Jane Street Interview Questions

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?

You have two dice: one 10-sided and one 6-sided. You may guess any number between 2 and 16. If the sum of the two dice equals your guess, you win that number of dollars. What number should you guess to maximize your expected winnings?

Suppose you are standing at one-third the length of a bridge when you hear a train coming from behind. You have just enough time to run back and get off the bridge before the train reaches you, and you also have just enough time if you run forward. What is the relative speed between you and the train?

1) What is 12% of 47? 2) If I pick 2 cards from a shuffled deck (with no jokers), what is the probability that both are queens? 3) i) If I toss 4 fair coins and earn a dollar for every head, what is the expected value of this game? ii) If I can re-toss all 4 coins and must take the value from the second round, what is the expected value now? 4) How confident are you that you got 0, 1, 2, 3, or all questions correct, giving percentages? 5) If two teams play a best 4 out of 7 series, where each team has a 50% chance to win each round, what is the probability that the series lasts all 7 games?

What is one million minus one hundred eleven?

What is the result of multiplying 567 by 39?

What is the probability that if you roll two dice, the sum is greater than 7?

You roll a six-sided die and receive the amount you roll in cash. How much should you pay to play this game? What if you do not like your first roll and are allowed to roll exactly once more (but you must take what you get the last time)? What if you can roll up to three times, always keeping the last roll? What if you can roll infinitely many times?

A cube that is white on the inside is painted blue on the outside and then cut into thirds along each dimension, resulting in 27 smaller cubes. Blindfolded, I randomly pick one of the smaller cubes and toss it so it lands with one side down. I observe that all of the visible sides are white. What is the probability that the side facing down is blue?

You have a tricycle and plan to travel one thousand miles. You also have two spare tires with you. If you want each of the five tires to be worn equally by the end of the journey, what is the minimum number of stops you must make to achieve this?

It is currently 10:02. What is the angle between the hour and minute hands on a clock?

In a best-of-7 game between two players, you wish to place 50/50 bets before each point such that if player A wins the series you win £1000, and if player B wins the series you lose £1000. How can you structure your bets to achieve this outcome?

How many times does the digit '1' appear in all the numbers from 1 to 1,000,000 inclusive?

Sum all the odd numbers between 1 and 100.

Estimate the weight of Mount Kilimanjaro.

Consider a game where you roll a fair six-sided die. What is the expected value of a single roll? What is the expected value if you can roll twice and either keep the result of the first roll, or discard it and are forced to keep the second roll? How does this extend to three rolls or an infinite number of rolls?

What is the result when you subtract 12 from 1,000,000?

What is 2 to the power of 10?

If I spin a roulette wheel, roll a die, and pick a card from a 52-card deck, what is the probability that all three show the same number? How confident are you in your answer?

If you flip ten coins, what is the expected value of the product of the number of heads and the number of tails?

If you have only 5-cent and 11-cent stamps, what is the smallest amount that cannot be formed using any combination of these stamps?