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 a just 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 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 Barkeeper if you are up for a challenge

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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:
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The blonde woman:
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The man in the light suit:
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The brunette woman:
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You have 10 trees and you have to plant them in five rows, but each row must contain 4 trees.

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Barbershop

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He went into the first one and was shocked by the dirtiness and the hair everywhere. The place was a mess! He looked at the barber and the barber had a really messy haircut, all in his face and uneven. He went across the street to the other barber and saw the place was immaculate, clean and shining like new. The barber was nicely dressed and had a dazzling haircut: it was perfect. However, the man walked across the street and got his haircut at the shabby barbers.

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Why?

Bridge

Statement:
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There was a woman who desperately needed to get into Switzerland, and she knew she didn't have time to get a pass. It would take her at least six minutes to cross the bridge, but she managed to do it.

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Brain Teasers - Barkeeper

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Firefighter

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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.

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Bartender

Situation:
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How is this?

Hats

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  • The third from the front was wearing a red hat.
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The one who guesses the color of his hat wins the prize. Who is it?

Pirates

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Five pirates are trying to split up 1000 gold pieces. The rules are as follows:

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The pirates are infinitely greedy, infinitely ruthless (the more dead pirates the better), and infinitely intelligent.

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What is the highest amount of gold pieces that pirate #1 can keep and what would his proposal be?

Chicken

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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.

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How does he get himself, the fox and the two chickens across the river safely?


Brain Teasers - Lethal Duel

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Coins

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Imagine, we are sitting together at a perfectly round table. We both have an infinite pile of quarters. These are the rules of the game: “We'll take turns putting one quarter down on the table, no overlapping allowed, and the quarters must rest flat on the table surface. The first guy who can't put a quarter down loses."

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Who should start in order to win, why and how does your strategy work?

Marbles

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There are 8 marbles that weigh 1 ounce each, and 1 marble that weighs 1.1 ounces. The marbles are all uniform in size, appearance, and shape. You have a balance that contains 2 trays. You are only able to use the scale 2 times.

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How do you determine which marble is the heaviest using only the scale and marbles in 2 weighings.

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.

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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.
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Question:

The police instantly arrested the murdered. 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.

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Which box should you remove a marble from to determine the contents of all three boxes?


Brain Teasers - U2 Concert

Solved 2221 times | Rating: (4.4 / 5.0)
Difficulty: Intermediate | Style: Brain Teaser | Topics: Brain teaser

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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.”

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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?


Brain Teasers - Light Bulb

Solved 1674 times | Rating: (3.8 / 5.0)
Difficulty: Intermediate | Style: Brain Teaser | Topics: Brain teaser

Light Bulb

Situation:

You are standing in front of a room with one light bulb inside of it. You cannot see if it is on or off. Outside the room there are 3 switches in the off positions. You may turn the switches any way you want to. You can open the door and enter the room, but you cannot use a switch anymore afterwards

Question:

How can you determine which switch turns the light on and off?

Coins

Situation:

You have a pile of 24 coins. Twenty-three of these coins have the same weight, and one is heavier. Your task is to determine which coin is heavier and do so in the minimum number of weighings. You are given a beam balance (scale), which will compare the weight of any two sets of coins out of the total set of 24 coins.

Question:

How many weighings are required to identify the heavier coin?

Truth or Lie

Situation:

You are in a room with 2 doors leading out. Behind 1 door is a coffer overflowing with jewels and gold, along with an exit. Behind the other door is an enormous, hungry lion that will eat anyone opening the door.

You do not know which door leads to the treasure and exit, and which door leads to the lion. In the room you are in with 2 men. The first is a knight, who always tells the truth, and a knave, who always lies. Both of these individuals know what is behind each door. You do not know which individual is the knight, or which one is the knave.

Question:

You may ask one of the individuals exactly 1 question. What should you ask in order to be certain that you will open the door with the coffer behind it, instead of the hungry lion?

Dogs

Situation:

Two scruffy dogs were walking down the street. The first dog turned to the other and said, "Do you realize that if one of your fleas jumped onto me we would have the same number of fleas?" The second replied, "Yes, but if one of your fleas jumped onto me I would have five times as many fleas as you."

Question:

How many fleas are on each dog to begin with?