How to answer the “crazy” questions in Google hiring interviews?

How to answer crazy questions in Google recruitment interviews?

The most important thing about critical thinking about numbers is to allow yourself to use wrong answers to math problems, intentionally wrong answers.

Engineers and scientists do it all the time, and there's no reason why we can't, too. Their secret comes down to one thing: the art of estimating, or back-of-the-napkin calculations. As the British writer Saki said, "A little error can avoid a lot of troublesome explanations."

For the past decade, Google has asked candidates unanswered questions during interviews. Google is a company that survives and thrives on innovation - inventing things that didn't exist before, improving existing methods and technologies, and allowing consumers to do things they couldn't do before.

Compare this to how interviews are conducted at most other companies: During the skills portion of the interview, Google needs to know if you can do what they need you to do.

But Google doesn’t know what specific skills their new hires need. What they need to know is whether an employee can solve a problem using his or her own thinking.

Piano tuners and skyscrapers

Consider this question that was once asked in a Google interview: How much does the Empire State Building weigh?

In any actual scenario, there is no correct answer to this question because no one knows the answer. Google isn't interested in answers either; they're interested in the thought process. Google hopes to see a logical and rational solution path, so that it can understand how the applicant thinks and whether the applicant is a careful thinker.

There are usually four responses to this question. People wave their hands and say "This can't be answered", or they try to find the answer somewhere.

The third response is to ask for more information. In the case of the weight of the Empire State Building, do you mean including furniture or excluding furniture? Do you want to include people in the building? But these trivial questions won’t get you closer to solving the problem; they will only delay you from starting the problem-solving process.

The fourth reaction is the correct one: use estimates, which some people call guessimating. These types of problems are often called estimation problems or Fermi problems, named after the physicist Enrico Fermi, who was known for making estimates without exact data. And famous. Estimating involves a systematic series of reasonable guesses, breaking the problem into manageable parts, defining assumptions, and using common sense from the objective world to fill in the missing information to solve the problem.

So how do you solve it? How many piano tuners are there in Chicago? What about this Fermi problem?

Where to start? As with many Fermi problems, it is often helpful to have an estimate of the amount of data used in the calculation. This is not the amount that the problem ultimately asks you to estimate, but the amount that will help you calculate the final result. In this case, it might be easier to start with how many pianos there are in Chicago, and then figure out how many tuners are needed to keep those pianos in tune.

We first list the data we need to know, followed by some assumptions:

1. How often a piano needs to be tuned

2. For a piano How long does it take to tune?

3. How many hours does a piano tuner work on average in a year?

4. How many pianos are there in Chicago

Knowing these questions helps us get answers. If you know points 1, 2, and 3, just multiply by point 4 to figure out how much time it takes to tune all the pianos in Chicago each year. Divide this number by the number of hours each tuner works per year to get the number of tuners.

Hypothesis 1: Each piano is tuned an average of times per year.

Where does this data come from? I made it up! But that's what you need to do when estimating. And it has to be at a reasonable level: a piano is not tuned just once every ten years, nor ten times a year. Once a year seems like a reasonable guess.

Hypothesis 2: Tuning a piano takes two hours. This is a guess, maybe an hour, but two hours is within a reasonable range of magnitude, so that number is fine.

Hypothesis 3: How many hours does a piano tuner work on average per year? Let’s assume that the work week is 40 hours and the sound engineer takes two weeks of vacation each year: 40 hours/week x 50 weeks = 2000 hours/year. Does the job of a piano tuner require time on the road? No one will move the piano around? So the tuner will spend 10% to 20% of his time in transportation. We will cut this part out of the final result.

Hypothesis 4: Estimating the number of all pianos in Chicago, you might guess that there is one piano for every 100 people? Again, this is just a guess, but it's probably within reason. In addition to this, pianos are purchased by schools and other organizations, many of which own multiple pianos. It is a bit difficult to estimate this way, but taking this factor into account and dividing it equally among the number of pianos owned per capita, it is about two pianos for every 100 people.

Now let’s estimate the total number of people in Chicago. If you don't know, you might think that this is the third largest city in the United States, behind New York (8 million people) and Los Angeles (4 million people). You might guess that Chicago has a population of 2.5 million, which means 25,000 people own pianos. We double this number to include the number of pianos organized by institutions, so the result is 50,000 pianos.

So, our estimates are as follows:

1. Chicago has a population of 2.5 million

2. There are two pianos for every 100 people

3. There are 50,000 pianos in Chicago

4. Pianos are tuned once a year

5. It takes two hours to tune a piano

6. Pianos Tuners work 2,000 hours per year.

7. In one year, each piano tuner can tune 1,000 pianos (2,000 hours/year divided by 2 hours/piano).

8. 50,000 pianos require 50 tuners (50,000 pianos divided by 1,000 pianos/tuners).

9. Add 15% of the time to account for transportation time, which means there are approximately 58 piano tuners in Chicago.

What is the correct result? There are 83 piano tuners listed in the Chicago Yellow Pages. This includes duplicate registrations (the same tuner will be registered again if there are multiple phones), as well as piano technicians (who do not perform tuning work). Excluding 25 people who are not tuners, our estimated answer of 58 is still very close.