D. E. Shaw Interview Questions
77 real D. E. Shaw quant questions: probability and expectation brain-teasers, regression and statistics, stochastic calculus and option pricing, and clean algorithmic coding.
Inside the D. E. Shaw interview
D. E. Shaw is one of the original systematic / quantitative hedge funds, hiring Quant Researchers and Quant Analysts. Its interviews lean hard on probability and expectation, statistics and regression, and the stochastic calculus behind pricing, with clean algorithmic coding alongside.
What they test
The single biggest block is probability and expected-value reasoning — optimal-stopping games, hitting times, loop-counting, conditional survival, and dice/coin puzzles. Sitting next to it is a substantial statistics and regression core (OLS slopes of Y on X vs X on Y, R-squared bounds, demeaning, pooling two regressions), plus a stochastic-process / option-pricing strand (Brownian martingales, Girsanov, Black-Scholes, Monte Carlo Asian options) and a steady stream of algorithmic coding (streaming statistics, sliding-window, matrix scans).
The recurring shapes
Expect to set up a recursion or condition on the first step and solve for a fixed point — many expectation problems reduce to E = 1 + (chance you must start over) × E. On the stats side they probe whether you truly understand least squares: the regression of Y on X and of X on Y share a correlation but not a slope, and their product is exactly R-squared.
How to approach
State assumptions out loud, exploit symmetry and linearity of expectation before grinding algebra, and sanity-check answers against small cases and extreme limits. For the regression and stochastic-calculus questions, derive from first principles (normal equations, risk-neutral expectation) rather than quoting formulas, and for coding problems narrate the streaming / one-pass invariant before writing it.
The mix leans medium with a solid hard tail (stochastic calculus, option pricing, game theory, and the tougher coding problems) and a handful of easy warm-ups, so build fluency across all three pillars rather than betting on one.
D. E. Shaw coding questions (25)
- Count Pairs With a Given Difference (Online Insert/Delete)
- Pairs Equal After at Most One Digit Swap
- Planting Trees: Empty Segments At Least minLength
- Largest Plus/Cross With Center at Least Every Arm
- Coin Selection Closest to a Target
- Count String Pairs Where One Is a Suffix of the Other
- FIFO Tax Calculator (Arcesium)
- Per-Minute VWAP in One Pass
- Rearrange Sequence to Avoid Adjacent Repeats
- Median of Two Sorted Arrays
- Tuple vs. List in Python
- Generate All Permutations and Combinations
- Minimum Coin Change
- Sliding Window Maximum and Minimum with Monotone Deques
- Multiset with O(1) Push and Random Pop
- Streaming Rolling 95th Percentile
- Search in a Sorted Matrix
- Second Largest with Minimum Comparisons
- Maximize an Expression by Inserting Parentheses
- Median from a Data Stream
- Largest Centered Cross in a Matrix
- Point Covered by the Most Lamp Intervals
- C++: const Pointer Declarations
- Python List vs. Hash Map: Internals and Performance
- Streaming Majority Element in O(1) Space
D. E. Shaw expected value questions (15)
- Expected Number of Passengers Who Get Their Preferred Meal
- Expected Flips for Two Consecutive Heads
- Expected Number of Loops from Random Noodle Pairing
- Optimal Stopping for Uniform Draws
- Expected Hitting Time on a 3x3 Grid Random Walk
- Expected Draws Until Uniform Sum Exceeds One
- Expected Longest Piece From Two Random Cuts
- Optimal Guess in a Dice Payout Game
- Optimal Stopping: Three-Roll Dice Game
- Expected Number of Loops from Tying Rope Ends
- Color Elimination Card Game
- Expected Flips to See Tails-Then-Heads
- Expected Distance to the Diagonal
- Tower Property of Conditional Expectation
- Expected Maximum of Two Dice
D. E. Shaw probability questions (9)
- A Coin-Flip Wager: Fairness, Heterogeneity, and Correlation
- Expected Number of Non-Dominated Students
- N Points in a Semicircle
- Dice Sum vs. Coin Flip Count
- Hidden Face of a Painted Cube
- Random Walk Survival Probability on a Grid
- Convergence in Probability vs. Almost Sure Convergence
- Two Bullets in a Revolver: Conditional Survival
- Russian Roulette Survival Probability
D. E. Shaw regression questions (8)
- OLS Regression of X on Y vs Y on X
- Pooled R-Squared from Two Separate Regressions
- Effect of Demeaning Variables in OLS
- What R-Squared Equal to One Implies
- Linear Regression: Model, Estimation, and When to Use It
- Combining R-Squared from Two Single-Variable Regressions
- OLS Slopes of Y on X vs X on Y
- R-Squared Bounds for a Joint Regression
D. E. Shaw game theory questions (4)
D. E. Shaw stochastic processes questions (4)
D. E. Shaw optimization questions (3)
D. E. Shaw statistics questions (3)
D. E. Shaw options pricing questions (3)
D. E. Shaw combinatorics questions (2)
D. E. Shaw brain teasers questions (1)
D. E. Shaw interview FAQ
What kind of questions does D. E. Shaw ask in quant interviews?
Candidates most often report coding, expected value and probability questions. This page collects 77 of them, 60 stamped with the month they were last reported — each with a full worked solution.
How hard are D. E. Shaw interview questions?
The set spans 11 easy, 49 medium and 17 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 D. E. Shaw quant interview?
Work through this set by topic (use the sidebar), starting from your weakest area. 11 problems are free to open with their full solution, so you can judge the quality before anything else. Then walk the full D. E. Shaw interview guide for the round-by-round funnel and the online assessment.
Are these the actual D. E. Shaw interview questions?
They are built from candidate-reported D. E. Shaw 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. 60 of 77 carry the month they were last reported.