Jane Street Interview Questions

What is the cube root of 169381?

Choose a subset of numbers from 1 to 30 such that no two elements in the subset share a common factor (i.e., they are pairwise coprime). What is the subset with the largest possible sum?

I have a number in mind such that the product of each of its digits is 96, and no digit is 1. What are the largest and smallest numbers I could think of?

Imagine an infinite chessboard. If a knight starts from a particular square, in how many different squares can it possibly end up after 10 moves? You do not need to calculate an exact number, but instead provide a 95% confidence interval for the number of possible ending squares. Pen and paper allowed.

If the chance of rain on Saturday is 70% and on Sunday is 60%, what is the probability that it will rain at least once during the weekend?

You have 3,000 apples to transport from city A to city B, which are 1,000 miles apart. When there are apples on the truck, one apple is consumed per mile driven. Assume unlimited gasoline. What is the maximum number of apples that can be transported to city B? Given your answer is x, what market would you make on a lottery: you win $10 if your answer is correct, otherwise $0. (All calculations must be done without pen and paper.)

You play a 100-round game: in each round, you can either roll a fair 20-sided die (with outcomes 1 to 20) or 'lock in' the current face value and collect that same reward for all remaining rounds. You must roll in the first round. What is your optimal stopping or locking strategy, and what is your expected value?

You have a drawer with an infinite supply of socks in a 1:1 ratio of two colors. What is the expected number of draws needed to get a matching pair?

For an odd number of fair coin flips, what is the probability of getting an even number of heads? What about for an even number of flips? How does this probability change if some of the coins are unfair?

1. One bus leaves. At each stop, three-quarters of the people get off the bus, while seven get on. It continues this way until the end of the route. What is the minimum number of passengers at the beginning? 2. Roll two dice and multiply their results. What is the probability that the product is a perfect square?

You are playing a one-player game with two opaque boxes. At each turn, you can choose to either 'place' or 'take.' 'Place' puts $1 from a third party into one box randomly, while 'take' empties out one box randomly and the money is yours. The game consists of 100 turns, and at each turn you must either place or take. Assuming optimal play, what is the expected payoff of this game? Note: You do not know how much money you have taken until the end of the game.

If you flip a fair coin, what is the probability of getting a head? What is the probability of getting a certain number of heads if you flip two coins? How does this generalize for n coins?

What is the weight of each of five melons if their pairwise weights sum to 16, 17, 18, 19, 20, 21, 22, 24, 25, and 26?

How can you simulate the roll of a fair 15-sided die using a standard 6-sided die?

How many people do you need to have in a room before you can be certain that at least 5 of them were born in the same month?

Two teams, A and B, played football twice in independent matches. In match 1, the average number of shots by team A is greater than that of team B. In match 2, the average number of shots by team A is also greater than that of team B. Can we conclude that, when combining data from both matches, the average number of shots by team A is still greater than that of team B? If so, why? If not, provide an example.

There are 30 people, consisting of 15 couples. Everyone shakes hands with other people, except nobody shakes hands with their own partner. You are told that 29 people each shook hands with a different number of people (for example, one person shook hands with 4 people, another with 5, etc.). How many people did the 30th person shake hands with?

You roll a 6-sided die and a 10-sided die. I will pay you the sum of the numbers on the dice only if you correctly guess the sum before the roll. What number should you guess to maximize your expected payout?

What is the minimum number of people required to guarantee that there exist seven people who are born in the same month?

Find the smallest integer such that the product of its digits is 3,000,000.

Devise a strategy for playing a game where a fair 100-sided die is rolled, and you are paid the value shown on the die in pounds. Each roll of the die costs £1.

If there is a 0.3 probability it will rain on Saturday and a 0.4 probability it will rain on Sunday, what is the range of possible probabilities that it will rain on at least one day?

It rains 30% of the time on Saturday and 40% of the time on Sunday. How often does it rain on the weekend?

You flip a coin 4 times. What is the probability of getting exactly 2 heads?

I am thinking of a number that does not contain the digit 1. The product of its digits is 96. What is the smallest possible number? What is the largest?

Player 1 chooses a number, then Player 2 chooses a different number. Two dice are tossed, and whoever is closer to the outcome (the sum of the two dice) wins. Would you rather be Player 1 or Player 2? What number would you choose?