Consulting Brainteasers

of Consulting Case Study Training

You’ll probably hear a lot about Brainteaser problems in Consulting interviews, but they rarely actually appear in consulting interviews these days. Guesstimate Cases and Business Situation Case Studies are now used in virtually all Case Study interviews for Consulting, while many of the firms have abandoned Brainteasers altogether. Brainteasers were once used to see how a candidate responds under pressure, but over time interviewers realize that the full Case Studies are a better guide to both the candidate’s ability to respond under pressure and the candidate’s aptitude for the skill set actually required by Consultants on the job.

That said, understanding what a brainteaser problem is and going through a few examples is worth doing, in case you come across one. The creative thinking involved in these problems can also help foster creativity in other cases.

Brainteasers tend to be short, generally unusual problems where the answer sometimes appears counter-intuitive—if there is a definitive answer at all. Our key recommendation, if you face a Brainteaser, is to stay composed and realize that the straightforward ones (which are usually basic numbers with assumptions) are reasonably easy, while few candidates successfully answer the tricky problems. (Often the ones who do either get lucky or have heard the case before!) Ultimately, this part of the interview is rarely a make-or-break situation (provided you do not get flustered); thus you should try to relax and have fun with the Brainteaser should it come along.

Make a good attempt at an answer, be logical and structured, ask for clues where appropriate, and be sure to acknowledge any mistakes made in the process and ideas missed.

The following are examples Brainteaser problems that have been around in some format or another over the years in Consulting interviews.

Brainteaser Example #1

What is the ratio of the weight of an elephant to the weight of an ant?

Answer: Approximately 1 billion. The average elephant weighs about 3,000 kilograms while the average ant weighs about 3 milligrams. 3,000 kilograms = 3,000,000 grams = 3,000,000,000 milligrams. You can estimate these values and if you arrive within an order of magnitude you’ve done very well.

Brainteaser Example #2

There are 12 black socks and 12 white socks together in a drawer. It is dark, and you cannot tell them apart. What’s the smallest number of socks you need to take out without looking to be sure of having a matching pair?

Answer: 3 socks. Assume the first sock is black. The second one could be black, in which case you have a matching pair. If the second sock is white, the third sock will be either black and match the first sock, or white and match the second sock.

Brainteaser Example #3

Is there anything “interesting” about the following sequence of numbers?

8, 11, 5, 4, 9, 1, 7, 6, 10, 3, 12, 2, 0

Answer: The digits are in alphabetical order. (Eight, eleven, five, four, nine, one, seven, six, ten, three, twelve, two, zero)

Brainteaser Example #4

You are driving a bus and tracking the number of passengers on the bus. At the first stop, the bus picks up 26 people. At the second stop, 15 of those people get off the bus, and 8 new passengers get on. At the third stop, 2 passengers get off, and 11 new passengers come on. At the fourth stop, 3 passengers get off, and 4 passengers get on. What is the color of the bus driver’s eyes?

Answer: The first sentence is the important one: “You are driving a bus…!” (And yes, this question has actually been used before!)
(By the way—if you are counting, there will be 29 people on the bus after the fourth stop.)

Brainteaser Example #5

In a tiny cabin in the woods, two men lay dead. The cabin is not burned, but the woods around it burned. How did the men die?

Answer: It is the cabin of a plane and the plane crashed. This is known as a “Lateral Thinking” exercise, and it revolves around your ability to see that the word “cabin” can mean multiple things. Do not be dismayed if you do not get this one—but remember to keep your composure!

Brainteaser Example #6

I am the owner of a pet store. If I put in one canary per cage, I have one bird too many. If I put in two canaries per cage, I have one cage too many. How many cages and canaries do I have?

Answer: Four canaries and three cages. If you put one canary in each cage, you have an extra bird without a cage. However, if you put two canaries in each cage then you have two canaries in the first cage, two canaries in the second cage and an extra cage.

Algebraically:

C = number of canaries
L = number of cages

CL = 1
L – (C ÷ 2) = 1

From the first equation:

L = C – 1
(C – 1) – (C ÷ 2) = 1
2C – 2 – C = 2
C = 4
L = 4 – 1 = 3
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