This is a challenging, and quite popular, question of pure logic you could easily encounter as a hedge fund job interview question. We suggest you don’t skip right to the answer, but take some time to digest the problem if it stumps you. Also, remembering the principles of the solution may be easier than remembering the details. Good luck!

Question:
You are given a set of scales and 12 marbles. The scales are of the old balance variety. That is, a small dish hangs from each end of a rod that is balanced in the middle. The device enables you to conclude either that the contents of the dishes weigh the same or that the dish that falls lower has heavier contents than the other.

The 12 marbles appear to be identical. In fact, 11 of them are identical, and one is of a different weight. Your task is to identify the unusual marble and discard it. You are allowed to use the scales three times if you wish, but no more.

Note that the unusual marble may be heavier than the others, or it may be lighter. You are asked to both identify it and determine whether it is heavy or light.

Answer:
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It would be a royal pain not to know the answer to this puzzler in a job interview!

Question:
This is an absolute classic. A king demands a tax of 1,000 gold sovereigns from each of 10 regions of his nation. The tax collectors for each region bring him the requested bag of gold coins at year end. An informant tells the king that one tax collector is cheating and giving coins that are consistently 10% lighter than they should be, but he does not know which collector is cheating. The king knows that each coin should weigh exactly one ounce. How can the king identify the cheat by using a weighing device exactly once?

Answer:
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Analysing this simple number-based strategy game isn’t too difficult outside the stressful context of a job interview, so put yourself under some time pressure to come up with the answer…

Question:
We shall play a competitive game, taking turns to call out integers. The first person to call out “50″ wins. The rules are as follows:

1. The player who starts must call out an integer between one and 10, inclusive
2. A new number called out must exceed the most recent number called by at least one and by no more than 10. For example, if the first player calls out “nine,” then the range of valid numbers for the opponent is 10 to 19, inclusive.

Do you want to go first, and if so, what is your strategy?

Answer:
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Hedge fund job interviews can take many directions. One thing is for sure, your logic and quantitative abilities will be tested. Here is a common question that asks the candidate to dip their toe in the water - so to speak.

Q: You start with a single lily pad floating in an empty pond. If that pad grows and the surface area of the pad doubles every day, it will take 30 days to cover the entire surface of the pond. If instead of one lily pad you start with eight lily pads (each identical in characteristics to the original lily pad), how many days will it take for the surface of the pond to become covered?

A: The trick here is to figure out the relationship between …
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We were talking to Charlie Panoff from Objective Solutions International about hedge fund job interviews and he asked us this question - and, for the record, no we did not get it right. Hopefully, you’ll be better prepared and when asked this one, a lightbulb will go on.

Q: A windowless room contains three identical light fixtures, each containing an identical light bulb. Each light is connected to one of three switches outside of the room. Each bulb is switched off to begin. You are outside the room, the door is closed, you can not see anything inside the room. You have one, and only one, opportunity to flip any of the external switches. After flipping your chosen switch(es), you may go into the room and look at the lights. You may not touch the switches again. How can you tell which switch goes to which light?

A: Turn on switch #1 for a short while, then turn it off. Turn on switch #2 and immediately enter the room.

The illuminated bulb represents switch #2. The warm but turned off bulb represents switch #1. The cold, non-illuminated bulb represents switch #3.

Note: This solution works if at the beginning all bulbs are off. What if they are all on? You won’t be able to tell from the heat, so just guess. You have a 1 in 6 chance if they are random, however, most light switches/fixtures are not random. Your chances improve based on standard configurations.

Although we learned of this question in our interview with Charlie Panoff, we found it in written form in Timothy Crack’s Heard on the Street: Quantitative Questions from Wall Street Job Interviews. Buy the book for more questions like these.

These interviewing tips from a hedge fund recruiter could make the crucial difference when you go looking for a quant job or, for that matter, any hedge fund job. Craig’s firm, Comprehensive Recruiting, is a financial shop in Arizona with a strong Wall Street practice.

Interviewing Tips & How To Differentiate Yourself
by Craig Stocksleger

It is one of the most highly recruited and sought after positions on Wall Street, the Quant Analyst. As a Quantitative Analyst you will be called upon to support one of the main profit centers of the Investment Bank or Asset Management firm, the Trading Desk. You possess an advanced degree and expertise in Numerical Analysis and advanced Mathematics as well as solid communication skills and the ability to work under pressure. You also have strong programming skills and have the ability to create and maintain complex pricing models in several languages (C++, VBA). The reality is in today’s marketplace these are the same qualities that 90% of your competition also possess. So just how do you plan on standing out from the pack?

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Interviews for hedge fund jobs … We don’t want you to get blind sided by this question. It’s a good one.

Q: Inside of a dark closet are five hats: three blue and two red. Three smart men go into the closet, and each selects a hat in the dark and places it unseen upon his head. Each man knows both that the closet contains three blue hats and two red and that the other two men have the same knowledge.

Once outside the closet, no man can see his own hat. The first man looks at the other two, thinks, and says, “I cannot tell what color my hat is.” The second man hears this, looks at the other two and says, “I too cannot tell the color of my hat.” The third man is blind. The blind man says, “Well, I know what color my hat is!”

What color is the blind man’s hat and how do you know?

A: If the first man saw the other two both wearing red hats, he would know his own hat was blue. Since he says he does not know its color, the second and third both know that between them, they are wearing both blue, or else one red and one blue.

Therefore if the second man could see a red hat on the first or third, he would know his own hat was blue. So, when the second announces that he cannot determine his own hat color, he effectively tells the third that his hat is blue.

Special thanks for this interview question to Timothy Crack, author of Heard on the Street: Quantitative Questions from Wall Street Job Interviews

Although you probably won’t be given a Rubik’s Cube to solve during your hedge fund job interview, you should be ready to solve a puzzle of some sort. Make sure you think through the question before jumping into an answer. And, for goodness’ sake, answer the question that is asked! Nothing decreases your chance of getting a job you are qualified to do faster than not answering the right question.

Q: Picture a 10×10x10 “macro-cube” on the table. This big cube is made up of 1×1x1 “micro-cubes”. Your dog walks by and knocks the macro cube off with his tail, causing it to crash to the ground. When it hits, the impact causes the entire outer layer of micro-cubes to fall off. How many micro-cubes are on the floor?

A: First, don’t beat the dog, he was just happy to see you. This is a popular question and you should be ready for it. There are a couple ways to solve this. The first (not the best), is to count the number of cubes on each face and add them up. This math is confusing for most people.

The better solution is to focus on the structure of the problem. The original macro-cube and new smaller macro-cube hold the answer. The difference between their volumes is how many micro-cubes fell off. The volume of a cube is n cubed. The answer is, therefore, 10 cubed - 8 cubed. So, 1,000 - 512 = 488.

Note: A common mistake is for people to think because only one layer fell off, the solution is 10 cubed - 9 cubed.

Special thanks for this interview question to Timothy Crack, author of Heard on the Street: Quantitative Questions from Wall Street Job Interviews

Hedge fund job interviews are meant to test your ability to think on your feet. Before you draw any attention to your shoes, make sure they are polished and your socks match…

Q: Let’s say you need to get up very early for an interview - in fact, before sunrise. You don’t want to wake your spouse, so you need to select your socks in the dark. In your drawer you have 8 red socks and 11 blue socks that are otherwise identical. What is the minimum number of socks you will need to take out of your drawer and carry into the other room to ensure you have a matching pair?

A: An oldie but goodie, this question is commonly asked and the solution is quite simple. The answer is you need to take three socks, that’s it. Two socks can be different, but a third must match one of the first two.

Special thanks for this interview question to Timothy Crack, author of Heard on the Street: Quantitative Questions from Wall Street Job Interviews