SIG Interview Questions - Complete List

Quant Interview Questions

149 questions

If you roll two dice and add their results, what is the probability of obtaining a sum of 6?

Trader Interview

Compress a string such that repeated characters are replaced by the character followed by the number of repetitions. For example, given 'AAABBCC', output 'A3B2C2'.

Senior Software Engineer Interview

Write a method that returns a stock ticker value based on a company name found within a string of text, which may also contain random words in addition to the company name. Optimize the method for performance, assuming there could be millions of companies to search through.

Sr Software Engineer Interview

Calculate the probability of having a disease given that a diagnostic test result is positive. What is the probability if the test result is positive twice?

Quantitative Researcher Interview

Is 1599 a prime number?

Software Developer Interview

A painted 3x3 cube consists of 27 small cubes. If one small cube is selected at random and thrown, and you observe only the unpainted sides, what is the probability that the selected cube is completely unpainted?

Quantitative Researcher Interview

Nine white cubes are arranged into a 3x3 cube and the outside surfaces are painted green. A cube is randomly selected and rolled. If the side facing up is white, what is the probability that this cube was the middle (center) cube?

Quantitative Researcher Interview

Two points are uniformly distributed around the circumference of a unit circle. What is the expected value of the distance between them?

Quantitative Researcher Interview

A deck of 18 custom playing cards is numbered from 1 to 18. A card is drawn 6 times with replacement. If X is the number of draws that result in a prime number, what is the expected value of X (E(X))?

Quantitative Researcher Interview

Two points are randomly selected on a circle. What is the expected distance between them?

Quantitative Research Interview

Given an n-by-n real matrix A where every entry is nonnegative and A squared (A^2) is the zero matrix, what is the maximum number of positive entries that A can have?

Quantitative Researcher Interview

If you break a unit stick randomly at two points, what is the expected length of the smallest piece?

Quantitative Researcher Interview

Three real numbers are chosen independently and uniformly at random from the interval [0, 3]. What is the probability that the smallest number is between 0.5 and 1?

Quantitative Researcher Interview

You are a player on a basketball team that is losing by 2 points. You have the ball, and there are 3 seconds remaining. You have two options: pass to a teammate for a 3-point shot (with a 37% probability of making it and winning the game), or pass for a 2-point shot (with a 77% probability of making it and tying the game). In the event of a tie, your team goes to overtime, where there is a 50% chance of winning. What should you do, and why?

Assistant Trader Interview

A boat fires torpedoes at another boat. The probability that a torpedo hits is 1/3. If a torpedo hits the boat, the boat is destroyed. Two torpedoes are fired. What is the probability that the ship is destroyed?

Assistant Trader Interview

You have 17 coins and I have 16 coins. We flip all the coins at the same time. If you have more heads than I do, you win; if we have the same number of heads or you have fewer, then I win. What is your probability of winning?

Assistant Trader Interview

You roll a die and win twice the value of the face if it is even, or the face value if it is odd. What is the fair amount to charge to play this game? If you are given the option to roll again and will only be paid based on the result of the second roll if you choose to roll again (i.e., the result of the last roll), what is the fair charge to play the game with this option?

Assistant Trader Interview

Every morning, Mike the security guard at CP High School opens all 1000 doors in the building, numbered 1 to 1000. The next guard closes all even-numbered doors. Each subsequent guard toggles (opens if closed, closes if open) every nth door, where n is the guard's number, until the 1000th guard toggles only door 1000. How many doors are left open in the end?

Assistant Trader Interview

What is the expected value of a single roll of a fair six-sided die?

Assistant Trader Interview

I have a painting. If it is an original, it is worth $500,000; if it is not, it is worth $10,000. The probability that it is an original is 0.2. I have an option to pay $100,000 for the painting after inspection. What is the value of this option?

Assistant Trader Interview

You start with 1 dollar and your friend starts with 2 dollars. You bet 1 dollar per round until one of you runs out of money. Each round, you have a 2/3 chance of winning the bet. What is the probability that you win all your friend's money before losing yours?

Assistant Trader Interview

Given a multiplication table showing values such as 2^2, 2^3, and so on, estimate the range for the value of 14^7 divided by 5^3.

Assistant Trader Interview

We are playing Russian roulette with a standard 6-chamber revolver. Two bullets are placed in adjacent chambers. I spin the cylinder, point the gun at my head, and pull the trigger. I survive. Now it's your turn. You can either (a) re-spin, aim at your head, and pull the trigger, or (b) not spin, aim at your head, and pull the trigger. Which option gives you a higher chance of survival? Additionally, given that I spun the cylinder, what is the probability that I die this time?

Assistant Trader Interview

A group of people wants to determine their average salary on the condition that no individual is able to discover anyone else's salary. How can they accomplish this?

Assistant Trader Interview

Which is larger: 2 to the power of 1/3 or 10 to the power of 1/10?

Assistant Trader Interview

A submarine is targeted by two torpedoes, each with a 1/3 probability of hitting the target independently. What is the probability that at least one of the torpedoes will hit the submarine?

Assistant Trader Interview

You have five friends of different ages going to dinner. What is the probability that they will sit in age order around the table, either clockwise or counterclockwise?

Assistant Trader Interview

You have 1,000 bottles of wine, one of which is poisoned. You have a number of slaves you can use for testing, and you want to minimize the number of deaths while guaranteeing you find the poisoned bottle. The poison is fast-acting and fatal within an hour, and you have just over an hour before your guests arrive. Each slave can taste test any number of bottles. What strategy will allow you to find the poisoned bottle using the fewest number of slaves?

Assistant Trader Interview

You have 17 coins and I have 16 coins. We flip all the coins at the same time. If you have more heads, then you win; if we have the same number of heads or you have fewer, then I win. What is your probability of winning?

Assistant Trader Interview

Solve for x in the equation x^{x^{x^{...}}} = 2, where the power tower extends infinitely.

Assistant Trader Interview

Given an array of integers and an integer k, find the k-th largest element in the array.

Software Engineer Interview

Explain how hash tables work.

Software Engineer Interview

Since the average time complexity of a hashtable is O(1), why do we still use binary search trees? Can you describe some occasions where we use a binary search tree instead of a hashtable?

Software Engineer Interview

What is garbage collection, and how is it performed in Java?

Software Developer Interview

Why do we use hashtables, and what is their time complexity?

Software Engineer Interview

What is a Binary Search Tree, and what is its time complexity for search, insert, and delete operations?

Software Engineer Interview

Implement a Stack data structure with methods such as push(), pop(), and top(), in a programming language of your choice (preferably C#). The stack should accept only 12-bit integer numbers as input, and all exceptions should be handled properly.

Software Engineer Interview

A group of friends are tracking the miles per gallon (MPG) for each of their cars. Each time they fill up their gas tank, they record the following in a CSV file: person name, car name, miles driven since last fill-up (float), gallons filled at this fill-up (integer), and the fill-up date. Write a program that lets a group member determine the MPG for each of their cars during a specific time range. The principal function for querying MPG is: GetRangeMPG(PersonName, StartDate, EndDate), which returns a list of objects containing (CarName, MPG), where MPG is calculated as (total miles driven during the time period) / (total gallons filled during that time period). The query's date range should be treated inclusively.

Software Developer Interview

Check if a string is a permutation of a palindrome without using any additional data structures.

Software Engineer Interview

Given an array of integers, write a program in the language of your choice to do the following: (1) reverse the array; (2) find all perfect numbers in the array.

Software Developer Interview

How would you implement a garbage collector for a programming language?

Software Engineer Interview

Develop an algorithm to reverse a string.

Software Developer Interview

How do you reverse a linked list?

Software Engineer Interview

Given an array of numbers, find the maximum value in the array.

Intern Interview

A frog is traveling from point A(0, 0) to point B(4, 6), and each step can only be 1 unit up or 1 unit to the right. The frog also refuses to move three steps in the same direction consecutively. Compute the number of ways the frog can move from A to B.

Intern Interview

If you are playing a game and your opponent doubles the stakes, what probability of winning should you require to prefer accepting the doubled stakes over resigning from the game?

Intern Interview

How many ways can five people sit in a circle such that you are sitting next to your best friend?

Intern Interview

Given a character array representing a sentence, reverse the order of words in the sentence in place.

Intern Interview

It costs $1 to play a game where you flip a fair coin four times. If you get four consecutive heads, you win $10. Should you play the game?

Intern Interview

A bag contains 30 balls: 10 black, 5 orange, 10 green, and 5 blue. Without replacement, what is the probability that the second black ball is drawn on the third draw?

Intern Interview

A painting has a 20% chance of being real and an 80% chance of being fake. If it's fake, you can sell it for $10,000; if it's real, it's worth $500,000. 1. What is the expected value of the painting? 2. If you could buy the option to purchase the painting for $100,000 after learning whether it is real or fake (but are not obligated to buy), what is the value of this option?

Intern Interview

What is inheritance? What is polymorphism? What is the probability that three people have their birthdays on the same day of the week?

Intern Interview

We are racing, and at any time we may signal to double our bet. We have each put down 100 to start. If, during the race, I signal that I want to double the bet, what is the minimum probability of winning that you would need in order to accept continuing with the doubled bet?

Intern Interview

Suppose you and your opponent each have three fair coins and flip all three at once. After flipping, if both of you have the same number of heads from your own coins, your opponent pays you $1. If the numbers are different, you pay your opponent $2. Should you agree to play this game?

Intern Interview

If the probability of seeing a meteor outside within one hour is 84 percent, what is the probability of seeing at least one meteor outside in 30 minutes?

Intern Interview

Flip coins sequentially until the sequence 'HT' or 'TT' appears. What is the probability that 'HT' appears before 'TT'?

Quantitative Trader Interview

A frog is traveling from point A(0, 0) to point B(4, 6). Each step can only be 1 unit up or 1 unit to the right. The frog refuses to move three steps in the same direction consecutively. Compute the number of ways the frog can move from A to B.

Quantitative Trader Interview

A painting is on sale for X amount. The probability that it is real is Y. If it is real, it is worth A; if it is a fake, it is worth B. What is the expected gain on purchasing this painting?

Quantitative Trader Interview

Given a standard shuffled deck of cards, you draw a card from the top. How much would you bet that the next card is higher than the one you drew? Please discuss bet sizing strategies and whether the order of the cards matters.

Quantitative Trader Interview

You have $100 and receive an additional $100 to play a casino game where you bet on flips of a fair coin, with a 4:5 payout. You are required to bet a total of at least $500 before you can cash out. How do you maximize your expected earnings?

Quantitative Trader Interview

A can finish a job in 100 minutes, and B can finish the same job in 120 minutes. A and B work together on the job, but after 40 minutes, C comes to help them, and they finish the job in an additional 10 minutes. How long would it take C to finish the job by himself?

Quantitative Trader Interview

What is the expected number of times you need to roll a die to get a 6?

Quantitative Trader Interview

What is the fair price to enter a game where you win the amount shown on a single rolled die?

Quantitative Trader Interview

Person A completes a job in 100 minutes. Person B completes the same job in 120 minutes. They work together for 30 minutes, then person C joins. Together, the three complete the job in another 20 minutes. How long would it take for person C to complete the job alone?

Quantitative Trader Interview

Given an unsorted array of integers, find the k-th largest element in the array.

Software Engineer Interview

1. How would you process data by reading from a file in C++? 2. What is a vector in C++ and what is the difference between a vector and an array? Discuss memory management differences. 3. How would you debug a multithreaded implementation in C++? 4. How would you implement std::shared_ptr from scratch in C++?

Software Engineer Interview

Explain how hash tables work.

Software Engineer Interview

What is garbage collection? How is it done in Java?

Software Developer Interview

Why do we use a hashtable, and what is its time complexity?

Software Engineer Interview

Since the average time complexity of a hashtable is O(1), why do we still use binary search trees? Can you describe some situations where a binary search tree is preferred over a hashtable?

Software Engineer Interview

Implement a stack data structure in a programming language of your choice (e.g., C#), including all standard methods such as push(), pop(), and top(). The stack should accept only 12-bit integer numbers as input, and all exceptions should be handled properly. Complete this task within one hour.

Software Engineer Interview

How does a dictionary work?

Software Engineer Interview

Given a matrix, if an element is 0, set its entire row and column to 0. Modify the matrix in place.

Software Engineer Interview

Reverse a string.

Software Developer Interview

Given two strings, return the characters that are common to both.

Software Engineer Interview

Given a CSV file where each row contains: person name, car name, miles driven since last fill-up (float), gallons filled at this fill-up (integer), and the fill-up date, write a program to calculate the miles per gallon (MPG) for each car a person has driven during a specific date range (inclusive). Implement a function GetRangeMPG(PersonName, StartDate, EndDate) that returns a list of objects containing (CarName, MPG), where MPG is calculated as total miles driven divided by total gallons filled within the date range.

Software Developer Interview

Check if a given string is a permutation of a palindrome without using any additional data structures.

Software Engineer Interview

How would you implement a garbage collector for a programming language?

Software Engineer Interview

What is Object-Oriented Programming? Develop an algorithm to reverse a string.

Software Developer Interview

How do you reverse a linked list?

Software Engineer Interview

Is 1599 a prime number?

Software Developer Interview

A painting has an 80% chance of being fake. If it is real, it is worth $500,000; if fake, it is worth $10,000. The seller asks for $120,000. Based on this information, should you buy the painting?

Trading Intern Interview

Given the probabilities of an event occurring on each of two days, find the probability that the event occurs on at least one of those days.

Trading Intern Interview

In a population, 50% do not smoke, 20% are light smokers, and 30% are heavy smokers. Heavy smokers are twice as likely to die as light smokers, and light smokers are twice as likely to die as non-smokers. What is the probability that a person was a heavy smoker given that they have died?

Trading Interview

What is the expected value of a fair six-sided die?

Trading Interview

What is the probability that a group of people sitting around a round table are seated in strictly ascending or strictly descending order of age?

Trading Interview

How much would you pay for the option to reroll a die, given that you receive the dollar value of the number you roll, and can choose to reroll once if you wish?

Quant Trader Intern Interview

You have 25 horses and a race track with 5 lanes. Each race can race at most 5 horses at a time, and you cannot use a stopwatch. What is the minimum number of races required to determine the fastest three horses?

Quant Trader Intern Interview

A deck contains ten cards: two 10s, two Js, two Qs, two Ks, and two As. You are dealt five cards without replacement from the deck. Compute the expected number of pairs.

Quant Trader Intern Interview

What is the expected number of fair coin flips required to get two consecutive heads (i.e., 'HH') for the first time?

Quant Trader Intern Interview

What is the probability of obtaining 3 heads in a row when tossing an unbiased coin 5 times?

Quant Trader Intern Interview

What is the probability of rolling two sixes with a pair of standard six-sided dice?

Quant Trader Intern Interview

There are two fair dice. For each die, you roll it again if you do not get a 6. Calculate the expected number of times you get a 6 on die 1.

Internship Interview

Can you reverse a string?

Internship Interview

Aaron, Bryce, and Craig are all of different integer ages. They had the following conversation: (i) Bryce to Craig: 'You're the youngest.' (ii) Aaron to Bryce: 'Your age is exactly 70% greater than mine.' (iii) Aaron to Craig: 'Your age is the average of my age and Bryce's age.' (iv) Craig to Aaron: 'I'm at least 8 years older than you.' However, not all of these statements are true. Whenever speaking to someone older, a speaker always tells the truth; when speaking to someone younger, a speaker always lies. How old is Craig?

Quantitative Analyst Interview

Mickey and Minnie plan to meet at a cafe, but each will independently arrive at a uniformly random time between 9:00 and 10:00. Mickey will wait 10 minutes for Minnie before leaving, and Minnie will wait 30 minutes for Mickey before leaving. What is the probability that they meet each other?

Quantitative Analyst Interview

100

Given 5 fair dice, what is the probability of obtaining a result where exactly 3 of the dice show the same value?

Quantitative Analyst Interview

101

For a fair coin, what is the minimum, maximum, and expected (average) number of flips needed to get either 3 heads or 3 tails?

Quantitative Analyst Interview

102

A property has a 10% chance of containing oil, making it worth $1 million, a 30% chance of containing coal, making it worth $500,000, and if no resources are found, it can be sold for $200,000. What is the expected value of this property?

Equity Research Associate Interview

103

Five guys walk into a bar. In how many ways can they sit so that they are arranged from oldest to youngest?

Equity Research Associate Interview

104

If you have 8 marbles and one is lighter than the rest, how would you determine which one is lighter using a balance scale in two weighings?

Equity Research Associate Interview

105

What is the difference between bagging and boosting?

Quant Researcher Interview

106

We have three pancakes. One is burnt on both sides, one is burnt on one side, and one is not burnt at all. The pancakes are stacked on a plate so that all that can be seen is a burnt side on top. What is the probability that the fully burnt pancake is the one on top?

Quant Researcher Interview

107

There are different levels of smokers, with some being more likely to die than others. If a person has died, what is the probability that they were a heavy smoker?

Quantitative Trading Intern Interview

108

You are betting $50 on a basketball game and your friend is betting $20. If you win, you gain your friend's $20; if you lose, you forfeit your $50 to your friend. What is your expected profit?

Quantitative Trading Intern Interview

109

You are playing a game where both you and your opponent have each put $10 in the pot. Your opponent now bets another $10. What is the minimum probability of winning required for you to call this $10 bet?

Summer Intern Interview

110

Pick three numbers between 1 and 20. What is the probability that one of the numbers is the average of the other two?

Graduate Quant Trader Interview

111

What is the probability of getting the sequence HHT before HTH when flipping a fair coin repeatedly?

Graduate Quant Trader Interview

112

You play a game where you have $100 to split between yourself and a random person. You decide how to split it, and the other person can either accept (so you both receive the split amounts) or refuse (in which case both of you get $0 and the game ends). What split do you propose? What if the amount to split is $1,000,000?

Graduate Quant Trader Interview

113

What is the probability of rolling six consecutive 3s with a fair six-sided die?

Junior Trader Interview

114

Suppose we have a $10 bet. At any time, I can ask to double the bet. If you accept, we both put in another $10, so the winner gets $20. If you lose, you forfeit everything; if you reject the double, you lose the initial $10. What is the minimum probability of winning that would make you accept the double?

Junior Trader Interview

115

Suppose you and I are playing a game and have bet $10, which will go to the winner. At some point, I offer to double the bet to $20. If you accept, the game continues with the new bet; if you refuse, you lose the game and forfeit the original $10. What is the minimum probability of winning that you would need to accept the increased bet?

Junior Trader Interview

116

You have two torpedoes to hit a boat. Each torpedo has a 2/3 chance of hitting the boat. If you launch both torpedoes, what is the probability that the boat is hit?

Junior Trader Interview

117

You can roll a fair six-sided die a maximum of two times. After each roll, you can choose to accept the current roll's value or roll again (if it is your first roll). You must accept the value on your last roll. What is the expected value of this strategy?

Junior Trader Interview

118

If you randomly cut a cake n times, what is the expected number of pieces?

Quantitative Researcher Interview

119

What is the average distance between two random points on the circumference of a unit circle?

Quantitative Researcher Interview

120

You toss a fair coin repeatedly. What are the odds that the sequence HTH appears before the sequence HHT?

Quantitative Researcher Interview

121

What is the probability of getting the sequence HTH before HHT when repeatedly flipping a fair coin?

Quantitative Researcher Interview

122

Calculate the probability that a person has a disease given that the test result is positive. What is the probability if the test result is positive twice?

Quantitative Researcher Interview

123

1. A painted 3x3 cube consists of 27 small cubes. If one small cube is selected at random and thrown, and upon landing only its unpainted sides are visible, what is the probability that this cube is completely unpainted? 2. Eight people are sitting around a table. If three are selected randomly, what is the probability that at least two of the selected people were sitting next to each other?

Quantitative Researcher Interview

124

Nine white cubes are arranged to form a 3x3 cube, and the outside surfaces are painted green. A single cube is randomly selected and rolled. If the side facing up is white, what is the probability that the selected cube was the middle cube?

Quantitative Researcher Interview

125

Two points are uniformly distributed around the circumference of a unit circle. What is the expected value of the distance between them?

Quantitative Researcher Interview

126

A deck of 18 custom playing cards is numbered from 1 to 18. A card is drawn 6 times with replacement. If X is the number of draws that result in a prime number, what is the expected value E(X)?

Quantitative Researcher Interview

127

Two points are randomly selected on the circumference of a circle. What is the expected distance between them?

Quantitative Research Interview

128

Given an n-by-n real matrix A where every entry is nonnegative, and A squared is the zero matrix, what is the maximum number of positive entries A can have?

Quantitative Researcher Interview

129

If you break a unit stick randomly in two places, what is the expected length of the smallest piece?

Quantitative Researcher Interview

130

Three real numbers are chosen independently and uniformly at random from the interval [0, 3]. What is the probability that the smallest number is between 0.5 and 1?

Quantitative Researcher Interview

131

If you randomly cut a cake n times, what is the expected number of pieces?

Quantitative Researcher Interview

132

List and explain the properties of a nilpotent matrix.

Quantitative Research Associate Interview

133

Let A and B be two covariance matrices. Is A + B also a covariance matrix? How about A squared (A^2)? What about the product AB?

Quantitative Research Associate Interview

134

1. X and Y are Gaussian variables with given parameters. Find P(X > Y), and estimate the value of X when X + Y is observed. 2. Compare the expected payoffs of taking the maximum of two dice rolls versus rolling once and having the option to roll again. 3. Given C++ code involving base and derived classes, describe the code's output and identify and fix any bugs.

Quantitative Research Associate Interview

135

If you toss 100 fair coins, what is the probability of getting more than 60 heads?

Quantitative Research Associate Interview

136

A fair coin is tossed repeatedly until either the sequence HHT or HTH occurs. What is the expected number of tosses required?

Graduate Trader Interview

137

What is the probability of receiving exactly 3 heads in 5 tosses of a fair coin?

Graduate Trader Interview

138

There are 4 green balls and 11 red balls. What is the probability that the 4th green ball is picked on the 9th draw?

Graduate Trader Interview

139

You have 8 balls, one of which is slightly heavier than the others. What is the minimum number of weighings required to identify the heavier ball using a balance scale?

Graduate Trader Interview

140

Write a program to check if a given input string is a palindrome.

Technology Associate Interview

141

What is a hash tree?

Technology Associate Interview

142

How could you implement several Java features, such as inheritance and abstract classes, in C?

Technology Associate Interview

143

When using a virtual method, how does the machine determine to call the derived class's implementation rather than the base class implementation, under the hood?

Technology Associate Interview

144

Write a function to determine whether a given point lies within a triangle in 2D space.

Technology Associate Interview

145

Write a function to traverse a binary search tree using both recursive and non-recursive methods.

Technology Associate Interview

146

What is the worst-case construction of a binary search tree?

Technology Associate Interview

147

What is the fair price of a call option, given the strike price and the probabilities of the underlying stock reaching specific prices?

Equity Research Analyst Interview

148

You toss a fair coin repeatedly. What is the probability that the sequence HTH appears before the sequence HHT?

Quantitative Researcher Interview

149

What is the probability of getting the sequence HTH before HHT when flipping a fair coin repeatedly?

Quantitative Researcher Interview

Quant Interview Questions

If you roll two dice and add their results, what is the probability of obtaining a sum of 6?

Compress a string such that repeated characters are replaced by the character followed by the number of repetitions. For example, given 'AAABBCC', output 'A3B2C2'.

Write a method that returns a stock ticker value based on a company name found within a string of text, which may also contain random words in addition to the company name. Optimize the method for performance, assuming there could be millions of companies to search through.

Calculate the probability of having a disease given that a diagnostic test result is positive. What is the probability if the test result is positive twice?

Is 1599 a prime number?

A painted 3x3 cube consists of 27 small cubes. If one small cube is selected at random and thrown, and you observe only the unpainted sides, what is the probability that the selected cube is completely unpainted?

Nine white cubes are arranged into a 3x3 cube and the outside surfaces are painted green. A cube is randomly selected and rolled. If the side facing up is white, what is the probability that this cube was the middle (center) cube?

Two points are uniformly distributed around the circumference of a unit circle. What is the expected value of the distance between them?

A deck of 18 custom playing cards is numbered from 1 to 18. A card is drawn 6 times with replacement. If X is the number of draws that result in a prime number, what is the expected value of X (E(X))?

Two points are randomly selected on a circle. What is the expected distance between them?

Given an n-by-n real matrix A where every entry is nonnegative and A squared (A^2) is the zero matrix, what is the maximum number of positive entries that A can have?

If you break a unit stick randomly at two points, what is the expected length of the smallest piece?

Three real numbers are chosen independently and uniformly at random from the interval [0, 3]. What is the probability that the smallest number is between 0.5 and 1?

A boat fires torpedoes at another boat. The probability that a torpedo hits is 1/3. If a torpedo hits the boat, the boat is destroyed. Two torpedoes are fired. What is the probability that the ship is destroyed?

You have 17 coins and I have 16 coins. We flip all the coins at the same time. If you have more heads than I do, you win; if we have the same number of heads or you have fewer, then I win. What is your probability of winning?

What is the expected value of a single roll of a fair six-sided die?

I have a painting. If it is an original, it is worth $500,000; if it is not, it is worth $10,000. The probability that it is an original is 0.2. I have an option to pay $100,000 for the painting after inspection. What is the value of this option?

You start with 1 dollar and your friend starts with 2 dollars. You bet 1 dollar per round until one of you runs out of money. Each round, you have a 2/3 chance of winning the bet. What is the probability that you win all your friend's money before losing yours?

Given a multiplication table showing values such as 2^2, 2^3, and so on, estimate the range for the value of 14^7 divided by 5^3.

A group of people wants to determine their average salary on the condition that no individual is able to discover anyone else's salary. How can they accomplish this?

Which is larger: 2 to the power of 1/3 or 10 to the power of 1/10?

A submarine is targeted by two torpedoes, each with a 1/3 probability of hitting the target independently. What is the probability that at least one of the torpedoes will hit the submarine?

You have five friends of different ages going to dinner. What is the probability that they will sit in age order around the table, either clockwise or counterclockwise?

You have 17 coins and I have 16 coins. We flip all the coins at the same time. If you have more heads, then you win; if we have the same number of heads or you have fewer, then I win. What is your probability of winning?

Solve for x in the equation x^{x^{x^{...}}} = 2, where the power tower extends infinitely.

Given an array of integers and an integer k, find the k-th largest element in the array.

Explain how hash tables work.

Since the average time complexity of a hashtable is O(1), why do we still use binary search trees? Can you describe some occasions where we use a binary search tree instead of a hashtable?

What is garbage collection, and how is it performed in Java?

Why do we use hashtables, and what is their time complexity?

What is a Binary Search Tree, and what is its time complexity for search, insert, and delete operations?

Implement a Stack data structure with methods such as push(), pop(), and top(), in a programming language of your choice (preferably C#). The stack should accept only 12-bit integer numbers as input, and all exceptions should be handled properly.

How does a dictionary work?

Reverse a given string.

Given two strings, return the characters that are common to both strings.

Check if a string is a permutation of a palindrome without using any additional data structures.

Given an array of integers, write a program in the language of your choice to do the following: (1) reverse the array; (2) find all perfect numbers in the array.

How would you implement a garbage collector for a programming language?

Develop an algorithm to reverse a string.

How do you reverse a linked list?

Given an array of numbers, find the maximum value in the array.

A frog is traveling from point A(0, 0) to point B(4, 6), and each step can only be 1 unit up or 1 unit to the right. The frog also refuses to move three steps in the same direction consecutively. Compute the number of ways the frog can move from A to B.

If you are playing a game and your opponent doubles the stakes, what probability of winning should you require to prefer accepting the doubled stakes over resigning from the game?

How many ways can five people sit in a circle such that you are sitting next to your best friend?

Given a character array representing a sentence, reverse the order of words in the sentence in place.

It costs $1 to play a game where you flip a fair coin four times. If you get four consecutive heads, you win $10. Should you play the game?

A bag contains 30 balls: 10 black, 5 orange, 10 green, and 5 blue. Without replacement, what is the probability that the second black ball is drawn on the third draw?

What is inheritance? What is polymorphism? What is the probability that three people have their birthdays on the same day of the week?

We are racing, and at any time we may signal to double our bet. We have each put down 100 to start. If, during the race, I signal that I want to double the bet, what is the minimum probability of winning that you would need in order to accept continuing with the doubled bet?

Suppose you and your opponent each have three fair coins and flip all three at once. After flipping, if both of you have the same number of heads from your own coins, your opponent pays you $1. If the numbers are different, you pay your opponent $2. Should you agree to play this game?

If the probability of seeing a meteor outside within one hour is 84 percent, what is the probability of seeing at least one meteor outside in 30 minutes?

Flip coins sequentially until the sequence 'HT' or 'TT' appears. What is the probability that 'HT' appears before 'TT'?

A frog is traveling from point A(0, 0) to point B(4, 6). Each step can only be 1 unit up or 1 unit to the right. The frog refuses to move three steps in the same direction consecutively. Compute the number of ways the frog can move from A to B.

A painting is on sale for X amount. The probability that it is real is Y. If it is real, it is worth A; if it is a fake, it is worth B. What is the expected gain on purchasing this painting?

Given a standard shuffled deck of cards, you draw a card from the top. How much would you bet that the next card is higher than the one you drew? Please discuss bet sizing strategies and whether the order of the cards matters.

You have $100 and receive an additional $100 to play a casino game where you bet on flips of a fair coin, with a 4:5 payout. You are required to bet a total of at least $500 before you can cash out. How do you maximize your expected earnings?

A can finish a job in 100 minutes, and B can finish the same job in 120 minutes. A and B work together on the job, but after 40 minutes, C comes to help them, and they finish the job in an additional 10 minutes. How long would it take C to finish the job by himself?

What is the expected number of times you need to roll a die to get a 6?

What is the fair price to enter a game where you win the amount shown on a single rolled die?

Person A completes a job in 100 minutes. Person B completes the same job in 120 minutes. They work together for 30 minutes, then person C joins. Together, the three complete the job in another 20 minutes. How long would it take for person C to complete the job alone?

Given an unsorted array of integers, find the k-th largest element in the array.

Explain how hash tables work.

What is garbage collection? How is it done in Java?

Why do we use a hashtable, and what is its time complexity?

Since the average time complexity of a hashtable is O(1), why do we still use binary search trees? Can you describe some situations where a binary search tree is preferred over a hashtable?

Implement a stack data structure in a programming language of your choice (e.g., C#), including all standard methods such as push(), pop(), and top(). The stack should accept only 12-bit integer numbers as input, and all exceptions should be handled properly. Complete this task within one hour.

How does a dictionary work?

Given a matrix, if an element is 0, set its entire row and column to 0. Modify the matrix in place.

Reverse a string.

Given two strings, return the characters that are common to both.

Check if a given string is a permutation of a palindrome without using any additional data structures.

How would you implement a garbage collector for a programming language?

What is Object-Oriented Programming? Develop an algorithm to reverse a string.

How do you reverse a linked list?

Is 1599 a prime number?

A painting has an 80% chance of being fake. If it is real, it is worth $500,000; if fake, it is worth $10,000. The seller asks for $120,000. Based on this information, should you buy the painting?

Given the probabilities of an event occurring on each of two days, find the probability that the event occurs on at least one of those days.

In a population, 50% do not smoke, 20% are light smokers, and 30% are heavy smokers. Heavy smokers are twice as likely to die as light smokers, and light smokers are twice as likely to die as non-smokers. What is the probability that a person was a heavy smoker given that they have died?

What is the expected value of a fair six-sided die?