67 Consulting Brain Teasers With Answers
Consulting case interviews can include full cases as well as brainstorming, estimation, brain teasers etc. So, what is a brain teaser? The definition of brainteaser is “a puzzle or problem whose solution requires great ingenuity.” In other words, a brain teaser is a short riddle designed to challenge your ability to think logically and make not immediately obvious connections. And your ability to solve a brain teaser gives an indication to the interviewer about how flexible your mind is and if you can think logically. Additionally, it can indicate if you give up easily when you encounter a difficult problem, quality firms certainly don’t want in future consultants.
Before we dive into various types of brain teasers, and then 67 consulting brain teasers and answers, we would like to share with you an interactive download we prepared for you as a gift, based on FIRMSconsulting book on brain teasers for consulting, banking, and tech interviews. This download includes 20 brain teasers not covered in this article, including explanations on how to approach solving each of those brain teasers. You can get a link to download your copy below. It is completely free. Enjoy!
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Brain teasers as part of your consulting case interview preparation
So, as is clear from the above, consulting brain teasers should be a part of your case interview preparation. It helps to keep your mind sharp and helps you develop a habit of solving problems calmly and confidently, but with a sense of urgency. And the most important part of solving a brain teaser is how you approach a problem. Just blurting out a correct answer because you already heard a particular brain teaser before will not win you points. Similarly, giving an incorrect or illogical answer or arguing with the interviewer saying your answer is correct will also usually hurt you.
For example, imagine the brain teaser interviewer gives you is as follows. “It’s dark in your room. You have a lot of white socks and black socks in your drawer. You want to get a matching pair, but socks are not organized. All socks are identical except for the color. What is the minimum number of socks you need to take to get a matching pair to wear?”
Now imagine you say, “I would say two. The task is to find a minimum number of socks. A minimum number of socks could be as followed. The first sock you get is black, the second sock you get is black. Similarly, the minimum number of socks could be the first sock you get is white, the second sock you get is white.”
This is the actual answer we got from one of the members of FC community. This answer is incorrect.
If you try to push for it you will fail. The question is, “What is the minimum number of socks you need to take to get a matching pair to wear?” You need to read between the lines. In other words, “What is the minimum number of socks you need to take to guarantee you get a matching pair to wear?” The correct answer to this question can be found below in brain teasers with answers section.
Types of consulting brain teasers
What are some types of consulting brain teasers I can expect during a case interview?
The Estimation teaser or “How Many” Brain Teaser:
Another type of brain teaser, known as an estimation teaser or the “how many” brain teaser, is especially common in the world of management consulting interviews, and it’s a skill consultants will use in their careers. Many of the techniques we use to solve and teach estimation cases were developed by FIRMSconsulting, based on our years in management consulting. Examples of these types of questions are practically infinite: “How many marbles can you fit in a standard Subaru?” “How many boxes of tissues were sold in the average American pharmacy in 2019?” “How many driver’s licenses does Wisconsin allocate in a typical summer?” One of the most common questions from this category is “How many gas stations are there in the U.S.?” You get the idea.
These teasers can leave you entirely stumped. After all, how are you meant to determine answers when you’ve been given no solid data to work with? They can feel like non-starters, but that isn’t the case at all. Estimation teasers are one of the most important types of all because they’re the best at showcasing how you go about solving problems. The answer is not as important as the approach you use, the assumptions you made and how you test the final answer. There is a lot to teach here. Their lack of definite answers is exactly what makes them so valuable; there’s no way to cheat your way around them or to land a correct solution out of sheer good luck. As a matter of fact, the people who are asking you questions like this almost certainly don’t know the answers themselves. Because of this, you won’t find any estimation teasers in this post.
Estimation brain teasers require an exchange of ideas by nature, between the interviewer and interviewee, something which a written page cannot accurately replicate. Any attempt to condense the solution to an estimation teaser into one small paragraph would defeat its purpose entirely.
Refer to estimation cases in The Consulting Offer (for example The Consulting Offer, Season 1, with Felix) to learn how to answer these questions. You can enroll to receive access to all programs on StrategyTraining.com by becoming an Insider (Insider status is granted when you become an annual Premium member). Your ability to answer this type of question during consulting case interviews is crucial. This type of question may be asked separately or as part of a full business case.
Though we won’t explore this type of brain teaser any further in this post, try to practice them regularly on your own. Even outside of the consulting world, they’re some of the most useful mental exercises that you can perform.
If you need more details on how to solve estimation cases, we would like to share with you a comprehensive estimation cases guide download we prepared for you as a gift, based on FIRMSconsulting book on how to prepare for consulting case interviews. This download includes a step by step guide on how to solve estimation cases, including a detailed example with an answer. You can get a link to download your copy below. It is completely free. Enjoy!
FREE GIFT #2 BONUS TUTORIAL DOWNLOAD – A Comprehensive Estimation Cases Guide
The Math Brain Teaser, Math Puzzles and Math Riddles:
Examples of mathematical brain teasers are probability questions. This barely qualifies as a brain teaser since it tests your math skills vs. your critical thinking and problem-solving ability.
Mathematical brain teasers can be intimidating, but they’re usually relatively straightforward in nature, even if they don’t initially seem to be. If you do a real deep dive, you’ll find some that require an extensive array of equations, formulas, and calculations in order to reach their solution.
On the other hand, the simpler, less specialized ones tend to focus on probability.
Interestingly, mathematical teasers can be a little difficult to identify since they often don’t involve numbers outright, whereas other types of brain teasers occasionally do. This can be a good thing since it encourages you to approach the problem with an open mind rather than an assumption that you’re going to have to adhere to tried and true math-solving techniques.
These days, most people associate math with subjects like computer science, but it’s important to remember that it didn’t start that way. At its core, the system of mathematics is designed to help us understand functions of the natural world, not to overly complicate them. When it comes to brain teasers, math is your friend!
The Riddle Brain Teaser:
In such a brain teaser the interviewer gives you particular problematic situation and asks you to find a solution. Riddles are the type of brain teaser that most requires you to think in an unconventional manner. They typically feature language that tries to misdirect you and often involve words and phrases that don’t mean what they initially appear to. These tend to be the most difficult type of teaser since they’re the ones that most aggressively push you out of your comfort zone. They can also be the most rewarding; there are fewer things more satisfactory than coming up with a single simple solution to a riddle that first seemed impossible.
One example that will appear later below is the following: “If a plane crashes directly on the border between the U.S. and Mexico, where will the survivors be buried?” Another example is a question about a farmer, fox, carrot and rabbit below.
When solving a riddle, the most important thing that you can do is identify it as just that—a riddle. Once you recognize that a question is most likely trying to trick you, you can be much more wary, and thereby avoid falling into its traps. Each word in a riddle tends to be carefully considered so be sure not to overlook anything—not even the tiniest scrap of punctuation. To the best of your ability, try to consider the information presented to you in a vacuum. Assumptions and snap judgments are a riddle master’s worst enemy. Above all else, remind yourself that you can solve anything if you put your mind to it. Relax, take your time, and—of course—enjoy!
“Why is” Brain Teaser:
“Why”-type brain teasers are used to test your ability to analyze the world around you. They can be some of the most difficult teasers to approach since many people will often have trouble knowing where to even begin. They often take a widely accepted quirk of the world around you and challenge you to propose a reason for why that thing works the way it does. One example that will appear later in this book is the following: “Why is a tennis ball fuzzy?” This is a commonly used “why”-type teaser that highlights something which the majority of people have never questioned.
Working through this type of teaser is a great way to begin thinking more critically about our surroundings, especially those which have been created or engineered by other people. We accept most modern conveniences for what they are, never thinking to question what made them that way—but nothing ever works a certain way “just because.” Everything that we use that is menmade is crafted with intention, and the more that we can train ourselves to recognize that fact, the more effectively we’ll be able to solve problems of our own—even when we don’t have a clue, for instance, about the history of tennis.
Job Interview Questions That Are Not Brain Teasers
Some job interview questions may be difficult but may not be a brain teaser. Such questions often ask something about you vs. about some external problem you need to solve. Examples include:
“Are you more of a hunter or a gatherer?”
“If you were a box of chocolates, what kind of chocolates would you be and why?”
“How honest are you?”
“How would you explain the internet to a 3-year-old?”
These job interview questions can mostly be divided into two opposite realms: subjective and knowledge-based.
A subjective job interview question tends to have no correct answer, or at least an answer that depends on the person answering it. In a job interview, this might look like the typical prompt of “What is your greatest weakness?” or “Do you see yourself as more of a leader or a follower?” There are certainly right and wrong ways to go about responding to a question like this, but you can succeed for the most part simply by being honest about your experiences and abilities. In other words, a subjective question will never be trying to trick you in the same way that a brain teaser often will.
A knowledge-based job interview question measures your competence in a particular area; often a highly specialized one. When a job interviewer presents you with one of these, they’re trying to gauge your familiarity with a topic that will likely be central to the position for which you’re applying. You can think of these questions as the type that you might find on a high school history quiz. As long as you have your facts straight, you should be able to answer knowledge-based questions easily without taking too long to contemplate and problem-solve.
Compared to these other types of questions, brain teasers can be both easier and harder, depending on how you tend to problem-solve. You’ll never have to make an argument for yourself as a candidate when you’re dealing with a brain teaser, and you also won’t have to study a pile of facts beforehand. You can, however, increase your general aptitude to solve brain teasers via practice. Think of brain teasers like exercises for your mind. Your brain is a muscle like any other, and the more you use it, the stronger it will get. That’s why this post exists: to provide you with an additional opportunity to practice and get better at solving brain teasers. With that in mind, that’s another element of brain teasers that differentiates them from many other types of job interview questions: When you relax and take your time, they can be a whole lot of fun!
Practice consulting brain teasers with other FC members
The good news is you can become better at solving brain teasers by practicing brain teasers on a daily basis. Below you will find some consulting brain teasers with answers. You can also join our Consulting Case Interviews facebook group where we post new brain teasers with answers on a daily basis and you can engage in conversation with other members of FC community about how to solve a particular brain teaser or about anything related to case interview prep. Everyone is welcome to join.
Consulting brain teasers with answers
Now, let’s look at some actual brain teasers. When you read each brain teaser try to calmly, confidently and with a sense of urgency solve it. Think through the problem and think through it as slow as your brain needs to get to the answer.
I remember when I was studying difficult subjects in university if I would try to go through my reading fast I would get lost. Instead, what I needed is to slow down and carefully think through all the connections the author was making to explain a particular point. Taking the time to think through a problem in steps often leads to much faster and better results versus rushing through it.
We see it all the time with members using The Consulting Offer training and even members using our advanced consulting skills training. Members who rush through the material, jump from episode to episode, from program to program, trying to find shortcuts and get through the material fast don’t do as well as members who are diligently working through the programs in the order in which we recommend it, carefully absorbing and mastering various concepts and approaches.
This same logic is applicable in solving brain teasers. If you rush you will probably get to the wrong answer.
For example, if we look again at a brain teaser we looked at above, the one about socks. Some candidates may immediately start panicking, “Oh, this is probably statistics. I need to understand probabilities. Oh my God, I don’t know how to solve it!”
Yet, all you need to do is to imagine you are in a dark room, there are white and black socks in the drawer. You need to get a matching pair. What are the possible scenarios? Well, you can get 2 socks but then there is no guarantee they will match.
Let’s say you get 3 socks, the next lowest number. What are the possible scenarios? Well, you could get 3 black socks, 3 white socks, 2 white socks, and 1 black sock or 2 black socks and 1 white sock. In each possible scenario, you end up with a matching pair. You see, when you calmly think through the problem, when you let your brain to process the information, the answer is easy and obvious. The key is to trust that you are smart and you will figure it out, and let your brain work through it at a speed it is comfortable at to figure it out.
And have fun with it. As you solve any cases during your case interview preparation or during an actual case interview have fun with it. Try to enjoy it. Having a solid problem-solving skill is powerful. You can do a lot of good in the world if you are good at problem-solving. So enjoy the process and trust in your ability to figure things out.
Practice consulting brain teasers
It’s important to note that difficulty is subjective, especially when it comes to problems that are structured with the goal of getting you to think outside of the box. If you find yourself stuck on a brain teaser, try working on some different ones before returning to it, and rest assured that you’ll get faster and faster as you familiarize yourself with reliable methods of problem solving.
If you want to check your solutions or if you just can’t seem to figure out a particular brain teaser no matter how much you scrutinize it, you can always flip to the bottom of the section, which contains solutions for every brain teaser. Each numbered solution will contain an “Answer” which is a straightforward statement providing the correct response to the teaser, and, where needed an “Explanation,” which goes into greater depth in examining the strategies or thinking pattern that one might employ in solving that particular teaser. You’re strongly advised to read the “Explanation” parts of the answer key, even if you were able to come to the correct conclusion by yourself. Oftentimes, these bits will highlight ways to optimize your thinking, making future brain teasers of a similar nature that much easier.
With that being said, get ready: It’s time to hit the mental gym.
Simple consulting brain teasers
The following 41 brain teasers are grouped under the “Easy” label, but that doesn’t mean that they won’t be challenging. In fact, some people find brain teasers like this to be the most difficult of them all because of their simplicity. If you’re used to relying on calculations and complex lines of logic, you’re best advised to set aside any preconceptions about how you should go about addressing these problems.
The most important tip to keep in mind for this section is to look very carefully at each question. If it seems too easy, it’s probably misleading you—and the same is true if it seems too hard. Keep an eye out for tricks of phrasing, double meanings, and convergence of the literal with the metaphorical. You’re looking for an “Aha!” moment that will frame the original teaser in an entirely new light.
Let’s start with a simple riddle. Ready? Set. Go!
(1) A farmer is trying to cross a river. He is taking with him a rabbit, carrots and a fox. He has a very small raft so he can only bring one item at a time across the river. How does he cross the river? Assume that the fox does not eat the rabbit if the farmer is there. Assume both rabbit and fox are not trying to run away.
This riddle can be solved easily if you put yourself in place of Jason.
(2) Jason’s father has 4 children; Suzan, Jeffrey, Jennifer. Who is the fourth?
The answer to this one will likely immediately be intuitive and then you can check the answer by thinking through the steps logically.
(3) The day before yesterday John was 17. Next year he will be 20. What day is his birthday?
(4) Two fathers and two sons sat down to eat eggs for breakfast. They ate exactly three eggs, each person had an egg. Can you explain how?
For this one, again, if you carefully think through connections the answer is obvious.
(5) Your mother’s brother’s only brother-in-law is asleep on your couch. Who is asleep on your couch?
This was the most popular riddle we posted so far in our consulting case interviews facebook group. We broke down this question above.
(6) It’s dark in your room. You have a lot of white socks and black socks in your drawer. You want to get a matching pair, but socks are not organized. All socks are identical except for the color. What is the minimum number of socks you need to take to get a matching pair to wear?
Easy one if you carefully think through connections. Assume a speaker is not looking in the mirror.
(7) Brothers and sisters I have none but this man’s father is my father’s son. Who is the man?
(8) What has a head and a tail, but does not have a body?
(9) John’s father has three sons: Jeffrey, Jack and _____ ?
This one is similar to the earlier brain teaser.
(10) 2 mothers and 2 daughters were fishing. They managed to catch one small fish, one big fish, one medium fish. Since only 3 fish were caught, how is it that they each took home a fish?
This one is a piece of cake, if you pay attention.
(11) How many times can you subtract the number 5 from 25?
Another fun, easy one.
(12) What has many keys but cannot open any doors?
This one is very intuitive.
(13) What is something you can keep after giving it to someone else?
(14) How many apples can you put into an empty containter?
Here is another easy one to help you warm up.
(15) When you add 2 letters, a 5 letter word becomes shorter. What is it?
Another simple one if you visualize what is happening.
(16) How far can a dog run into the woods?
And another fun one.
(17) A cowboy rides into town on Monday. He stays from 2 days and leaves on Monday. How is this possible?
(18) A man went for a walk and got caught in the rain. The man did not have an umbrella and he was not wearing a hat. His clothes got soaked but not a single hair on his head got wet. How is it possible?
And here is an obvious one.
(19) How many months have 28 days?
This one is intuitive.
(20) What is an odd number where if you take away one letter from it it becomes even?
And I love this one.
(21) What invention lets you look right through a wall?
(22) What never asks a single question but is often answered?
(23) The more you take the more you leave behind.
(24) What is full of holes but still holds water?
(25) It goes in dry and it comes out wet. The longer it is in the stronger it gets. What is it?
(26) A family lives in a large apartment building, on the 17th floor. They have a son. Every morning he takes the elevator from the 17th floor to the ground floor and goes to school. In the afternoon he uses the elevator to get to the 6th floor and then uses the stairs for the remaining floors. Why?
(27) You hold it without using your hands or arms. What is it?
(28) One brick is one kilogram and half a brick heavy. What is the weight of one brick?
(29) If Rebecca’s daughter is my daughter’s mother. What am I to Rebecca?
(30) Say speaker backward.
(31) When you have me you immediately feel like sharing me. But once you share me you no longer have me.
(32) If electric train is traveling south, which way is smoke going?
(33) How many times can you subtract 10 from 100?
(34) Amanda’s mother had 3 children. First one was named April, second child was named May. What is the name of the 3rd child?
(35) The more there is, the less you see. What is it?
(36) What always ends everything?
(37) I have seas without water, coasts without sand, towns without people, and mountains without land. What am I?
(38) You can find it in Mercury, Earth, Mars, Jupiter and Saturn, but not in Venus or Neptune. What is it?
(39) What coat is best put on wet?
(40) It’s at the center of gravity. You can also find it in Venus, but not in Mars. What is it?
(41) A clerk in a butcher shop stands six feet 5 inches tall and wears size 11 shoes. What does he weigh?
Answers to Simple consulting brain teasers
- Takes the rabbit, sails back. Takes the fox, and sails back with the rabbit. Drops off the rabbit and takes carrots; sails back and takes the rabbit. However, there is an alternative answer. Take rabbit, sail back to take carrots, sail back with the rabbit to take fox, come back again to take the rabbit. The carrots and fox in 2nd step are interchangeable.
- Jason. Jason, Suzan, Jeffrey, and Jennifer are siblings.
- December 31. The day before yesterday is 30th December when he was 17, yesterday was the 31st December when he turned 18, today is the 1st of January and he will be 19 this year, and next year he will be 20.
- Three generations of one family. One of the ‘fathers’ is both a son and a father.
- The answer is your dad, assuming your mother and father are married.
- You need at least 3 socks. If the first sock is black and the next sock is black you got a pair. If the first sock is black, the second sock is white, you will get a pair regardless of if the third sock is white or black.
- The man is the speaker’s son.
- A coin.
- 3 generations of people went fishing. Grandma, mom and daughter.
- Only 1 time.
- Piano or any keyboard.
- Your word.
- Only one. After that it will not be empty.
- ANSWER: Short. EXPLANATION: Speaking this brain teaser out loud makes it a lot more difficult since you don’t have the visual aid of the word “shorter.” When you write it down, however, the solution is right in front of you. A word doesn’t lessen in length if you add two letters to it; rather, it becomes “shorter”—it literally turns into the word “shorter.” And if you subtract those two letters, you end up with your answer: “short.”
- Only until a do gets to the middle of the woods. After that a dog will be running out of the woods.
- ANSWER: His horse is named Monday. EXPLANATION: There are multiple ways to read this question. Most people’s default will be to assume that it’s referencing a day of the week in which case it has no possible solution. Two days after Monday will always be Wednesday, regardless of the month, year, et cetera. With that in mind, how can we find our solution? Something like “time travel” may seem to be the only remaining possibility if “Monday” is in fact referring to the day of the week. But there’s no actual confirmation of this within the brain teaser itself. The information we’re given is that the a man rides into town on Monday. This must mean that he physically rides upon something called “Monday”—most likely a horse.
- ANSWER: The man is bald. EXPLANATION: This type of brain teaser makes us challenge our assumptions about the world. Of course everyone knows that some people are bald. However, due to bald men being the minority compared to those with hair, our default image of a “man” typically is not a bald one. Working with this default image, this brain teaser can be quite puzzling indeed—but if we allow ourselves to think outside the box, the answer becomes obvious.
- 12 months. Each month has at least 28 days.
- A window.
- A doorbell.
- A sponge.
- A tea-bag.
- Because he cannot reach buttons higher than 6.
- Your breath.
- 1 brick is 2 kg heavy.
- I am Rebecca’s daughter.
- “Speaker backward.”
- ANSWER: A secret. EXPLANATION: This is actually a very easy brain teaser to unravel, so long as you follow each step to its logical conclusion. First, recognize that you’re looking for an “it”—an object, entity, or concept. Next, consider the single fact about this “it” that’s been provided to you: By nature, it cannot be shared. What thing is defined by its exclusivity? A secret. If you tell a personal secret to someone, it is no longer a secret by definition.
- There is no smoke since it is an electric train.
- Only 1 time because the next time you will be subtracting 10 from 90.
- The letter G.
- A map.
- The letter R.
- A coat of paint.
- The letter V.
- ANSWER: Meat. EXPLANATION: Oftentimes, brain teasers will try to mislead you with extraneous information, while simultaneously masking any facts that are of true importance. Here, the key to solving the riddle lies within the first three words: “John the butcher.” Part of a butcher’s professional duties is the weighing of meat to sell to customers. The brain teaser distracts you with information about John’s size, but that isn’t enough on its own to determine his weight; therefore, “weigh” must not be operating as a reflexive verb. John regularly calculates the weight of something else, and since he’s a butcher, that “something” is meat.
Medium difficulty consulting brain teasers
And here is a more difficult one for you.
(1) What do you notice about the following sequence of numbers?
– 8, 11, 4, 9, 1, 6, 3, 0
And here is another somewhat difficult one.
(2) You have a 3-gallon jug and 5-gallon jug. You need to fill the 5-gallon jug with exactly 4 gallons of water. What would you do?
Another relatively easy one if you keep your mind open.
(3) How can you throw a ball, make it stop and travel in the opposite direction all while touching the ball only once.
Similarly, this one is relatively easy if you keep your mind open.
(4) Imagine you had to put a coin into an empty bottle, then close the bottle with a cork. How could you take the coin out without removing the cork or breaking the bottle?
This one if one of my favorites.
(5) You have 3 boxes. One is with apples, one is with oranges and one has a combination of apples and oranges. All boxes are incorrectly labeled. In other words the label identifies incorrect content of the box. You can only open 1 box and without looking at the box you can take out 1 fruit and look at it. How can you label all the boxes correctly?
Here is another one of my favorites.
(6) You’re in a room with 3 light switches. Each light switch controls one of 3 light bulbs in the next room. How will you determine which switch controls which bulb if you can inspect the other room only once and cannot see into the other room from the other?
Here is another fun one.
(7) How can a pant’s pocket be empty yet still have something in it?
(8) Which weights more, a pound of feathers or a pound of bricks?
An interesting one.
(9) A little girl fell off 29-meter ladder but did not get hurt. How is it possible?
And here you will need to do some math.
(10) Using only addition how can you get to number 1,000 by adding up eight 8’s?
(11) Heavy it is but reverse it’s not. What is it?
(12) What comes once in a minute, twice in a moment, but never in a thousand years?
(13) It’s as light as a feather. However, most people cannot hold it for longer than 2 minutes. What is it?
(14) What gets more wet while it dries?
(15) A man shaves several times a day but still has a beard. Who is he?
(16) You’re driving a city bus. At the first stop, 3 women get on. Then at the second stop, two children get on. At the 3rd stop, one man gets off and a man gets on. The bus is yellow and it’s snowing outside in December. What is the hair color of the bus driver?
(17) Two boxers are in a match scheduled for 12 rounds. One of the boxers gets knocked out after only 5 rounds, yet no man throws a punch. How is this possible?
(18) If a plane crashes directly on the border between the U.S. and Mexico, where will the survivors be buried.
Answers to Medium difficulty consulting brain teasers
- The digits are in alphabetical order. (Eight, eleven, four, nine, one, six, three, zero)
- Fill the 3-gallon jug. Pour it into the 5-gallon jug. Fill the 3-gallon jug again and pour slowly into the 5-gallon jug until it is full. Because the 5-gallon jug already had 3 gallons in it only 2 more gallons will fit. And now you have 1 gallon in the 3-gallon jug. Remove water from the 5-gallon jug, pour 1 gallon from the 3-gallon jug. Refill the 3-gallon jug and pour into the 5-gallon jug. You now have exactly 4 gallons of water in the 5-gallon jug. OR, there is an alternative way. Fill the 5-gallon jug, pass it over to the 3-gallon jug. Now you have 2-gallons remaining in the big jug. Empty the small jug and pass the 2-gallons from the big to the small jug. Now you have space for 1-gallon in the small jug. Fill the big jug completely then seek to fill the 3-gallon jug with the 1-gallon that was missing there. Now you have 4-gallons in the big jug.
- Throw it up.
- Push the cork in.
- Here is an actual long explanation from one of FC members: “Let’s call 3 label Os (all oranges), As (all apples), OA (a combination of orange and apple. Since all boxes are incorrectly labeled, possible fruits with each box are: OA (all oranges, all apples), As (all oranges, combination of both), Os (all apples, combination of both). Next, take out 1 fruit from one having label OA. Scenario 1: if it’s orange, then the box is with all oranges, correct label must be Os. Then the one with As label must have a combination of both fruits, correct label OA. The last box, correct label As. Scenario 2: if it’s an apple, similar logic.” This is a correct answer, but it will help to make it more crisp during an actual interview.
- An actual correct answer from one of FC members: “Let’s call 3 switches 1, 2, 3. Turn switch 1 for the longest time, for example, 2 minutes; switch 2 for 20s. Go to the other room. The hottest light bulb is controlled by switch 1, the slightly warm bulb switch 2, the remaining bulb switch 3.” There is an alternative faster way to do this. Turn switch one for a short time, long enough for the bulb to warm up. Put it off. Then turn on switch 2. Go into the room. Warm bulb which is not on will be switch 1, bulb that is on will be switch 2 and the other one will be switch 3.
- There is a hole in the empty pant’s pocket.
- Neither. They both weigth 1 pound.
- She fell off from the lowest step.
- The letter M.
- A towel.
- A barber.
- Your color since you are driving the bus.
- The boxers were women.
- ANSWER: They won’t be buried. At least, not any time soon.
EXPLANATION: The issue of geographical boundaries is an irrelevant one because the survivors won’t be buried at all. The victims, of course, are another matter, but not one that matters to this particular question. Always be on the lookout for questions that, despite being confidently stated, don’t actually make any sense under closer examination!
Hard consulting brain teasers
Next, let’s take a look at this much more difficult riddle.
(1) Who makes it, has no need for it. Yet, who buys it, has no use for it. And who uses it can neither see nor feel it. What is it?
A sad and difficult one.
(2) A woman was born in 1996 and died in 1957. How is this possible?
This one is quite difficult.
(3) I have a dog that has 3 puppies: Barney, Cookie, and Sun. What is the mother’s name.
Here is a fun but slightly difficult one.
(4) What was the world’s tallest mountain before Mount Everest was discovered?
Here is a poetic but somewhat difficult brain teaser.
(5) What is at the beginning of eternity, the beginning of every end, the end of every place, and the end of time?
(6) What word looks the same backward and upside? Hint: There is more than 1 answer. One of the answers has something to do with water.
(7) Why tennis ball is fuzzy?
Answers to hard consulting brain teasers
- The answer is very dreary. A coffin.
- 1996 and 1957 were the room numbers in the hospital.
- Mount Everest.
- This is a lateral thinking problem. The answer here has nothing to do with the meaning of the words but instead with the words themselves. The answer is the letter e.
- SWIMS, NON.
- ANSWER: The fuzz on a tennis ball ensures that it moves more slowly through the air.
EXPLANATION: This is a very common brain teaser, and one that initially leaves most people drawing a complete blank. Don’t panic—that’s the worst thing you can do in a situation like this. Your interviewer certainly won’t expect you to have an advanced knowledge of tennis ball construction techniques, so it’s completely okay if you don’t know where to start. Take a step back and consider your objective. It’s true that tennis balls are fuzzy, and that this characteristic distinguishes them from balls used in other types of sports. With this established, your next task is to figure out what unique features of tennis would require a modification to its particular type of ball. After puzzling this out for a while, you’ll come to the conclusion that it’s the only sport in which the ball’s time in the air is the most important factor. This means that the fuzz must be somehow related to that particular aspect. From here, you can conclude that it helps to slow the ball, thereby making the game actually playable. You can figure all of that out without even the slightest knowledge of physics!
It is difficult to predict which brain teaser questions you will likely to get during case interviews. But it certainly does not hurt to work out your problem-solving and critical thinking “muscles” with daily practice.
The “hardest logic puzzle ever” (originally published in 1996 by the Harvard Business Review)
If worked through those brain teasers and riddles, and if you’re still concerned about interviews, or if you just feel up for an even bigger challenge, try looking up other pre-written brain teasers in your spare time. Though this brain teasers article contained brain teasers with various levels of difficulty, there are far more advanced brain teasers, riddles and logic puzzles all over the internet. Just one example is the so-called “hardest logic puzzle ever,” originally published in 1996 by the Harvard Business Review.
Mathematician Richard Smullyan, with a nickname “the undisputed master of logical puzzles” developed a very challenging brainteaser. Smullyan’s colleague, an MIT logic professor named George Boolos, called it “the Hardest Logic Puzzle Ever” and it will become very clear why.
If you want to put your new skills to the test, go ahead and give it a shot:
You’re given the opportunity to communicate with three divine entities, which will be referred to in this brain teaser as A, B, and C. One of them always speaks the truth, one of them always lies, and one of them responds randomly with either the truth or a lie. They have a unique language that has never been translated by mortals, and though they can understand any language spoken to them, they will only respond with their own. Furthermore, the entities will only speak one of two words to you: “ja” and “da.” One of these words means yes and one of them means no, but you have no idea which is which.
You may ask these entities a total of three questions, which they will answer in their language. Only one entity can be addressed with each question. Using this, find a way to determine the identity of all three of them.
Before you start to brainstorm, take a moment to reflect on the different strategies that you’ve devised throughout your time spent working through previous brain teasers.
The “hardest logic puzzle ever”: Solution
If you find yourself scratching your head, know that you’re not alone; this brain teaser is cited as the world’s most difficult for a good reason! At the same time, though, it isn’t impossible. Everything that you need to know in order to find the correct solution is laid out in the riddle itself. There are no tricks or shortcuts this time; the steps that you need to take are purely logical. If you’re completely stumped, the internet can give you a hand—but try to avoid skipping to a solution right away. Instead, pull out a pen and paper and give it your best shot!
Here are the three questions you should ask, according to Nautilus:
1. To god A: “Does ‘da’ mean ‘yes’ if and only if you are True and if and only if B is Random?” (We supposed A said, “ja,” making B True or False).
2. To god B: “Does “da” mean ‘yes’ if and only if Pluto is a dwarf planet?” (We supposed B said, “da,” making B True.)
3. And to god B (True) again: “Does ‘da’ mean ‘yes’ if and only if A is Random?” Since B’s True, he must say “da,” which means A is Random, leaving C to be False.
Don’t worry if you’re still confused. You can start thinking through the solution with this 2008 paper, which states they came up with the easiest answer to the brain teaser. Or maybe you’d rather not dive right into the biggest challenge possible, which is completely understandable. In any case, whether or not you feel confident in your brain teaser solving abilities, don’t stop practicing. Bodybuilders don’t quit the gym just because they achieved their ideal weight, and the same principle applies here. Keep it up, and don’t let yourself get out of shape. There are numerous books, articles, and websites dedicated to the compilation of brain teasers, and now that you’ve familiarized yourself with some of the essential techniques, you’ll be amazed at how quickly and easily you can solve many of them.
Whether you’re an aspiring consultant, a seasoned professional, or just a curious person with a bit of spare time, you can always benefit from a good cerebral workout. At the end of the day, you’re going to be the one to set your own challenges—and remember that even the toughest problems have their solutions. As long as you believe in yourself, anything is possible.
Hope you enjoyed these consulting brain teasers with answers we selected for you to practice with. If you have good consulting brain teasers to add to this article please let us know in the comments below.
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Kris Safarova (CEO, FIRMSconsulting.com, StrategyTraining.com)
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