Case

Brain Teasers - Ping pong balls

Solved 800+ times
Difficulty: Beginner | Style: Brain Teaser | Topics: Brain teaser

Problem Definition

Calendar Cube

You are given two cubes with 6 sides each (total 12 sides). What digits would you put on each cube for you to be able to show all the days of the month with these two cubes?

Chopped Cube

You are given a large cube made up of small cubes. Each side of the large cube is as wide as ten small cubes. Can you calculate the number of small cubes that make up the outside of the large cube?

Exporting ping-pong balls

You are given a task of exporting ping-pong balls. How many ping pong balls do you think you can fit in a Boeing 747 airplane?


Comments

Brain Teasers are short questions with difficult logical or creative answers. They are a good way to test your analytical skills and capacity to think out of the box. These short questions also show the interviewer your ability to elaborate on difficult tasks from the real world. Each Brain Teaser is supposed to be solved by the interviewee in about 5-10 minutes.

If the interviewee gets stuck in a brain teaser (i.e. spends more than 10 minutes), propose to go on to the next one.


Short Solution


Detailed Solution

Calendar Cube

Put 0,1,2,3, 4 and 5 on one and 0, 1, 2, 6, 7 and 8 on the other one. Digit 6 can be flipped over and used as digit 9.

Chopped Cube

  • It is given that each side of the large cube has 10 small cubes.
  • The large cube is composed of 10 small cubes in each dimension, so it is composed of 10*10*10 or 1000 small cubes in all
  • The number of small cubes that are on the inside is 8*8*8 = 512 cubes
  • Therefore 1000-512 = 488 small cubes make up the outside of the large cube

Exporting ping-pong balls

  • Let us calculate the volume of Boeing 747 airplane by approximating it to a cylinder of length 200 feet and diameter 20 feet
  • Volume of Boeing 747 would be pi*length*radius^2 = pi*200*100 = 20000ft³*pi
  • Assumption - the diameter of a ping-pong ball is 2 inch and 25% of the space is wasted
  • Volume of a ping-pong ball: 1.33*pi*radius^3 = 1.33*pi*1 = 1.33in²*pi
  • The units are differing, so we transform 20,000 ft³ into in³ (x2000)= 40m
  • Therefore, 75 % of 40,000,000pi/1.33pi or 22.5m balls can fit in a Boeing 747 airplane

Difficult Questions

Related consulting question(s)

Hey, I am new to this too, but I think I have some ideas for your problem. Your approach looks good, but I think you have a mistake in how you time the trains. You say that there is one train ev... (more)

Best answer so far:
Ex BCG | MBB Specialist | #1 Expert for meetings done (900+) and recommendation rate (100%)

Hi Anonymous, there may be several reasons for that; some of them, in order of frequency, are: Your structure is not complete enough – you are just using not MECE/ not complete structure... (more)

Best answer so far out of 2 answers:
Marco
Expert
Interview specific coaching: company you are applying to; 1st or 2nd round; your professional background and more

Hi, here's how I would approach it - Define the geographic area to be covered [the whole world? the U.S.? NYC? Manhattan?...for this example I'll use Manhattan] - Population living there [~ 1... (more)

Hey! The cases usually test strategy, finance and business development. You should be familiar with the common business concepts and financial terms and calculations (CF, BS etc). Abo... (more)

Hi, thanks for your question. I think the case is essentially testing your ability to segment a massive concept like 'internet websites' to its components. Below is my answer for this case: Assume... (more)

Related BootCamp article(s)

Brain Teasers

Learn how to tackle brain teasers and what purpose they serve in consulting case interviews

1 Comment(s)

Typical Question Types in Written Tests

Questions among all tests can be categorized in math, GMAT-style, chart reading and brain teaser questions. Each type needs to be approached differently.

4 Comment(s)
4.2 (102 ratings)
4.2 5 102
Case exhibits

No case exhibits yet