Tower Research Capital Interview Questions
The real Tower Research Capital quant-interview problems candidates report — coding, expected value and probability — each with a full worked solution.
Inside the Tower Research Capital interview
Tower Research Capital is a high-frequency proprietary trading firm whose interviews lean hard on algorithmic coding (often with a low-latency, C++/systems flavor), probability, and the quantitative math that underpins fast markets. Expect to write clean, efficient code and reason crisply about random processes.
What they test
The largest block is algorithmic coding — data structures, graph/shortest-path, streaming and online algorithms, plus a strong dose of C++ internals (lifetimes, smart pointers, object layout) reflecting the firm's low-latency engineering. Around it sit two big quantitative pillars: probability and expectation (random walks, hitting times, EV under fills), backed by a stats / regression / optimization core for signal and portfolio reasoning.
The recurring shapes
Coding rounds favor problems with a tight optimal complexity — sliding-window medians, online top-K, shortest paths with weird edge constraints. The math side keeps returning to hitting times and stopping rules on random walks, generating fair randomness from biased sources, and order-book / fill expectations. A clean closed form usually beats brute force.
How to approach
For coding, state the brute force, then argue the data structure or invariant that buys the optimal bound — and be ready to discuss memory and cache cost. For probability, set up the right conditioning or martingale before computing; for stats/regression, know the bias–variance and shrinkage trade-offs cold. Verbalize complexity and assumptions as you go.
The mix leans medium, with a meaningful hard tail and a handful of easy warm-ups to anchor the fundamentals.
Tower Research Capital coding questions (27)
- C++ Rule of Five: Buffer Lifetime, Moves, and Vector Growth
- Circular Black/White Balls (Lucas Number)
- Placement New, Alignment, and Object Pools in C++
- Shortest Path on a Grid with Alternating Move Directions
- Rolling String
- HRML Attribute Parser
- Virtual Destructors in C++
- C++: const Pointer Declarations
- Online Top-K Sum with Arbitrary Deletes
- BFS on a Grid with Alternating Obstacles
- C++ Unique Pointer with Custom Deleters
- Streaming Consecutive Failure Detection
- Reverse Polish Notation to Infix Conversion
- Shortest Path with State-Dependent Tolls
- Sliding Window Median with Efficient Deletions
- Virtual Dispatch and Object Slicing in C++
- Shortest Path with Bounded Edge Count
- Shortest Paths with Edge Weights in {0, 1, 2}
- Reservation System Overlap Detection
- Sorting a K-Sorted Array
- Capped Push Data Structure
- Streaming Top-K Sum With Updates
- Collision-Free Hash Table for a Fixed Key Set
- Search in a Sorted Matrix
- Three Sum
- Breaking shared_ptr Cycles with weak_ptr
- Largest All-Zeros Submatrix
Tower Research Capital expected value questions (16)
- Generating Arbitrary Probabilities from a Fair Coin
- Expectation of Ratio of Uniform Random Variables
- Expected Mid Change From Poisson Order Flow
- Adverse Selection: Passive Bid vs. Improved Price
- Expected Time to Reach Front of Limit Order Queue
- Optional Stopping and the Doubling Strategy
- Expected Time to First Profitable Fill
- Mean and Variance of a Clipped Normal
- Expected First Passage Time for a Biased Random Walk
- Unbiased Coin from a Biased Coin
- Expected Hitting Time on a 3x3 Grid Random Walk
- Hitting Time for Random Walk with Reflecting Boundary
- Expected Height of a Random Binary Tree
- Expected Arc Length Between Random Points on a Sphere
- Coupon Collector's Problem
- Expectation of the Ratio of Two Dice
Tower Research Capital probability questions (16)
- Betting with a Drawdown Constraint
- Russian Roulette Survival Probability
- Order Probabilities and Expectations for I.I.D. Variables
- Comparing Maxima of Two Halves of a Random Permutation
- Generating Two Independent Uniforms from One
- Probability That One Interval Contains All Others
- Birthday Problem
- Splitting One Uniform Into Two Independent Uniforms
- Symmetric Random Binary Tree
- Normal Approximation to Binomial by Hand
- Bayesian Coin Identification
- Uncorrelated but Not Independent
- Fair Outcome from an Extremely Biased Coin
- Three Coins: Bayesian Update After Two Heads
- Two Bullets in a Revolver: Conditional Survival
- Extinction Probability of a Bacterium
Tower Research Capital statistics questions (9)
- Partial Correlation Formula and Interpretation
- Ledoit-Wolf Shrinkage: Conditioning and Optimal Alpha Selection
- Time-Series Mean Reversion Test
- Testing for Heavy Tails in Index Returns
- Sequential Probability Ratio Test with Explicit Boundaries
- Bayes-Optimal Decision Rule Under a Hidden Regime
- Multiple Testing: Max of 500 Null t-Statistics
- Winsorization Impact on OLS
- Minimum Backtest Length to Reject a Sharpe Ratio of 8
Tower Research Capital regression questions (9)
- Omitted Variable Bias in a Return Factor Model
- Ridge vs OLS Bias-Variance Trade-Off
- OLS Fitted Values with a Redundant Feature
- Multicollinearity Effects and Mitigation
- R-Squared Invariance Under Transformations
- OLS with Equicorrelated Predictors
- Regression with Duplicated Data
- Range of R-Squared in Multiple Regression
- When Can R-Squared Go Negative?
Tower Research Capital optimization questions (8)
- Arbitrage in Betting Markets
- Optimal Two-Signal Trading Rule
- Kelly Criterion for Multi-Match Bet Sizing
- Shrinkage Covariance Estimator for Mean-Variance Portfolios
- Constrained Least Squares Estimation of Triangle Side Lengths
- Inventory-Averse Quoting with Quadratic Penalty
- Beta-Neutral Portfolio Variance
- Optimal Accept-Reject Threshold for Fills
Tower Research Capital stochastic processes questions (7)
- Return Probability on a Cayley Tree
- Brownian Motion, Brownian Bridge, and MCMC for Jump Processes
- Martingale Stopping Time: Optional Stopping and Expected Duration
- Coin-Flipping Robot Stationary Distribution
- Simulating Correlated Brownian Motions via Cholesky
- Brownian Motion Hitting the Positive Y-Axis
- Stationary Distribution of a Three-State Markov Chain
Tower Research Capital random variables questions (3)
Tower Research Capital market microstructure questions (2)
Tower Research Capital combinatorics questions (1)
Tower Research Capital time series questions (1)
Tower Research Capital machine learning questions (1)
Tower Research Capital interview FAQ
What kind of questions does Tower Research Capital ask in quant interviews?
Candidates most often report coding, expected value and probability questions. This page collects 100 of them, 87 stamped with the month they were last reported — each with a full worked solution.
How hard are Tower Research Capital interview questions?
The set spans 13 easy, 56 medium and 31 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 Tower Research Capital quant interview?
Work through this set by topic (use the sidebar), starting from your weakest area. 17 problems are free to open with their full solution, so you can judge the quality before anything else. Then walk the full Tower Research Capital interview guide for the round-by-round funnel and the online assessment.
Are these the actual Tower Research Capital interview questions?
They are built from candidate-reported Tower Research Capital 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. 87 of 100 carry the month they were last reported.