Hill Estimator and Extreme Quantile Confidence Intervals
- Testing Whether One Strategy Has a Higher Sharpe Ratio
- Benjamini-Yekutieli FDR Control for Backtested Strategies
- Generalized Likelihood Ratio Test for a Single Change-Point
- Moving-Block Bootstrap Confidence Interval for the Median
- One-Sided CUSUM for Detecting a Mean Shift
- Sequential A/B Testing With Alpha-Spending Functions
- White's Reality Check for Data Snooping Across Multiple Strategies
- Benjamini-Hochberg Procedure for Correlated Alpha Signals
Hudson River Trading market microstructure questions (7)
- Glosten-Milgrom Zero-Profit Bid-Ask Quotes
- CARA Market Maker Optimal Quotes with Inventory Skew
- Execution Cost of Block Sale vs. Sliced Orders
- One-Period Kyle Model Equilibrium
- Two-Period Kyle Model with Asymmetric Noise Variance
- VWAP Slippage Distribution
- Detecting Informed Trading in a Prediction Market
Hudson River Trading stochastic processes questions (5)
Hudson River Trading regression questions (5)
Hudson River Trading linear algebra questions (4)
Hudson River Trading game theory questions (4)
Hudson River Trading optimization questions (4)
Hudson River Trading options pricing questions (4)
Hudson River Trading finance questions (2)
Hudson River Trading machine learning questions (2)
Hudson River Trading time series questions (2)
Hudson River Trading combinatorics questions (1)
Hudson River Trading random variables questions (1)
Hudson River Trading interview FAQ
What kind of questions does Hudson River Trading ask in quant interviews?
Candidates most often report expected value, probability and coding questions. This page collects 107 of them, 106 stamped with the month they were last reported — each with a full worked solution.
How hard are Hudson River Trading interview questions?
The set spans 15 easy, 41 medium and 51 hard problems. Most sit at medium difficulty — solvable in a few minutes with clean reasoning — with a harder tail that rewards knowing the canonical tricks.
How do I prepare for the Hudson River Trading quant interview?
Work through this set by topic (use the sidebar), starting from your weakest area. 20 problems are free to open with their full solution, so you can judge the quality before anything else. Then walk the full Hudson River Trading interview guide for the round-by-round funnel and the online assessment.
Are these the actual Hudson River Trading interview questions?
They are built from candidate-reported Hudson River Trading questions. We rewrite each prompt for clarity and author the worked solutions ourselves — we don't claim the wording is verbatim, and we never invent questions or recycle generic lists. 106 of 107 carry the month they were last reported.