Jane Street Interview Questions

Design a real-time system to process millions of trades per second. How would you ensure low latency, fault tolerance, and exactly-once processing?

If I roll two dice, what is the expected value of the product of the two faces?

Suppose we play a game with a die where we roll and sum our rolls. We can stop at any time, and the sum is our score. However, if our sum is ever a multiple of 10, our score becomes zero and our game is over. What strategy will yield the greatest expected score? What about if the target multiple is a value other than 10?

Implement the game Tetris in 30 minutes.

What is the optimal strategy for winning in rock-paper-scissors if your opponent can only choose between rock and paper?

In n coin tosses, what is the probability that the number of heads is even? Prove your result rigorously.

If it rains today, will that affect the probability that it rains tomorrow? Explain your reasoning using probability theory.

What is the sum of the first 30 even numbers?

Which of the following has the highest expected value: the square of a single die roll, the product of two dice, or the square of the median of three dice rolls?

What is the smallest number whose digits multiply to give 96?

There is a p% chance of raining on Saturday and a q% chance of raining on Sunday. What are the maximum and minimum probabilities of it raining on both days?

Two dice are rolled. What is the probability that the sum of the numbers shown is a perfect square?

Given two dice, where it is known that the first die shows a 6, what is the probability that both dice show a 6?

Three fair coins are tossed. What is the probability of getting at least two heads?

Calculate the angle between the hour and minute hands of a clock at a given time.

I'm flipping three coins. If all three are the same (all heads or all tails), then I will receive $10 and may finish the game. If not, I may choose to flip any number of the coins again. What is the expected gain from playing this game?

What is the expected value of the number of heads if you flip 4 coins and, after the initial flips, you can flip over any pair of coins that both show tails?

What is the expected waiting time to get three consecutive heads when flipping a fair coin repeatedly?

What is the final digit of 17 raised to the 17th power (17^17)?

You have a shuffled deck of 26 red and 26 black cards. You play a game by repeatedly looking at the top card and either discarding it or ending the game. At the end, if the color of the next card matches the top card, you win; otherwise, you lose. What is the optimal strategy?

Find the sum 1 + 3 + 5 + ... + 99 (the sum of all odd numbers below 100).

A grey cube of size 3x3x3 is painted red on all its edges. Then, it is split into 1x1x1 cubes. One of these small cubes is chosen uniformly at random and placed randomly on a table. What is the probability that no red edges are visible on this small cube?

What is the last digit of 17 raised to the 17th power (17^17)?

I'm thinking of an integer with no 0s or 1s. When you multiply all the digits of the number together, you get 10,000. What is the largest number I could be thinking of? What is the smallest such number?

Find the probability that a randomly chosen 3-digit number has its first digit even, its second digit odd, and its third digit different from the first two digits.

You have a number whose digits multiply to 96, and none of the digits is 1. What are the largest and smallest such numbers you can form?

Three coins are in a bag. The first coin flips heads with probability 50%, the second coin flips heads with probability 60%, and the third coin flips heads with probability 70%. I pull out a coin at random and flip it; it lands heads. If I flip this coin again, what is the probability it will land heads?

Flip a fair coin 8 times. What is the probability that the number of heads is a multiple of 3?

What is the probability of getting exactly 2 heads when tossing a fair coin five times?

What is the probability that the sum of the first eight prime numbers is odd?