Citadel / Citadel Securities Interview Questions
The real Citadel / Citadel Securities quant-interview problems candidates report — probability, coding and expected value — each with a full worked solution.
Inside the Citadel / Citadel Securities interview
Citadel and Citadel Securities run a multi-strategy hedge fund and one of the world's largest market makers, and the interview reflects that breadth: fast probability and expected-value reasoning for the trading desks, real algorithmic coding for the dev and quant tracks, and the statistics, regression and machine learning the research desk lives on. This 100-problem set spans that whole range.
What they test
Three pillars carry most of the funnel: probability & expected value (dice/coin games, optimal stopping, random walks — the market-making core), algorithmic coding (classic data-structures-and-algorithms, large in the SWE and quant-dev tracks), and statistics, regression & ML (the quant-researcher core). Around them sit optimization, combinatorics, game theory, market microstructure and options.
The recurring shapes
Each pillar has a signature move. Probability/EV collapses to linearity of expectation and state machines. Coding is canonical DS&A — caches, edit distance, quickselect, union-find, sliding windows. Stats leans on omitted-variable bias, ridge/lasso, and deriving OLS; a few items reach into Glosten-Milgrom microstructure and risk-neutral option pricing.
How to approach
Match the tool to the track. On a trading screen, look for symmetry or an indicator decomposition and keep the arithmetic mental. On a coding problem, get the data structure right before you write a line. On a stats question, name the estimator and its bias. A clean one-line argument beats a page of casework everywhere.
Work the set across all three difficulties (about 21 easy, 54 medium, 25 hard) and across the pillars — the breadth is the point, because Citadel's tracks pull from all of it.
Citadel / Citadel Securities probability questions (18)
- Probability of More Heads Than Tails With Odd Flips
- Conditional Probability for Bernoulli Sum
- Poisson Errors on a Rug
- How Many Green Gloves in the Box?
- Monty Hall with an Imperfect Host
- Optimal Sequential Rank Guessing
- Two Subdecks: Race to the First Ace
- Breaking a Stick into a Triangle
- Acute Triangle from Random Points on a Circle
- Probability No One Gets Their Own Hat
- Generate Uniform 1-7 from Uniform 1-5
- Generating a Uniform Distribution over {1, 2, 3} from an Arbitrary RNG
- Probability of No Consecutive Heads in N Coin Tosses
- HTH vs HTT Pattern Race
- Second Ace vs. Two of Spades: Which Appears First?
- World Series Win Probability and Expected Length
- Probability That You Have the Bad Coin
- Posterior Probability That One Coin Is Fairer
Citadel / Citadel Securities coding questions (17)
- Number of Islands in a Grid
- Two-Sum on a Sorted Array
- Sieve of Eratosthenes: Find All Primes up to N
- Edit Distance (Levenshtein Distance)
- LRU Cache
- LFU Cache
- Median of Two Sorted Arrays
- Trapping Rain Water
- Longest Increasing Subsequence
- Trie Prefix Search Implementation
- Quickselect: Finding the K-th Smallest Element
- Streaming Median With Two Heaps
- Minimum Window Substring
- Union-Find with Path Compression and Union by Rank
- Fast-Doubling Fibonacci with Modular Arithmetic
- Largest Rectangle in Histogram
- Knuth-Morris-Pratt Pattern Search
Citadel / Citadel Securities expected value questions (15)
- Expected Value of the Maximum of Two Dice
- Expected Product of Two Dice
- Expected Fixed Points of a Random Permutation
- Fair Price of a Coin-Flipping Game
- The St. Petersburg Paradox
- Unbiased Coin from a Biased Coin
- Optimal Stopping: Three-Roll Dice Game
- Bugs on a Bar
- Coupon Collector With Unequal Types: Playing Cards
- Sharpe Ratio Selection Bias
- Expected Tosses for Consecutive Heads
- Expected Number of Flips for Consecutive Heads
- Optimal Guess to Minimize Expected Relative Error
- Expected Rolls with a Fair Die
- Umbrella Markov Chain: Expected Rainy Commutes Until Getting Wet
Citadel / Citadel Securities regression questions (9)
- Omitted Variable Bias in OLS
- Deriving the OLS Estimator
- Least Squares Solution in Linear Regression
- L1 vs. L2 Regularization
- Ridge vs. Lasso Regression
- Interpreting an OLS Regression Plot
- Recursive Least Squares Update
- Omitted Variable Bias and Suppressor Variables
- Two-Stage Least Squares with Overidentification
Citadel / Citadel Securities machine learning questions (6)
- Diagnosing Overfitting and Cross-Validation
- PCA vs. Autoencoders for Dimensionality Reduction
- K-Means Clustering From Scratch
- Gradient Boosting vs. Random Forests, Batch Normalization, and SGD Momentum
- Why L1 Regularization Produces Sparse Solutions
- L0, L1, and L2 Regularization: Sparsity and Geometry
Citadel / Citadel Securities statistics questions (6)
Citadel / Citadel Securities optimization questions (5)
Citadel / Citadel Securities combinatorics questions (5)
Citadel / Citadel Securities game theory questions (4)
Citadel / Citadel Securities random variables questions (3)
Citadel / Citadel Securities market microstructure questions (3)
Citadel / Citadel Securities options pricing questions (2)
Citadel / Citadel Securities time series questions (2)
Citadel / Citadel Securities finance questions (2)
Citadel / Citadel Securities linear algebra questions (1)
Citadel / Citadel Securities brain teasers questions (1)
Citadel / Citadel Securities stochastic processes questions (1)
Citadel / Citadel Securities interview FAQ
What kind of questions does Citadel / Citadel Securities ask in quant interviews?
Candidates most often report probability, coding and expected value questions. This page collects 100 of them, 100 stamped with the month they were last reported — each with a full worked solution.
How hard are Citadel / Citadel Securities interview questions?
The set spans 21 easy, 54 medium and 25 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 Citadel / Citadel Securities quant interview?
Work through this set by topic (use the sidebar), starting from your weakest area. 25 problems are free to open with their full solution, so you can judge the quality before anything else. Then walk the full Citadel / Citadel Securities interview guide for the round-by-round funnel and the online assessment.
Are these the actual Citadel / Citadel Securities interview questions?
They are built from candidate-reported Citadel / Citadel Securities 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. 100 of 100 carry the month they were last reported.