if you could sustain your body by eating nothing but donuts, and if you chose to do so… how many...
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If you could sustain your body by eating nothing but donuts, and if you chose to do so…
how many donuts would you eat during your life?
A Fermi Question is any question that can be answered by an order of magnitude estimate.
The answer might come from a straightforward calculation……but there won’t be much time for calculations!
The answer might be something you could look up…
…but without any reference materials, estimates will be necessary.
The answer is to be given as an order of magnitude; i.e., the nearest power of 10.
The answer might be something you can only estimate.
Here’s a straightforward calculation (too easy to be an actual question): how many millimeters are there in two kilometers?
1000 m 100 cm 10 mm2 km = 2,000,000 mm
km m cm
The correct answer is 6 (because the result is 2x106).
An answer of 6 would get you 5 points.
An answer of 5 or 7 would get you 3 points.
An answer of 4 or 8 would get you 1 point.
How many automobile mechanics are there in the St. Louis Metro area?
The question on the previous screen was too easy to be useful.
An example of an “easy” calculation-based question would be “how many millimeters is it from St. Louis to Kansas City?”
Let’s try another one.
Well, don’t just sit there. Answer the question!
How many automobile mechanics are there in the St. Louis Metro area?
You’ll need to make some assumptions and estimates to do this one!
There are about 2.6 million people in the St. Louis Metro area.
Suppose there is one car per every 2 people, you take your car in to the shop twice a year, and that one mechanic can work on 3 cars per day and works 250 days per year.
6 1 car 2 repairs2.6x10 people
2 people car-year
1 year 1 mechanic250 mechanic days 3 repairs
mechanic day
= 3470 mechanics
The correct answer would be 3. Answers of 2 or 4 would get 3 points, answers of 1 or 5 would get 1 point.
“Hogwash! I don’t take my car in twice a year!”
6 1 car2.6x10 people
2 people
1 year 1 mechanic250 mechanic days 3 repairs
mechanic day
= 1733
1 repairscar-
mecha
y r
n
a
ics
e
The correct answer is still 3!
“Well, my mechanic can repair 5 cars in a day.”
6 1 car 2 repairs2.6x10 people
2 people car-year
1 year250 mechanic d
1 mechanic5 repairs
mechays
a
= 2080 mechan
nic day
ics
The correct answer is still 3!
“What if my students estimate only 1 million people in the St. Louis Metro Area?”
6 1 car 2 repairs1x10 people
2 people car-year
1 year 1 mechanic250 mechanic days 3 repairs
mechanic day
= 1330 mechanics
Would the mechanics question be a “fair” one?
It requires basic knowledge of Missouri, and even if your students are off by a factor of 2 or 3 in population, it doesn’t guarantee a wrong answer.
A reasonable range of input estimations produces the same final answer.
I could look the number up.
Yes, it’s definitely a fair question.
Oh, by the way… the answer to “millimeters from St. Louis to Kansas City” would be 8.
“Where can I find more information about Fermi questions?”
Try the web site mentioned in the rules!
Or Google “Fermi questions.”
Hey, that’s a good Fermi question. How many web sites will Google find?
The answer on October 8, 2004, was 5 (77,100 web sites).
Some hints (from the Science Olympiad web page):
understand properties of exponents
round off before you do a calculation
That leads to a better Fermi question. What fraction of those sites will I ever look at?
Maybe I’ll look at 10 out of 77,100. The fraction is 10/77,100=0.00013, so the answer is -4.
6 1 car 2 repairs3.0x10 people
2 people car-year
1 year 1 mechanic300 mechanic days 3 repairs
mechanic day
= 3330 mechanics
Actually, I can just look at the above numbers and get the answer. Do you see the ½ and the 2 that cancel? That leaves me with 3 million divided by about 1000. A million divided by a thousand is a thousand. Answer = 3 with no calculator needed.
More hints (from the Science Olympiad web page):
always show the units
6 1 car 2 repairs3.0x10 people
2 people car-year
1 year 1 mechanic300 mechanic days 3 repairs
mechanic day
The units actually tell you how to do the calculation (and keeping track of the units may prevent errors).
etc.
How many seconds would it take you to run from ocean to ocean across the USA?
7day 86400 seconds3000 miles 1.04x10 s
25 miles day
Again, 3000 / 25 =100 and 100 x 100000 = 107, so you can get the answer without a calculator.
Yes, 3000 / 25 =100 if it’s a Fermi calculation!
“But a trained ultra-distance runner can go 100 miles in a day.” “But a trained ultra-distance runner can go 100 miles in a day.” Oh really? For more than 100 days in a row?
“This is really stupid. Scientific trivia. Waste of time.”
You should train your students to be accurate. Accuracy takes priority.
But the team that wins the billion-dollar contract will be the one that is accurate and fast.
The ability to do quick mental calculations is useful.
The ability to do quick mental calculations to check whether a result is right or wrong is even more useful.
I know why you are really here today.
You want to see the questions I am going to give next April, don’t you?
Well…here they are…
Yes, I have plenty of ideas, but no questions yet.
So how can your students prepare?
First, know the rules.
two on a team
50 minutes to answer as many questions as possible
one person—the team captain—will record the answers
answers are nearest power of 10; round 5 up to 10
5 points if correct, 3 if off by 1, 1 if off by 2, otherwise zero
bring pencils—nothing else (I’ll provide plenty of paper)
total time used is a tiebreaker
Are there penalties for guessing?Are there penalties for guessing? Not in our rules!
Here are some useful observations from the Science Olympiad web site (URL given in the rules):
your students should have good math skills—especially with exponents
large exponents seem to cause problems for students—so expect some problems with large exponents
read and understand the problem
make sure the answer has the correct units
not part of scoring, but wrong units mean wrong answer
critical thinking is important
don’t be exact—estimate quickly and move on
Understand your event supervisor!
I am a physicist, so there will be physics-related questions.
I won’t use physics to make a question difficult.
Examples of some things I would like your students to know: how big is an atom? How big are the earth, moon, sun? What are typical distances in the solar system? How far is far? How fast is fast? How long is a year?
Close familiarity with the metric system is a must!
Anything similar to examples at the web site referenced in the rules is fair game.
I teach a physics of the environment course. How big is a joule? How many people are there. How much ____ (fill in the blank with something important) gets used / consumed / produced every year.
Living systems are good candidates for Fermi questions. How much do I eat/drink/sleep/breathe? How many _____ (fill in the blank) are in my body right now.
I’ll try to give questions…
whose answers I can look up or calculate
that can be answered correctly using a wide variety of reasonable estimates that require a reasonable amount of background knowledge
Please check my Science Olympiad web page:http://www.umr.edu/~pringle/science_olympiad.
If you could sustain your body by eating nothing but donuts, and if you chose to do so…
how many donuts would you eat during your life?
1500 calories 365 days 80 years donutday year life 200 calories
220,000 donuts
Answer: 5.
Depressing...only 7½ donuts per day.