The Fermi Problem (Professor Word Problem)

Hi guys, it’s Richard here. Some of you might be reading the title and wandering, “What the hell is a fermi problem and why is he giving this kind of unknown terms in the heading?”(Sorry, bad joke)

Well, in physics or engineering studies Fermi Problems are considered to be an estimation problem designed to teach dimension analysis, estimation and it is more of the back-of-the-envelope-calculation. You can learn more about Fermi Problems through this Wikipedia link https://en.wikipedia.org/wiki/Fermi_problem.

One day in college me and Ray had to seat through the boring and monotonous lectures of our Mechanics teacher. Suddenly Ray had this amazing idea to “Calculate the number of words our teacher usually speaks during a class?”. I was very excited to solve that problem( you can clearly see that we are nerds) and Ray and I started to observe some parameters which were the main key to solving our “time pass problem“. There was three periods or stages of his class: lecture time, problem time and diagram time. You will eventually know about this later, for now let’s see what the parameters were,

• At the beginning of a class, sir always take 5 minutes to adjust the speaker(we have a sound system in our class).

• In every 3 minutes sir take a pause of 1 second to gather his thoughts throughout the time he talked.

• In every 15 minutes he rubs the board for about 10 seconds.

• There is a girl who asks a lot of questions(dumb ones though). We assumed she asks 3 questions per class and sir take 3 minutes each question to solve them.

• Sir waits for 10 second to look if we have any doubts(only once and nobody asks except for that girl).

• In average, sir give us 2 problems to solve and each question generally take upto 10 minutes and in that time he would dictate a problem for 1 minute and then give us 5 minutes to think and 5 minutes to teach us the solutions.

• Usually sir draws 4 diagrams(3 reused and 1 new), reused- 3 minutes/diagram and new- 5minutes/diagram.

• At the end of the class(phew! What a relieve) sir takes our attendance of total 170 students and takes about 6 minutes to complete that.

This was the parameters, now

Lecture time = total time – (problem time + attendance time + other things in that parameters that consists use of time)

And the rate of the words spoken was different for different parts of the period,

• Sir spoke regularly of 2.5 words/sec at the lecture time.

• At problem time when he dictates the problem it is 1 word/sec and when he teaches solutions it is regular as 2.5 words/sec.

• In attendance time sir uses 170 words for 170 students(obviously “words” meant their names).

This was the whole procedure, I will not bore you with the calculations(Ray suggested a calculator but I refused and did it all by myself) but the grand total was 6795 words. We will remember this number as long as we will remember the famous “Taxi Cab Number – 1729”. Also I didn’t use the term “approximately” in any of our parameters or our calculations because Fermi Problem means estimating calculations.

This was a very memorable and prestigious day for us because other student found it very fascinating and amusing. A girl(not the dumb one, she is very smart) also became a fan of these kind of problems and we also assured her that we will ask her to join us next time.

At last of the post, I have to say Fermi Problems are “just a nerdy thing” and I love to do it. Also we figured out what our next problem would be and I will be there for you to explain that. Until then just try to calculate the problem and tell me on the comment’s section if there’s any mistake. See you.