š
FREE Guide
ā¢
2025 Quant Firm Tier List ā
ī
Reviews
FAQ
Jobs
Login
BOOK A FREE QUANT CONSULT
Citadel
Interview Questions
List of Real Interview Questions from
Citadel
90 Questions
Updated 2026
Quant Interview Questions
90Ā
Questions
5
How can you prevent gradient instability caused by the sigmoid function?
Software Engineer Interview
45
You have r red balls and w white balls in a bag. If you keep drawing balls from the bag until only balls of a single color remain (i.e., you run out of one color), what is the probability you run out of white balls first? Express your answer in terms of r and w.
Quantitative Researcher Interview
152
Describe how the random forest algorithm works.
Quant Trading Intern Interview
151
Given a biased coin (with probability p of landing heads), what is the probability of flipping two heads (HH) in two consecutive tosses?
Quant Trading Intern Interview
150
What is the expected value of the sum when rolling two fair six-sided dice?
Quant Trading Intern Interview
149
If 0.1% of people have a certain disease, and you have a test that is correct 99% of the time, what is the probability that someone who tests positive actually has the disease?
Trading Intern Interview
148
You are tossing a fair coin. What is the expected number of tosses until you get two heads in a row?
Trading Interview
147
Explain why the volatility smile exists.
Trading Interview
146
1. Given a triangle defined by its vertices, determine whether a given point is inside the triangle. 2. Given a list of times, find the number of pairs of times that add up to 60.
Software Engineering Interview
145
Given a list of stock prices for consecutive days, determine the optimal strategy to maximize profit from buying and selling stocks. You may complete as many transactions as you like (i.e., buy and sell multiple times), but you must sell the stock before you buy again.
Quantitative Researcher (Intern) Interview
144
What is implied volatility? What is the probability distribution of X + Y, where X and Y are independent and identically distributed uniform random variables?
Quantitative Researcher (Intern) Interview
143
Two people plan to meet at a train station. Each arrives at a random time between 4:00 pm and 5:00 pm and will wait 10 minutes for the other. What is the probability that they will meet?
Quantitative Researcher Intern Interview
142
If a Binary Search Tree was implemented incorrectly, such that a number to the left of a node is not smaller as it should be, how would you detect this mistake? What is the most efficient way to identify such an error?
Software Developer Intern Interview
141
How would you solve a scheduling issue given a directed acyclic graph (DAG) of tasks and k computers? What if k is one or infinity?
Software Engineer Intern Interview
140
Find the number of pairs of indices (i, j) in an array v such that v[i] = v[j] = v[i+1] + v[i+2] + ... + v[j-1]. Design an algorithm with time complexity O(n log n).
Software Engineer Intern Interview
138
Given a vector of edges (e.g., A-B, A-C, C-D), write a function to determine if the resulting graph is a tree. If it is a tree, return its root.
Quantitative Developer Interview
139
Implement a class for the game Connect Four.
Software Engineer Intern Interview
137
Implement the k-nearest neighbor algorithm.
Quantitative Developer Interview
136
Write code to compute x raised to the power n (x^n) in O(log n) time.
Summer Intern Interview
135
What is the expected value when rolling two fair six-sided dice?
Summer Intern Interview
134
How do you implement a hash map in C#?
Senior Software Developer Interview
133
In C++ templates, in what cases is the keyword 'typename' used?
Senior Software Engineer Interview
132
In C++, would you prefer to store pointers or references in a vector? Explain your reasoning.
Senior Software Engineer Interview
131
Implement the native map function for arrays.
Senior Software Engineer Interview
130
You are given two ropes that, when lit, each burn for exactly one hour, but not necessarily at a constant rate. Which one of the following times CANNOT be measured using these ropes? a) 50 minutes b) 30 minutes c) 25 minutes d) 35 minutes.
Quantitative Trader Interview
129
Given a matrix of size N by T, where the entry at the i-th row and j-th column represents the price of buying i shares of a stock at time j, determine the minimum total cost of purchasing N shares by the end of time T.
Quantitative Trader Interview
128
What is the expected value of the cube of a fair six-sided die roll?
Quantitative Trader Interview
127
How do you generate a uniform distribution over a disk given access to two independent uniform random variables?
Quantitative Trader Interview
125
Sample points randomly from a unit sphere. If you generate independent standard normal variables X1, X2, X3 for the three coordinates and normalize by dividing by sqrt(X1^2 + X2^2 + X3^2), then (X1, X2, X3) / sqrt(X1^2 + X2^2 + X3^2) is a uniform random point on the sphere. What is the variance of each coordinate of the resulting uniform distribution on the sphere?
Quant Research Intern Interview
126
Given the numbers 1 to 1000 arranged around a circle in order, start at 1 and delete every alternate number (i.e., remove 1, then 3, then 5, and so on). Continue this process of deleting every other remaining number, wrapping around the circle as necessary, until only one number remains. Determine this final remaining number.
Quant Research Intern Interview
124
Analyze the variance of a momentum trading strategy.
Quant Research Intern Interview
123
1. Describe your past research experience related to reinforcement learning and model explainability. 2. Explain the bias-variance trade-off in random forests. 3. What is the closed-form solution to linear regression, with and without L2 regularization?
Quant Research Intern Interview
122
How do you derive the Black-Scholes formula for pricing European options?
Quant Research Intern Interview
120
You are given an array of integers, which may include both negative and positive values, and another integer S. Find three different integers in the array whose sum is closest to S. If multiple solutions exist, any is acceptable. Is there an algorithm to find the three integers in O(n^2) time?
Quantitative Research Analyst Interview
121
If you have a dataset with many features, what methods can you use to reduce its dimensionality?
Quant Research Intern Interview
119
Suppose you have three random variables. The correlation between A and B is 0.6, and the correlation between A and C is 0.8. What is the possible range of the correlation between B and C?
Quantitative Research Analyst Interview
118
How can you generate a probability of 1/4, 1/3, or 1/Ļ using only coin flips?
Quantitative Research Analyst Interview
117
How do you reverse a string using Python?
Internship Interview
116
Explain how to use a binomial tree to determine the price of a European call option.
Internship Interview
115
What is a probability density function?
Internship Interview
114
Calculate the Sharpe ratio of a 60/40 coin toss where each toss results in a gain of $1 or a loss of $1, respectively.
Internship Interview
113
Given an 8x8 chessboard, write code to calculate the number of ways to go from the top left corner to the bottom right corner, given that you can move down, up, left, and right.
Software Developer Interview
112
Write a program to schedule a stream of pizza delivery orders.
Software Engineer Interview
111
How do you reverse a linked list?
Software Engineer Interview
110
Find the number of ways to get from one corner of a grid to the opposite corner, moving only down or right at each step.
Software Engineer Interview
108
You have a worker and a gold bar. The worker will work for you for 15 days. He must have x/15 of the gold bar after the xth day of work. What is the minimum number of cuts needed to divide the gold bar so that you can pay the worker accordingly?
Software Engineer Interview
109
Implement a function to compute the nth Fibonacci number using memoization.
Software Engineer Interview
107
Write the code for a multi-reader/single-writer lock.
Software Engineer Interview
106
Given a matrix and the coordinates of the top-left and bottom-right corners, calculate the sum of the elements within the specified submatrix in (1) linear time and (2) constant time. You are allowed to preprocess the matrix.
Software Engineer Interview
105
In Python, use object-oriented design to implement a defaultdict from scratch.
Software Engineer Interview
104
Implement a hashtable data structure that handles hash collisions using probing.
Software Engineer Interview
103
Describe an algorithm for calculating the square root of x.
Software Engineer Interview
102
Given a sorted array of integers, can you find two numbers such that their sum equals a target integer?
Software Engineer Interview
101
Given a sentence containing three types of bracketsāparentheses (), square brackets [], and curly braces {}ādetermine if the brackets are properly matched and ordered.
Software Developer Interview
100
Given a set of numbers [a, b, c, d, e] and a target t, find the number of triplets from the set whose sum is less than or equal to t.
Software Engineer Interview
99
Implement a queue using a stack.
Software Engineer Interview
98
Given an array representing heights of points on a mountain and a starting position, what is the highest point that is visible from that position?
Software Engineer Interview
97
Given the head of a singly linked list, reverse the list and return the new head.
Software Engineer Interview
96
Design a financial instrument trading system. How would you ensure atomicity, consistency, and other properties in the system?
Software Engineer Interview
95
How can a deadlock occur?
Software Engineer Interview
94
Given an array representing user events, find the length of the longest contiguous subarray where the most frequent user in that subarray has the same number of events as the least frequent user in the entire event log. Write an efficient function to solve this problem.
Software Engineer Interview
93
Implement a balanced binary search tree from scratch, explain its time complexity, and optimize it to efficiently handle duplicate values.
Software Engineer Interview
92
Reverse a linked list in place.
Software Engineering Intern Interview
91
Return a minimum-length list of perfect squares whose sum equals a given value k.
Software Engineering Intern Interview
90
Given an n x n chessboard, return the minimum number of knight moves required to get from point (a, b) to point (c, d).
Software Engineering Intern Interview
89
Describe linear regression in detail.
Quant Researcher Interview
88
What is the difference between LASSO and ridge regression?
Quant Research Interview
86
If a Binary Search Tree was implemented incorrectly such that a node has a left child that is not smaller than itself, how would you detect this violation? What is the most efficient method to identify this issue?
Software Developer Intern Interview
87
There are three random variables, X, Y, and Z. The three correlations between the variables are equal, i.e., Ļ = Corr(X, Y) = Corr(Y, Z) = Corr(Z, X). What is the tightest possible bound you can give for Ļ? How about the general case for n random variables?
Quant Researcher Interview
85
Design an algorithm to randomly select people in a city such that the probability of selecting someone from a given district is proportional to the district's population size. Additionally, discuss how you would test your implementation and optimize its runtime, considering repeated calls to the selection function with an acceptable error margin.
Software Developer Intern Interview
84
How would you solve a scheduling issue given a directed acyclic graph (DAG) of tasks and k computers? What if k is one or infinity?
Software Engineer Intern Interview
82
Implement a class for the game Connect 4.
Software Engineer Intern Interview
83
Given an array v, find the number of pairs of indices (i, j) such that v[i] = v[j] = v[i+1] + v[i+2] + ... + v[j-1]. Your solution should have time complexity O(n log n).
Software Engineer Intern Interview
81
What is the probability of getting a three-of-a-kind in Texas Hold'em poker?
Trader Interview
80
What is the expected value of a fair six-sided die?
Trader Interview
79
Suppose I have two pancakes: one with both sides burnt, and one with one burnt side and one unburnt side. I randomly choose one pancake, then randomly look at one of its sides. If the side is burnt, what is the probability that I picked the pancake with both sides burnt?
Trader Interview
78
What is the probability of picking two diamonds and one card that is not a diamond from a standard deck of 52 cards?
Trader Interview
77
What is the probability of finding two consecutive ones in a randomly generated binary string of length n, where each bit is equally likely to be 0 or 1?
Trader Interview
76
How would you construct an options position that is long vega and short gamma?
Trader Interview
74
How can you detect a loop in a linked list?
Quantitative Analyst Interview
75
Write a function to traverse a binary tree without using recursion.
Intern Interview
73
Write a Python function to calculate the variance of a given list of numbers.
Quantitative Analyst Interview
72
How would you design a machine learning algorithm that uses Twitter data to generate a trading strategy?
Quantitative Analyst Interview
71
What are the assumptions of linear regression?
Quantitative Analyst Interview
70
1. You have two fair dice. What is the probability that their sum is a prime number? 2. Three people play a game where each flips a coin. The last person with a different result wins. What is the expected number of flips? 3. What is 17 multiplied by 23? 4. What is the square root of 2907 to two decimal places? 5. If the S&P moves 0.3% and AAPL's beta is 1.2, what is AAPL's expected move? 6. Write a function to find arbitrage opportunities in a currency exchange matrix. 7. Given real-time trade data, design an algorithm to detect wash trading. 8. Implement a fast moving median calculator for streaming data. 9. How would you arbitrage S&P 500 futures versus the underlying basket? 10. What happens to options prices during earnings announcements? 11. Design a mean-reversion strategy for ETF pairs trading. 12. 100 people wear either red or blue hats. Each person can see others' hats but not their own. They must all simultaneously guess their own hat color. They can plan beforehand. How do they maximize group survival?
Quantitative Analyst Interview
69
What is the expected value of a fair six-sided die?
Quantitative Analyst Interview
68
How would you run a Monte Carlo simulation in Python to predict the probability of obtaining 4 out of 6 coins as heads, without using for loops?
Quantitative Analyst Interview
67
Suppose you roll two fair six-sided dice. What is the probability that the sum of the two dice is equal to 8?
Quantitative Analyst Interview
66
Write a function to calculate Fibonacci numbers using recursion.
Quantitative Analyst Interview
64
How do you estimate the square root of 5?
Quantitative Researcher Interview
65
You have two strings, each of which takes exactly one hour to burn completely when lit at one end. The rate of burning is non-uniform and differs between the strings. Using only these two strings and a way to light them, how can you measure 45 minutes?
Quantitative Researcher Interview
63
Given that log X is normally distributed with mean 0 and variance 1, compute the expected value of X.
Quantitative Researcher Interview
62
What is the difference between Gaussian Naive Bayes (GNB) and logistic regression? Under what circumstances would you choose one over the other?
Quantitative Researcher Interview
61
How will the probability of an option ending up in the money change if the volatility of the underlying stock increases?
Quantitative Researcher Interview
60
You have two eggs and a 100-story building. If an egg is dropped from a floor below floor X, it will not break; if dropped from floor X or higher, it will always break. What strategy would you use to determine the exact value of X with the minimum number of drops in the worst-case scenario?
Quantitative Researcher Interview
59
Find the minimum value of the function f(x) = x^x for real x > 0.
Quantitative Researcher Interview
58
Write a program to output all the prime numbers smaller than a given integer N.
Quantitative Researcher Interview
57
Given an array of numbers, find three numbers such that their product is the maximum possible.
Quantitative Researcher Interview
56
Given an array of numbers: 1, 5, 3, 2, 4, 2, 3, 1, 2, 3, 2, 4, return another array where duplicate numbers are grouped in consecutive positions, maintaining the order of their first appearance. For example, the result should be: 1, 1, 5, 3, 3, 3, 2, 2, 2, 2, 4, 4.
Quantitative Researcher Interview
55
Given a series of real numbers, what is the optimal point on the real line that minimizes the sum of the distances to all these numbers? Follow-up: What is the best algorithm to calculate the median of a sequence of numbers? Follow-up 2: Design an algorithm that can update the median of a sequence as new numbers are added.
Quantitative Researcher Interview
54
What is the difference between regressing y on x and regressing x on y?
Quantitative Researcher Interview
Thank you! Your submission has been received!
Oops! Something went wrong while submitting the form.