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.
So, as is clear from the above, 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.
What are some types of brain teasers I can expect during a case interview?
The “How Many” Brain Teaser: For example, one of the most common questions from this category is “How many gas stations are there in the U.S.?” Refer to estimation cases in The Consulting Offer to learn how to answer these questions. Your ability to answer this type of question is crucial. This type of question may be asked separately or as part of a full business case.
The Math Brain Teaser: Examples are probability questions. This barely qualifies as a brain teaser since it tests your math skills vs. your critical thinking/problem-solving ability.
The Riddle Brain Teaser: In such a brain teaser the interviewer gives you particular problematic situation and asks you to find a solution. For example, a question about a farmer, fox, carrot and rabbit below.
“Why is” Brain Teaser: For example, “Why is a tennis ball fuzzy?”
Some 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?”
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.
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.
Let’s start with a simple riddle.
(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?
This is an easy one.
(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?
This one is relatively easy.
(8) What has a head and a tail, but does not have a body?
This one is easy.
(9) John’s father has three sons: Jeffrey, Jack and _____ ?
This one is similar to 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?
Here is another simple one.
(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?
This one is really simple.
(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?
This one is a piece of cake.
(22) What never asks a single question but is often answered?
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?
This one is quite easy.
(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?
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 a 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?
Here is a difficult one.
(6) What word looks the same backwards and upside? Hint: it has to do with water.
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.
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.
WANT DAILY CONSULTING BRAIN TEASERS PRACTICE (WITH ANSWERS)?: Join our Consulting Case Interviews group. It’s free and everyone is welcome to join.