Jane Street Interview Questions

If January 1st, 2015 was a Monday, which day of the week would January 1st, 2025 fall on?

What is the sum of all odd integers from 1 to 50?

What is the probability of obtaining exactly 2 tails in 5 coin flips?

There are two painters: Mr. Fast can paint a room in 1 hour, and Mr. Slow needs 1 hour 15 minutes. If they work together, how long does it take them to paint one room?

How many numbers from 0 to 1000 contain at least one digit 2?

What is the weight of a bowling ball with a diameter of 12 inches, given that one with a diameter of 8 inches weighs 10 pounds?

What is the probability that in n coin tosses, the number of heads will be even?

In a best-of-7, first-to-4 competition, what is the probability that a game 7 is played?

What is the probability of getting a sum of 10 when you roll three dice?

What is the largest amount of postage that cannot be obtained using any combination of 5-cent and 11-cent stamps?

A bus has some initial number of passengers. At the first stop, three quarters of the passengers get off and 7 get on the bus. At the second stop, the same process occurs: three quarters of the passengers get off and 7 get on. At the third stop, the same thing happens again. What is the minimum number of passengers to start with?

You are waiting for a bus which takes a round trip of 10 minutes to complete (starting again when it finishes one tour). What is your expected waiting time if you arrive at a random time (uniformly from 0 to 10 minutes)? Next, consider that there is an ice cream shop somewhere on the bus route; every time the bus passes it, the driver flips a fair coin and, if heads, spends 10 minutes eating ice cream before continuing the tour. What is your expected waiting time now? How does the answer change if the coin is biased?

It is noon. The hour hand and minute hand overlap. When is the next time these two hands overlap again?

There are three coins: one with heads on both sides, one with tails on both sides, and one with heads on one side and tails on the other. You pick a coin at random and toss it, resulting in heads. What is the probability that the coin you picked has heads on both sides?

You have 25 horses and can race 5 horses at a time. How many races do you need to conduct to determine the top three fastest horses among all 25?

You are bidding on a coin with a price uniformly distributed between 0 and 100. If your bid is greater than the price, you acquire the coin and can sell it to your friend at 1.5 times the price. What bid should you make to maximize your expected profit?

You flip four coins. At least two coins show tails. What is the probability that exactly three of them are tails? Solve this mentally without writing anything down.

N points lie on a circle. You draw lines connecting all the points to each other. These lines divide the circle into a number of regions. How many regions are created? Assume the points are positioned so as to give the maximum number of regions for that N.

In the land of 10-digit numbers, what is the probability that the product of these numbers ends with five zeros?

Create a four-wide market (i.e., offer four adjacent price ranges) on the possible values of the sum of four fair six-sided dice rolls.

Calculate the sum of all odd numbers from 1 to 100.

You have 27 cubes, each with all faces painted white. You assemble them into a 3x3x3 cube and paint the exterior blue. After breaking it apart, you pick a cube and place it on the table such that the five visible faces are all white. What is the probability that the non-visible face is blue?

Given a fair 6-sided die, you roll once and observe the outcome n (where n is the number rolled). What is your expected value (EV) of the roll? If you are allowed one optional reroll (meaning you can choose to accept the first roll or reroll), what is your EV now? If you are allowed to reroll one additional time (meaning you can roll up to two times, always choosing whether to accept the current roll or reroll), what is your EV?

What is 12% of 47?

If you toss 4 coins and receive $1 for 1 head, $2 for 2 heads, $3 for 3 heads, and $4 for 4 heads, how much should you be willing to pay to play this game? If you have the option to re-toss all 4 coins after the first toss (keeping the best outcome), how much should you pay now?

If I randomly choose 6 numbers from the first 12 prime numbers, what is the probability that the sum of those six numbers is odd?

If I roll a die multiple times and can keep the value of each roll, what strategy should I use to maximize my total without exceeding 6, given that if my sum reaches 7 or more I go bust?

Today is Monday. Ten years from now, on this same date, what day of the week will it be? Explain your reasoning and state your confidence level.

Find the probability that the first two top cards you pick from a standard deck of cards are both tens.

1. How many digits are in 99 raised to the power of 20? 2. What is the expected value of rolling 20 dice with 3 sides each versus 30 dice with 2 sides each? If you were playing a game, which option would you choose, or does it not matter? What is the probability that you will win?