Create an account and get free access to 50+ articles.
Sign up for free >>
BootCamp Articles

Articles read: 0/52

Brain teasers in case interviews are used to assess your ability to think quickly and out-of-the-box

Brainteasers are a special sub category of cases. In contrast to regular cases, they are less focused on multifaceted business problems and more on a single issue. The goal is to solve a problem that is usually not straightforward and requires out-of-the-box thinking.

Typical problems cover every-day life's topics and might even include unrealistic assumptions. All necessary information is usually included in the question, so that further assumptions are not necessary. Questions to the interviewer should focus on presenting solution approaches and checking if they will lead to the solution.

What should you expect during brainteasers?

First of all, in consulting case interviews, brainteasers are rarely used. Regular cases are considered as more suitable as they allow the interviewer to better test key skills needed in a consultant (structured, analytical and conceptual thinking).

During business cases, interviewers can add value through their expertise and a more fruitful and realistic interaction may arise, which is more in alignment to that of a consultant's daily life. Nevertheless, brainteasers provide the interviewer with valuable insights about the candidate's potential.

Brainteasers are an additional challenge to the candidate. They require a solution path different from standard frameworks. The candidate’s ability to recognize, structure and solve problems is tested at a different level. The necessary insights are usually hidden in the starting question and need to be deduced. For some brainteasers, an information overload can cover the essential hints. As a result, brainteasers put candidates under stress.

For a candidate, practicing brainteasers helps to focus on certain aspects. You can train your creativity, math skills and logical thinking with different questions. Because brainteasers require out-of-the-box thinking, you become more flexible in using and developing frameworks and solution paths. They also help to avoid excessive usage of standard frameworks.

How to solve brainteasers?

As with all case studies, the structure leading towards the solution of a consulting brainteaser is more important than actually finding the final answer.

  • Write down every piece of information you get. Listen very carefully because one specific word can convey the answer. Repeat the question to make sure you didn’t add or miss anything important.
  • Think of solutions or required information you might need without looking at the facts. There are three possibilities:

1. You’ll find a solution without any information. Sometimes common sense brainteasers can be solved this way. In this case, the only purpose of the starting information is to confuse you.

2. Both needed and given information match.

3. You need further information in order to be able to solve the brainteaser. In this case, convey to the interviewer how you would have solved it if that information were available. This will demonstrate your creativity.

  • Take notes of solutions that didn’t work and communicate the reason to the interviewer. Clearly communicate the reasons that would prevent you from repeating similar analysis.
  • Make the problem visible through schematics and graphs. These habits foster creative thinking.
  • Put yourself in the shoes of the person affected by the issue addressed by the consulting brainteaser. If the problem were your own, you might tackle it in a more creative way.

Quantitative brain teasers are about translating verbal problems into variables

Solve with equations

When you’re confronted with numbers, such as rates, percentages, amounts or a time, try to set up an equation. While brainteasers don’t require sophisticated math skills, they do require the knowledge of translating a verbal problem into variables.

Example: A man's youth lasted one sixth of his life. He grew a beard after one twelfth more. After one seventh more of his life, he married. 5 years later, he and his wife had a son. The son lived exactly half as long as his father. The man died four years after his son.

How many years did the man live?

Solution: The brainteaser requires you to formulate the facts into an equation. First, define the missing value. The question asks for the number of years he lived, so represent the age of death with the variable x. Then sum up the different periods of his life, which are either given as fraction of his lifespan or as an absolute number.

x/6 + x/12 + x/7 + 5 + x/2 + 4 = x

The solution of the equation is x = 84. The man lived for 84 years.

Brute Force

When the problem asks for a specific number, go for the trial and error approach. It is an efficient method if you know the possible number of solutions is restricted to just a few.

Example: Replace all 'x' with all of the digits 1, 2, 3, 4, 5 and 6 to make the statement true: xx * x = xxx

Solution: Instead of thinking about a complicated arithmetic solution, just plug in numbers until you reach the solution.

54 * 3 = 162

Qualitative brain teasers are about drawing the right conclusions out of the given information

Solve with Logic

Most brainteasers can be solved logically by inferring the right conclusions out of the given information. While that is, to a certain extent, necessary for every brainteaser, some will require special logical thinking. Make sure to prove that you draw the right logical conclusions from the given information.

Example: Five friends bought 10 cookies. To distribute the cookies, they have agreed to a rule: according to the order of their initial letters in the alphabet, Anton, Betty, Carl, Danielle and Emily each make a suggestion on how to split the cookies. So Anton starts first and Emily is last. A person is kicked out (and consequently doesn't receive any cookies), if they don't secure at least 50% of the votes with their suggestion. In that case, the next one makes a suggestion until an agreement is reached. What is the maximum Anton can demand without being kicked out?

Solution: Backwards induction will provide you with the answer. It is difficult to start right away with Anton’s decision, as we don’t know what the others would decide. So we have to figure out the others' decisions first:

If the game continues long enough for Emily to make a suggestion, she will be the only one left. So she will give herself everything.

If Danielle decides, she and Emily are left. Whatever Danielle says will be the final decision, because she makes up 50% of the votes. So Danielle will take everything herself.

If Carl decides, he has to convince at least one of the other two girls left. If he gives 1 cookie to Emily and keeps 9, Emily will agree because if Emily doesn’t agree, Danielle will decide. The case above then occurs, where Emily gets nothing.

If Betty decides, she also has to convince one of the other three left to receive 50% of the votes. If she gives 1 cookie to Danielle and keeps 9, Danielle will agree. If Danielle doesn’t agree, Carl decides. The case above then occurs where Danielle gets nothing.

If Anton decides, he needs two votes. If he gives 1 cookie to Carl, 1 to Emily and keeps 8, both Carl and Emily will agree because they are better off this way. If they don’t agree, Betty will decide. The case above then occurs, where Carl and Emily receive nothing.

Therefore, Anton can demand at max 8 cookies.

Solve with Brute Force

Similar to mathematical questions, if you get a brainteaser with a restricted amount of possible solutions, try a backwards approach. First, assume one of the solutions is correct and see if it works with the information you were given.

Example: I have a horse. Do you know what color it is? Allan said, "I guess it is not black". Brian said, "It is either brown or gray". Charlie said, "I know it is brown". I said, "At least one of you is right and at least one of you is wrong." What is the color of my horse if the color is one of the above?

Solution: The horse is brown, black or gray. So three options you have to check:
If the horse is brown, then everyone is right. This is not the answer. If the horse is black, then everyone is wrong. This isn't the answer either. Therefore, the horse is gray. To verify the answer, Allan was right, Brian was right, but Charlie was wrong.

Takeaways:

  • Brain teasers are not very common in consulting case interviews.
  • Your creative and out-of-the-box thinking is usually tested in brain teasers.
  • Brain teasers can usually be solved with brute force, logic or equations.

Check out our brain teaser Firefighter if you are up for a challenge

Do you have questions on this lesson? Pose it to our community!

Ask a question
Questions on this lesson
3 Can you please show me how you solved the equation (x/6 + x/12 + x/7 + 5 + x/2 + 4 = x)
Book a coaching with Hugo

2 Meetings

50 Q&A Upvotes

USD 149 / Coaching

Hi Cosma, Here is one way (not saying it's the only one :) First step: get all multiples of 2 to the same high denominator: x/6 + x/12 + x/7 + 5 + x/2 + 4 = x <=> 2x/12 + x/12 + x/7 + 5... (read entire answer)

Related case(s)

Brain Teasers - U2 Concert

Solved 9.6k times
Brain Teasers - U2 Concert Number sequence Situation: “You and I will take turns saying numbers. The first person will say a number between 1 and 10. Then, the other person will say a number that is greater than the first number. The difference between both numbers must be between 1 and 10. We will keep going back and forth in this way until one of us says the number 50. That person wins. You will start.”   Question: What number should you start with? U2 Concert Situation:  U2 has a concert that starts in just 17 minutes. To get there, all the band members must cross a bridge. Since the bridge is old, a maximum of two people can cross the bridge at any one time. To make matters worse, it is dark and there is only one torch. Anyone crossing the bridge must carry a torch. The torch cannot be thrown across the bridge. Instead, someone must walk it back to the other side. Each band member walks at a different speed. If two members cross at the same time, both must walk at the speed of the slower band member. Bono takes 1 minute to cross. Edge takes 2 minutes to cross. Adam takes 5 minutes to cross. Larry takes 10 minutes to cross. Question: Can the band make it to the concert in time? How will they manage this? Buckets Situation: You have a 5-gallon bucket and a 3-gallon bucket. (Assume that you have an unlimited supply of water and that the buckets do not have any markings for measurement. Question: How can you get 4 gallons of water into the 5-gallon bucket? Cigars Situation: A homeless man collects cigar butts. He uses 5 cigar butts to make a new cigar. Today, he has collected 25 cigar butts. Question: How many cigars can he smoke?
4.3 5 402
| Rating: (4.3 / 5.0) |
Difficulty: Intermediate | Style: Brain Teaser | Topics: Brain teaser

Number sequence Situation: “You and I will take turns saying numbers. The first person will say a number between 1 and 10. Then, the other person will say a number that is greater than the first number. The difference between both numbers must be between 1 and 10. We will keep going back and forth ... Open whole case

Brain Teasers - Motel

Solved 8.5k times
Brain Teasers - Motel Motel Situation: Three friends check into a motel for the night. The clerk tells them the bill is $30, payable in advance. They each pay the clerk $10 and go to their room. A few minutes later, the clerk realizes he has made an error and overcharged the trio by $5. He asks the bellhop to return $5 to the 3 friends who had just checked in. The bellhop sees this as an opportunity to make $2 as he reasons that the three friends would have a tough time dividing $5 evenly among them; so he decides to tell them that the clerk made a mistake of only $3, giving a dollar back to each of the friends. He pockets the leftover $2 and goes home for the day! Question:  Now, each of the three friends gets a dollar back, thus they each paid $9 for the room which is a total of $27 for the night. We know the bellhop pocketed $2 and adding that to the $27, you get $29, not $30 that was originally spent. Where did the other dollar go? Murder Situation: The midnight train is coming down the mountains. Art Farnanski seems to be sleeping in his seat. At the station, all the passengers get off the train except one. The conductor comes and taps him on the shoulder to let him know they have arrived. Art Farnanski does not answer. He is dead. Hours later the four people that had shared the train compartment with the dead man are at the police station. The man in the dark suit: "I'm innocent. The blonde woman was talking to Farnanski." The blonde woman: "I'm innocent. I did not speak to Farnanski." The man in the light suit: "I'm innocent. The brunette woman killed him." The brunette woman: "I'm innocent. One of the men killed him." Question: The police detective comes up to you and says: “I know that four statements are wrong and four are true. Who killed Farnanski? (Only one person is guilty).” Trees Statement: You have 10 trees and you have to plant them in five rows, but each row must contain 4 trees. Question: How is this possible?
4.6 5 451
| Rating: (4.6 / 5.0)
Difficulty: Intermediate | Style: Brain Teaser | Topics: Brain teaser

Motel Situation: Three friends check into a motel for the night. The clerk tells them the bill is $30, payable in advance. They each pay the clerk $10 and go to their room. A few minutes later, the clerk realizes he has made an error and overcharged the trio by $5. He asks the bellhop to return $5 ... Open whole case

Brain Teasers - Pirates

Solved 7.1k times
Brain Teasers - Pirates Pirates Situation: Five pirates are trying to split up 1000 gold pieces. The rules are as follows: Pirate #1 must divide the gold up in such a way that a majority of the pirates (including himself) agree to. If he does not get a majority vote, he will be killed, and pirate #2 will get to propose a solution to the remaining 3 pirates, and the same rules will follow. This continues until someone comes up with a plan that earns a majority vote. The pirates are infinitely greedy, infinitely ruthless (the more dead pirates the better), and infinitely intelligent.                        Question: What is the highest amount of gold pieces that pirate #1 can keep and what would his proposal be?             Chicken Situation: A man is traveling with a fox and two chickens, if he leaves the fox alone with the chickens the fox will eat the chickens. He arrives at a river and needs to cross it. He finds a small boat that can carry only him and one animal.          Question: How does he get himself, the fox and the two chickens across the river safely?
4.5 5 405
| Rating: (4.5 / 5.0)
Difficulty: Intermediate | Style: Brain Teaser | Topics: Brain teaser

Pirates Situation: Five pirates are trying to split up 1000 gold pieces. The rules are as follows: Pirate #1 must divide the gold up in such a way that a majority of the pirates (including himself) agree to. If he does not get a majority vote, he will be killed, and pirate #2 will get to propose ... Open whole case

Brain Teasers - Firefighter

Solved 6.6k times
Brain Teasers - Firefighter Firefighter Situation: A firefighter stood on the middle rung of a ladder, spraying water on a burning house. He then climbed up 6 rungs before the heat of the flames caused him to come down 10 rungs. After some minutes he was able to climb 18 rungs to the very top of the ladder. Question: How many rungs did the ladder have? Bartender Situation: There are two twin old men that go into the same bar every day. The bartender at the bar hates one of the twins, but there is only one way he could tell the difference between them: The one that he hates drinks very slowly and the one that he likes drinks fast. One day the bartender decides to kill the one that he hates. So when they came in that day he put the same amount of the drink in their cups, the same amount of ice, and the same amount of poison. When they are both done with their drinks the one that the bartender hates dies, but the one he likes lives. Question: How is this? Hats Situation: There are 4 people sitting in a row, trying to win a riddle. The one in front was wearing a red hat. The second from the front was wearing a blue hat. The third from the front was wearing a red hat. The last was wearing a blue hat and is blind-folded. Each of them was informed that they are all wearing a hat, the last person is blind-folded and that there are 2 red and 2 blue hats. They can only see the persons in front of them and are not allowed to turn around and see behind them. Question: The one who guesses the color of his hat wins the prize. Who is it?  
4.5 5 65
| Rating: (4.5 / 5.0) |
Difficulty: Intermediate | Style: Brain Teaser | Topics: Brain teaser

Firefighter Situation: A firefighter stood on the middle rung of a ladder, spraying water on a burning house. He then climbed up 6 rungs before the heat of the flames caused him to come down 10 rungs. After some minutes he was able to climb 18 rungs to the very top of the ladder. Question: How m ... Open whole case

Brain Teasers - Lethal Duel

Solved 5.9k times
Brain Teasers - Lethal Duel Duel Situation: Three men, Adam, Bertie and Charlie, agree to take part in a lethal three-way duel. They each have a pistol and several rounds of ammo, and they draw lots to see who will shoot first and who second. Then they stand an equal distance apart, and they take turns to fire. When it is a player's turn, he can take one shot at any target of his choice. Then, the turn passes to the next player. The duel continues until only one player is left alive. For simplicity, we can ignore the possibility of a player becoming injured and unable to shoot: a player is either alive or dead. We also assume that each player chooses to play in such a way as to give himself the best chance of winning. Now Adam and Bertie are crack shots and will always get a kill, but Charlie is only a moderate shot and will only get a kill two thirds of the time. All three men know this. Question: Of the three men, who has the best chance of winning the duel? Murder Situation: A man was found murdered on Sunday morning. His wife immediately called the police. The police questioned the wife and staff and got these alibis: The Wife said she was sleeping. The Cook was cooking breakfast. The Gardener was picking vegetables. The Maid was getting the mail. The Butler was cleaning the closet. Question: The police instantly arrested the murderer. Who did it and how did they know? Boxes Situation: Three closed boxes have either white marbles, black marbles or both, and they are labeled white, black and both. However, you're told that each of the labels is wrong. You may reach into one of the boxes and pull out only one marble. Question: Which box should you remove a marble from to determine the contents of all three boxes?
4.5 5 85
| Rating: (4.5 / 5.0) |
Difficulty: Intermediate | Style: Brain Teaser | Topics: Brain teaser

Duel Situation: Three men, Adam, Bertie and Charlie, agree to take part in a lethal three-way duel. They each have a pistol and several rounds of ammo, and they draw lots to see who will shoot first and who second. Then they stand an equal distance apart, and they take turns to fire. When it is a ... Open whole case