Investment Banking Job Interview Question: The Magic Cube

CubeAlthough you probably won’t be given a Rubik’s Cube to solve during your investment banking job interview (it has happened before), you should be ready to solve a puzzle of some sort. Make sure you think through the question before jumping into an answer. And, for goodness’ sake, answer the question that is asked! Nothing decreases your chance of getting a job you are qualified to do faster than not answering the right question.

Q: Picture a 10x10x10 “macro-cube” on the table. This big cube is made up of 1x1x1 “micro-cubes”. Your dog walks by and knocks the macro cube off with his tail, causing it to crash to the ground. When it hits, the impact causes the entire outer layer of micro-cubes to fall off. How many micro-cubes are on the floor?

A: First, don’t beat the dog, he was just happy to see you. This is a popular question and you should be ready for it. There are a couple ways to solve this. The first (not the best), is to count the number of cubes on each face and add them up. This math is confusing for most people.

The better solution is to focus on the structure of the problem. The original macro-cube and new smaller macro-cube hold the answer. The difference between their volumes is how many micro-cubes fell off. The volume of a cube is n cubed. The answer is, therefore, 10 cubed – 8 cubed. So, 1,000 – 512 = 488.

Note: A common mistake is for people to think because only one layer fell off, the solution is 10 cubed – 9 cubed.

Special thanks for this interview question to Timothy Crack, author of Heard on the Street: Quantitative Questions from Wall Street Job Interviews

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