In the product manager interview, have you ever encountered a strange and difficult question, similar to the following:

How many schools are there in Shenzhen?

How many product managers are there in Beijing?

How many Honda cars are there in Shanghai?

How many 7-11 convenience stores are there in Haizhu District, Guangzhou?

How many households are there in Zhuhai Haiyiwanpan Community?

How many biscuits can a pancake stand in a Beijing Hutong alley sell in a year?

First, it belongs to the "Fermi problem" in quantity estimation in academia .

Secondly, usually in product interviews, it is hoped that the candidates can be tested: logical thinking, analysis and psychological resistance . Because these kinds of questions are very open, they can be a good test of the analysis and inference made by candidates in the face of clueless questions and without industry background knowledge.

Finally, based on my experience in product interviews and thinking about work practices, here are some ideas for analysis and solutions:

## 1. Analysis strategy

PS: Because in product interviews, such Latest Mailing Database questions are more focused on "logical thinking". That is to split according to the problem, put forward a well-founded analysis, and then draw a conclusion, focusing on logic rather than correctness. This is the first and foremost, to avoid the mentality that dare not use your brain or express yourself.

There are three ways I can answer this question:

Open the bow from top to bottom/left and right: push down from the upper layer from the macro level/cut in horizontally from a certain point, and push it back up;

Upper and lower limits: Using the idea of upper and lower limits, "clamp" is forced out;

The third party: directly seeking the truth will not work, often the answer can only be known by calculating the third party. (...forgive the name)

Since quantity estimation is very open and has no unique answer, these three ideas can be used flexibly and mutually verified for different questions. At the same time, these are the skills of personal summary, and it is more difficult to explain with theory.

So, let's run through this thought by way of example:

### 1. Top-down, Bottom-up

(1) Estimate the number of Toyota cars in Shenzhen?

Level dismantling: Shenzhen Auto (first floor), Toyota Motor (second floor), Toyota (horizontal can be Tesla)

Analysis idea 1 : Top-down

Assume first that there are 3 million motor vehicles in Shenzhen City; (first floor)

Sampling in several traffic-intensive areas in Shenzhen, recording the proportion of Toyota vehicles in every 100 vehicles, and taking the average proportion; (2nd floor)

If the average proportion is 25%, then we get: 3 million × 25% = 750,000 vehicles.

Analysis idea 2: Bottom-up

First assume that there are 80,000 "Tesla" vehicles in Shenzhen; (the same level as Toyota)

A multi-point sampling in a certain place in Shenzhen shows that in every 100 cars, the proportion of "Tesla" cars is 2%, and the proportion of Toyota cars is 20%;

Then we get: 80,000/2%*20%=800,000 vehicles. (Using lateral pushback)

(2) To supplement the boundary

During the interview process, the interviewer often recognizes and improves the chances of success in the interview after listening to the answers that are logical and can think independently. However, some interviewers will choose to continue to ask questions and dig out the "boundary points" of the answers, so as to check whether your logical thinking is meticulous, whether your reaction speed is fast enough, and whether you can "justify yourself".

Generally, there are many points to consider the boundary, the common ones are: time, place, quantity, industry background knowledge, etc. Candidates often supplement the boundary, not only to examine the points just mentioned, but also to prove themselves "have knowledge and understand more".

For the above, I give a few examples:

When sampling Toyota cars, where do you choose? (Prove that the boundary is considered)

Is it correct to choose a dense area? For example, do ports, airports, shopping malls, etc. affect the authenticity of the data?

If only the traffic-intensive areas near the port are taken, the proportion may be high. (The vast majority of Hong Kong brand nanny cars are Toyota Alphard)

So how many should be taken to be more "balanced"?

How to analyze when sampling Tesla? (Prove that you have research on Tesla and know that it can be charged)

If the sampling location is near the "Tesla charging pile", it will also cause the data to be too high;

What is the position of Tesla in Shenzhen?

### 2. Use the upper and lower limits to "clamp"

Question: How many pancakes can a pancake stand at the mouth of a hutong in Beijing sell in a year?

Hierarchical disassembly

Time: 1 year, that is 365 days, that is 365*24 hours; Second, the pancake stalls are generally sold in the morning, noon and evening time periods, and one or three time periods can be selected; secondly, the production time of a pancake is about 30~60 seconds; (remember, there is no right or wrong, only logical reasoning, and the analysis is different according to different assumptions)

What are you looking for: how many are you looking for? That is to say, how many pancakes can be sold in a period of time. It is not difficult to come up with this number, the key is how to prove it is reasonable. Proving that the quantity is reasonable can be "clamped" with the upper and lower limits.