Jane Street Interview Questions

What is eleven million minus one thousand and eleven? Calculate the answer in your head without writing it down.

What is the sum of all even numbers from 0 to 100?

You have a tricycle (with three tyres) and two spare tyres, making five tyres in total. You plan to travel 1,000 miles. a) If you want each tyre to be worn equally by the end of the journey, how many miles will each tyre travel on the ground? b) What is the minimum number of stops needed to achieve this?

You play a game with an urn containing 75 blue balls, 25 red balls, and 1 yellow ball. You earn a dollar for every red ball drawn. If you draw the yellow ball, you lose all accumulated winnings. After drawing each ball, you can choose to stop and keep your winnings or continue drawing. What should be your optimal strategy in this game?

You play a game where you roll a 100-sided die labeled with the numbers 1 to 100. After each roll, you may either accept the payout equal to the number rolled in dollars or pay $1 to roll again. You can continue to pay $1 to reroll as many times as you like until you choose to accept your current roll. What is the optimal strategy for this game, and what are your expected winnings using this strategy?

You have a lottery ticket with 10 slots. Behind each slot is an independently and uniformly distributed number between 0 and 1. Your payout is the maximum of these ten numbers. How much should you be willing to pay for the lottery ticket (i.e., what is the expected value of your payout)?

What is the value of 49 × 51?

If I flip three coins, what is the probability that at least two of them are heads?

A tosses n+1 fair coins. B tosses n fair coins. B wins if he has at least as many heads as A. What is the probability that B wins?

What is the probability of getting at least 2 heads when tossing a fair coin 4 times?

In a best-of-7 game series between two teams, A and B, you get even odds on both teams for each game. Determine how much you should bet on each game so that you win $100 if Team A wins the series and lose $100 if Team B wins the series. Specifically, how much should you bet on the first game?

You roll an n-sided die. You can accept the outcome and get paid that amount, or pay 1/n dollars to reroll. How much would you pay to play this game, and how much would you sell the game for? (Provide approximate numbers. You have five minutes to answer.)

Consider the numbers from 1 to 1,000,000. How many times does the digit '2' appear in all of these numbers?

If you extend the faces of a tetrahedron as planes infinitely in all directions, how many regions does this divide three-dimensional space into?

Two people play a game with a 20-sided die. Player A chooses a number, and then Player B chooses a number. The die is rolled, and whichever player's number the result is closer to wins, and gets paid an amount. Who should be allowed to choose their number first to maximize fairness or advantage?

An apple costs $0.33. How many apples can you buy with $1? What is the change if you buy apples with $5?

If the probability of seeing at least one car in an hour is 544/625, what is the probability of seeing no cars in a 15-minute interval?

You and your opponent each pick a number, then roll two dice. The person whose chosen number is closer to the sum of the dice wins. Would you prefer to pick your number first or second, and how would you choose your number?

Calculate the sum of the digits of all the numbers from 1 to 1,000,000.

There is a token you can purchase for $XX, which allows you to propose a bet. If you win the bet, you retain the token for future use. If you lose, you may use the token to recover half of your bet. Based on the chips both sides have on that day, how much is the token worth?

You repeatedly flip a fair coin until either the sequence HHT or HTT appears. If you can choose which combination to bet on (HHT or HTT), which should you pick and why? Calculate the probability of winning for each choice.

If you have a 6 by 6 matrix where each element is either 1 or -1, how many unique matrices are there such that the product of the elements in each row and each column is 1?

You and a friend are playing a game where a random number X between 1 and 20 is chosen, and each of you picks a different number. The person whose chosen number is closer to X wins X dollars. Should you choose to pick first, and what number should you pick if you do?

How many ways are there to partition 20 into prime numbers?

Given an unlimited supply of coins of denominations 3, 8, and 20, what is the smallest positive integer that cannot be formed as a non-negative integer combination of these numbers?

A truck at a depot starts with 2,000 apples and can carry a maximum of 1,000 apples at a time. For every mile traveled, the truck loses 1 apple. What is the maximum number of apples that can be transported across a 1,000 mile desert?

Convert 16/32 to decimal.

Given a 12-sided die, you roll the die repeatedly until the cumulative sum is odd. What value of the cumulative sum occurs with the highest probability?

What is the nearest integer to the square root of 5500?

If you roll a fair coin 10 times, what is the expected value of the product of the number of heads and the number of tails?