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276
Even Before Odd
Probability
Difficulty
4/10
1 Part
"Suppose you roll a fair 6-sided die until you've seen all 6 faces. What is the probability you..."
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181
Race to Ace
Probability
Difficulty
5/10
1 Part
"What is the expected number of cards you need to get from a 52-card deck before you see ..."
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170
Highest Roll EV
Probability
Difficulty
5/10
1 Part
"Jim will roll a fair, six-sided die until he gets a 4. What is the expected value of the highest..."
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119
Dice Game 1
Probability
Difficulty
3/10
1 Part
"Two players take turns rolling two six-sided dice. Player A goes first, followed by player B ..."
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117
Ten Floor Building
Probability
Difficulty
4/10
1 Part
"A building has 10 floors above the basement. If 12 people get into an elevator ..."
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114
Dot Placement
Probability
Difficulty
1/10
1 Part
"You place three dots along the edges of a octagon at random. What is the probability that all ..."
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105
Portfolio Manager
Brainteaser
Difficulty
3/10
2 Parts
"You are the portfolio manager of a fund worth $75 million. Your fund has 5 possible asset classes..."
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104
First Steps
Probability
Difficulty
8/10
1 Part
"A baby is learning to walk with the assistance of its living room couch. The baby starts at the..."
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103
Conditional Die Rolls
Probability
Difficulty
4/10
3 Parts
"Dan rolls a dice until he gets a 6. Given that he did *not* see a 5, what is the expected..."
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87
Multiple of Six
Probability
Difficulty
3/10
1 Part
""You roll a fair six-sided and sum the outcomes until you reach a multiple of 6. What is the ...""
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78
Hungry Truck Driver
Brainteaser
Difficulty
5/10
1 Part
"A truck driver has been tasked with transporting 3000 apples between towns A and B, ..."
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76
Spherical Coordinate Variance
Statistics
Difficulty
6/10
1 Part
" Randomly chose a coordinate (x, y, z) on the unit sphere. What is the variance of the z-coordinate?"
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69
Painted Cube
Brainteaser
Difficulty
2/10
1 Part
"You have a 10 by 10 by 10 cube made out of individual unpainted unit cubes. If you dip the ..."
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69
Digit Sum of 19
Discrete Math
Difficulty
7/10
1 Part
"How many positive integers are there under 1 million..."
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68
Ascending Dice Rolls
Probability
Difficulty
2/10
1 Part
"You throw three fair dice consecutively. What is the probability that you obtain three numbers in..."
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67
Three Rings
Probability
Difficulty
5/10
2 Parts
"You are shooting arrows at a target with three rings: there is a circle with a 4 inch ..."
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66
King of Hearts
Probability
Difficulty
5/10
1 Part
"You take a standard shuffled deck of cards and keep flipping them over until the first ..."
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65
Burning Ropes
Brainteaser
Difficulty
4/10
1 Part
"You have two ropes. Each rope will take exactly 1 hour to burn all the way through. The densities..."
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60
Fruit Basket
Probability
Difficulty
5/10
1 Part
"You have a basket with an assortment of fruits. Inside this basket, there are 10 apples, 20 ..."
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58
Ten Topping Sundae
Brainteaser
Difficulty
1/10
1 Part
"At an ice cream parlor you are presented with 10 toppings to choose from. How many different ..."
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54
Biased Coin Sequence
Probability
Difficulty
5/10
1 Part
"You are given a coin with probability 2/3 to land on heads and 1/3 to land on tails..."
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54
How Many Heads
Probability
Difficulty
5/10
1 Part
"There are three coins in a hat. One with probability 1/3 of getting heads..."
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50
Four of a Kind
Probability
Difficulty
2/10
1 Part
"What is the probability of drawing a 4 of a kind from a standard 5-card hand?"
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50
3 Die Minimum
Statistics
Difficulty
9/10
1 Part
"Suppose you roll three fair 100-sided die. What is the expected value of the lowest roll?"
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49
Three Sticks
Probability
Difficulty
5/10
1 Part
"Assume you are given a stick that is 1 meter in length. Randomly select 2 points on the stick and..."
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49
Drinking Dan
Brainteaser
Difficulty
1/10
1 Part
"Dan has 2 glasses. The first glass was 3/4 full of water while the second was empty. He then ..."
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48
Consecutive Heads
Probability
Difficulty
5/10
1 Part
"You have a fair coin. Denote Xi as the number of flips required to see exactly i heads"
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48
More Heads
Probability
Difficulty
8/10
1 Part
"Alice and Bob each have a coin and flip it until they get a heads. If Bob flipped his coin more..."
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44
30-20 Game
Probability
Difficulty
5/10
2 Parts
"Two players, Philip and Brandon, have a 30-side and 20-side dice, respectively..."
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44
Expected Value of Highest Die
Probability
Difficulty
2/10
1 Part
"You roll two dice and select the one with the highest roll. What is the expected value of the die..."
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41
Grid Fill
Brainteaser
Difficulty
2/10
1 Part
"You are given a 3 by 3 grid upon which the numbers 1 through 9 are placed. Each number can only..."
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41
Will It Stand
Probability
Difficulty
7/10
1 Part
"Three legs are positioned uniformly and independently on the perimeter of a circular table. What..."
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39
Exactly 6
Probability
Difficulty
3/10
1 Part
"If I roll a die 36 times, what is the probability that each number appears exactly 6 times?"
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39
Inconsistent Bakers
Statistics
Difficulty
2/10
1 Part
"A donut shop has 25 different bakers, each of whom bake donuts. Each baker's output is..."
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39
Even Flips
Probability
Difficulty
5/10
1 Part
"Paul flips a fair coin until he obtains two consecutive heads or tails for the first time. Find..."
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38
First to 50
Brainteaser
Difficulty
3/10
1 Part
"Bob and Jill are playing a competitive game in which they take turns calling out numbers. The..."
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38
Four Integers
Discrete Math
Difficulty
2/10
1 Part
"We have 4 positive integers A, B, C, and D. We know AB = 16, BC = 14, and CD = 63. What is ..."
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36
Samuel Flips
Probability
Difficulty
2/10
1 Part
"Samuel flips a fair coin until he lands a tails. By playing this game, Samuel receives a minimum..."
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36
Complete Sets
Probability
Difficulty
4/10
1 Part
"There are 5 distinct sets with 3 blocks each. Six blocks are removed at random. Compute the..."
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34
Pirate Loot
Brainteaser
Difficulty
2/10
1 Part
"5 pirates have looted 100 coins from a tropical island. They must vote on how to divide these ..."
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33
Last to Discard
Brainteaser
Difficulty
5/10
1 Part
"Alice and Bob start a game with a stack of n cards. Let n be chosen by rolling a fair..."
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32
Royal Card Game
Probability
Difficulty
3/10
1 Part
"I give you a shuffled deck of $14$ cards which contain exactly one card from each rank and a Joker.."
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31
The Lucky Door
Probability
Difficulty
3/10
3 Parts
"You're on a gameshow and are tasked to choose the lucky door. Behind 1 door is $10,000. The ..."
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31
Dice Game 2
Probability
Difficulty
5/10
1 Part
"We play a game with two tetrahedral dice, red and blue, each with faces labeled 1-4 In each turn ..."
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31
Mystery Bills
Brainteaser
Difficulty
5/10
1 Part
"You and your friend each have a $100 bill. They could be real or fake with some unknown..."
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31
Odd Flips
Probability
Difficulty
3/10
1 Part
"Suppose you flip a fair coin 1"
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29
Straight Shooter
Probability
Difficulty
2/10
1 Part
"If we define a straight to be 5 cards with consecutive rank, not all sharing the same suit..."
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29
Gone Fishing
Probability
Difficulty
3/10
1 Part
"A bear wants to catch 3 fish from a river. when he has caught $3$ fish, he'll leave. When a fish..."
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29
Expected Couples
Probability
Difficulty
3/10
1 Part
"Eight people from four married couples are randomly assigned to seats around a round table..."
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28
Number of Runs
Statistics
Difficulty
5/10
2 Parts
"Imagine you are given a standard deck of 52 cards (half of the cards are red and the other half..."
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28
Same Birthday
Probability
Difficulty
2/10
2 Parts
"If you have 365 people in a room, what is the likelihood that at least 2 of them have ..."
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28
King Cake
Brainteaser
Difficulty
2/10
1 Part
"A king wants to hold a festival, for which he has 10 royal cakes. It is brought to his attention ..."
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28
2D Grid Game II
Discrete Math
Difficulty
4/10
1 Part
"As an extension of 2D Grid Game, this problem introduces a twist where we have power ups to get"
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27
Dice Game 3
Probability
Difficulty
3/10
1 Part
"You are offered a game where you roll 2 fair 6-sided die and add the sum to your total earnings..."
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27
Scattered Coins
Brainteaser
Difficulty
3/10
1 Part
"You are standing in a room in which the floor is scattered with 1000 coins. Out of those coins..."
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27
Normal Distributions
Probability
Difficulty
3/10
1 Part
"Consider that X and Y are independent standard normal random variables. What is the P[Y>4X]?"
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26
Lucky Bubble
Probability
Difficulty
3/10
1 Part
"Steven received an array of size n filled with a random permutation of the numbers..."
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26
Good Grid
Probability
Difficulty
1/10
1 Part
"Suppose that two integers a and b are uniformly at random selected from..."
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25
Sequential Pairs
Probability
Difficulty
2/10
1 Part
"Sam has a standard 52 deck of cards. He pulls two cards and they happen to share the same rank..."
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25
Deconstructed Rubik's Cube
Probability
Difficulty
3/10
1 Part
"You have a standard Rubik's Cube and you break it apart into 27 cubes. You put those 27..."
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24
Repeated Rolling
Statistics
Difficulty
3/10
3 Parts
"Suppose a game has you roll a fair six-sided die repeatedly, until you first encounter a number..."
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24
Heaviest Coin
Brainteaser
Difficulty
2/10
1 Part
"You are given 9 coins and one old-fashioned balance scale. All coins weigh the same, except ..."
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24
Grand Slam Tournament
Probability
Difficulty
3/10
1 Part
"In Wimbledon, 128 players with a distinct ranking compete to win a Grand Slam tennis title. Assume.."
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24
Find the Variance
Statistics
Difficulty
2/10
1 Part
"What is the variance of a uniform random variable X with probability density function ..."
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24
Dice Games EV
Probability
Difficulty
4/10
2 Parts
"You are playing a game where two players each roll two dice. If any one die matches the other ..."
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23
Optionality
Finance
Difficulty
2/10
1 Part
"Please complete the following sentences If the close price of ABC at expiration is $20, a $19.50..."
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23
Safe Codes
Discrete Math
Difficulty
3/10
1 Part
"An electronic safe has a three digit code. You are given two hints regarding the code to the..."
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23
Growing Lily Pad
Brainteaser
Difficulty
2/10
1 Part
"There is a single lily pad floating in a pond. Everyday, the lily pad doubles in area until it..."
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22
Hourglass Timing
Brainteaser
Difficulty
2/10
1 Part
"Given a 4-minute and 7-minute hourglass, how would you measure exactly 9 minutes?"
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22
Orb Draws
Probability
Difficulty
3/10
1 Part
"An urn containing 2 red and 1 blue orb is in front of you. At each step..."
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21
100-Yard Dash
Discrete Math
Difficulty
6/10
1 Part
"There are six runners in the 100-yard dash. How many ways are there for..."
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21
Uniform Quotient
Probability
Difficulty
4/10
1 Part
"If a and b are uniform in [0, 1] what is the probability that a/b is in [1,3]?"
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20
Red Rubik's cube
Probability
Difficulty
4/10
1 Part
"A white 3x3x3 rubik’s cube is dipped in paint so its entire external surface is colored..."
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19
Filet Mignon
Brainteaser
Difficulty
2/10
1 Part
"Your grill can hold a maximum of 3 pieces of Filet Mignon at a time. It takes one minute to cook..."
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18
Assign The Quants
Discrete Math
Difficulty
4/10
1 Part
"There are ten employees who must be assigned to various tasks. Three members will be working... "
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17
2D Grid Game
Discrete Math
Difficulty
4/10
2 Parts
"You are playing a 2D game where your character is trapped within a 6×6 grid. Your character starts.."
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17
Disease Incidence
Statistics
Difficulty
3/10
3 Parts
"A certain disease has an incidence rate of 2%. If the false negative rate is 10% and the false ..."
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17
Triple Coin
Probability
Difficulty
3/10
1 Part
"You have 3 coins. One always comes up heads, 1 always comes up tails, and 1 is just a regular..."
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16
Forgetting Neighbor
Discrete Math
Difficulty
3/10
1 Part
"Your neighbor has 3 children and you always forget how old they are. However, you know their ages..."
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16
Society of Women
Probability
Difficulty
3/10
1 Part
"You are off venturing in a rainforest where you suddenly come into contact with an isolated..."
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16
100 Switches
Brainteaser
Difficulty
2/10
1 Part
"There are 100 switches in a room and each of them are initially flipped to the left..."
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16
Deuces of Four
Discrete Math
Difficulty
3/10
1 Part
"Raj and Rachel are playing a special game of tennis with the following rules..."
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16
1000 Stones
Brainteaser
Difficulty
3/10
1 Part
"There are 1000 stones on a table. Two players take turns taking off either 1, 2, or 3 stones per..."
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16
Dinner For Four
Discrete Math
Difficulty
4/10
1 Part
"How many ways are there to seat four of a group of ten people around..."
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16
Rainbow Trains
Probability
Difficulty
2/10
1 Part
"There are three train cars: a blue one, a red one, and a green one. This train has a..."
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15
Maximize the Product
Probability
Difficulty
4/10
2 Parts
"Suppose you roll two fair 6-sided dice. What is the expected value of the product of the two dice..."
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15
Chess Club Photo
Discrete Math
Difficulty
4/10
1 Part
"Your school chess club wants to take a picture with a particular arrangement. They want the three..."
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15
Arabian Sultan
Brainteaser
Difficulty
2/10
1 Part
"Once upon a time, an Arabian sultan captured 50 wise men and kept them..."
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15
The Dealer's Deck
Probability
Difficulty
3/10
1 Part
"You walk into a casino and play a game with the dealer. You and the dealer are each..."
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14
River Crossing
Brainteaser
Difficulty
2/10
1 Part
"A farmer is on his way back from the market, with him he has a fox, a chicken, and some grain. When "
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14
Ant Journey
Brainteaser
Difficulty
2/10
1 Part
"An ant sits at one corner of a unit cube, wishing to travel to the corner farthest from it. What ..."
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14
Even Prime Sum
Probability
Difficulty
3/10
1 Part
"Two distinct prime integers between 1 and 20, inclusive, are selected uniformly at random..."
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14
Subtree Removal
Probability
Difficulty
3/10
1 Part
"You are given a rooted tree. On each step, you randomly choose a node and remove the subtree..."
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14
Soccer Match
Probability
Difficulty
2/10
1 Part
"Two teams, A and B, played soccer twice in two independent matches. The average accuracy of..."
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14
Token Tussle
Probability
Difficulty
7/10
1 Part
"Two players each start with 12 tokens. They roll three dice until the sum is either 11 or 14. If..."
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13
Linear Regression MLE
Machine Learning
Difficulty
9/10
1 Part
"Consider the linear regression setting in which you are given a training set ..."
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13
Sample Duplication
Statistics
Difficulty
2/10
1 Part
"You are in a research lab in a tropical rainforest and are studying the relationship between..."
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13
Number of Turns
Probability
Difficulty
4/10
1 Part
"Suppose you have a deck of 20 cards with values ranging from 1 - 10. Each card appears in the deck.."
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12
Semi-Working Gum Machine
Probability
Difficulty
3/10
1 Part
"You and two other friends get gum from a semi-functioning gum machine. This machine will pop out..."
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12
Date Projection
Brainteaser
Difficulty
3/10
1 Part
"Let 1, 2, ..., 7 be the days of the week (Sunday, Monday, ..., Saturday). What day of the week... "
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12
Coin Bundle
Brainteaser
Difficulty
3/10
1 Part
"You are given a pile of 100 coins. You may arrange these coins into however many stacks..."
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11
Diverging Roads
Brainteaser
Difficulty
2/10
1 Part
"A lone traveler seeks to visit a sage. Along his journey he arrives at a fork in the road, where..."
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10
Equal Rations
Brainteaser
Difficulty
2/10
1 Part
"Josiah, Charles, and Michael live together in a cottage and share everything equally..."
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10
Option Arbitrage
Finance
Difficulty
5/10
1 Part
"Jamison has two call options on the underlying S with initial price S_0 = 24 and strike K=21..."
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10
Counter Strike
Brainteaser
Difficulty
6/10
1 Part
"N undercover agents have been found in don's lair. Less than half of them are terrorists and the..."
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10
Find the Money Box
Probability
Difficulty
3/10
1 Part
"There are five boxes: one with $150, the rest are empty. At any time, you may pay X dollars to..."
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9
Sumo Wrestlers
Statistics
Difficulty
2/10
1 Part
"Two Sumo wrestlers (A and B) have on wrestling match each day for N days. Let Xi denote the..."
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8
Bon Apetit
Statistics
Difficulty
2/10
3 Parts
"The manager of a large Michelin star restaurant is disappointed with his staff and..."
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8
Favorite Color
Brainteaser
Difficulty
2/10
1 Part
"In a group of people, each person's favorite color is either red, blue, yellow, or green. If 15..."
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8
Restaurant Meal
Probability
Difficulty
2/10
1 Part
"Three friends all decide to visit a popular restaurant. If each friend randomly and independently..."
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8
Stamp Collector
Probability
Difficulty
2/10
1 Part
"A stamp collector is attempting to collect 4 different stamp types. If she is equally likely..."
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7
Buy and Sell Stock
Algorithmic Programming
Difficulty
2/10
1 Part
"You are given an array of stock prices where price[i] is the price of a given stock on the..."
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7
Straddle Strat
Finance
Difficulty
3/10
2 Parts
"Suppose the price of stock ABC is $62, interest rates and dividends are 0, and we are analyzing ..."
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7
Cube Cutting
Brainteaser
Difficulty
2/10
1 Part
"What is the smallest number of cuts required to create 64 unit cubes from a 4 by 4 by 4 unit..."
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7
Quilt Shop
Statistics
Difficulty
2/10
1 Part
"A quilt shop sells three different colored quilts: blue, red, and green. Of the first 1000 quilts..."
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6
The Grand Hotel
Brainteaser
Difficulty
3/10
3 Parts
"Suppose you own a hotel that has 1 floor and an infinite number of rooms that are all occupied..."
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6
Regression Coefficients
Machine Learning
Difficulty
3/10
1 Part
"Suppose that we have two datasets X and Y with Var(X) = 10 and Var(Y) = 20. We perform the..."
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6
Cards Reordering
Discrete Math
Difficulty
3/10
1 Part
"The standard procedure for shuffling a deck of cards is to take the pack face downwards..."
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5
Perfect Samples
Statistics
Difficulty
3/10
1 Part
"Assume that you are taking samples of size n from a population. For each sample, let p represent..."
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5
Top Buyer and Seller
Data Wrangling
Difficulty
4/10
1 Part
"Find the trader who bought and sold the most META stock in the past 30 days. Allow for ties and..."
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5
Closest Median Profit
Data Wrangling
Difficulty
2/10
1 Part
"The performance review cycle has begun and you are responsible for evaluating the traders..."
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5
Median Probability
Probability
Difficulty
3/10
1 Part
"Given three random variables independently and identically distributed from a uniform distribution.."
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4
Most Traded
Algorithmic Programming
Difficulty
2/10
1 Part
"Given a stream of stock data, create a data structure that can efficiently handle the following ..."
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4
Bolt Variance
Statistics
Difficulty
2/10
1 Part
"A manufacturer produces nuts and bolts. A random sample of twelve bolts returned a sample variance.."
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4
Sly Cat
Probability
Difficulty
2/10
1 Part
"You have a pet cat that has a sly tendency to leave your house while you are away..."
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3
Nomadic Manager
Data Wrangling
Difficulty
3/10
1 Part
"In New York City, there is a select group of hedge fund managers that cherish any opportunity..."
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3
Joint Model Evaluation
Statistics
Difficulty
2/10
1 Part
"Using OLS, we regress y onto X1 and find that the model has an R^2 of 0.45. We also regress..."
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2
Most Profitable Strategy
Data Wrangling
Difficulty
4/10
1 Part
"A quantitative hedge fund consists of a team of 35 traders. These traders execute trading ..."
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2
Growing Fund
Data Wrangling
Difficulty
4/10
1 Part
"A multi-billion dollar hedge fund has many subsidiary funds that each have their own investment..."
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129 Questions
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