Case

# Brain Teasers - Ping pong balls

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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?

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.

## 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

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## Brain Teasers

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

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## 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.

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