Fermi Questions

My brother Alex recently introduced me to the concept of “Fermi questions.” I would define it here, but it’s much easier to steal this site’s definition:

A “Fermi question” is a question in physics which seeks a fast, rough estimate of quantity which is either difficult or impossible to measure directly. For example: The question “How many drops of water are there in Lake Erie?” requires an estimate of the volume of a drop, the volume of Lake Erie from its approximate dimensions and conversion of units to yield an answer.

Another classic problem is, “How many piano tuners are there in Chicago?” (You can’t look at a phone book.) In other words, a Fermi question asks the solver to find some plausible mathematical way to at least guesstimate the answer to an utterly ludicrous question. And, as readers of this blog will know, there are few things I do better than asking utterly ludicrous questions.

So without further ado, here are a few problems for your consideration.

1. How many Olympic swimming pools full of methane are released by the world’s cows every year?
2. How many notes are played on the album A Hard Day’s Night?
3. How many coffee mugs’ worth of gasoline does America spill on its shoes every day?
4. If there was a giant bridge to the moon, how long would it take Forrest Gump to run there?
5. If you were smuggling contraband Post-It notes out of the country in cellos, how many cellos would it take to smuggle five million pads of Post-It notes?
6. How loud, in decibels, would it be if you stood in the middle of a field as cargo planes dropped 500 grand pianos around you?
–6a. How many splinters would you get?
–6b. How much would that stunt cost?
7. How many commas have ever appeared on Yahoo!?
8. If you wanted to turn yourself completely orange from head to toe, how many Cheetos would you need to use?
9. How many hippie bumper stickers are there in Austin, Texas?
10. How many times have you ever sneezed?
11.  If you wanted to build a full-size Lego replica of the Seattle Space Needle, how many Legos would it take?
12. If you wanted to build a Jenga block tower the height of the Seattle Space Needle, and had an indoor space controlling for wind and other atmospheric effects, how many blocks could you pull out before it fell over?
13. If you printed the Internet, how many sheets of paper would it take?
14. If you filled every bathtub in Tokyo, and then covered them all with rubber ducks, how many rubber ducks would that take?
15. How many pints of soy sauce would the world’s hungriest man require for his meal of 50,000,000 pieces of sushi?

Pictured: the world’s hungriest man’s nightstand.

16. I kind of like the idea of the world’s hungriest man. The world’s hungriest man wants to eat 3500 pounds of mashed potatoes. How many kitchen cabinets filled with Yukon Gold potatoes will he need?
17. How many flushing toilets would it take to equal the volume of Niagara Falls?
18. If you made a chain of people from Columbus, Ohio, to Columbus, Georgia, what’s the total number of calories they would eat in a day?
19. Assuming perfectly steady seas, how many individual strokes would it take to row from Miami Beach to Reykjavik?
–19a. If you left Miami on June 1, how long could you stay in Reykjavik before the temperature dropped below 0 Fahrenheit?
20. What’s the total number of years people are sentenced to in your state penitentiary?
21. If the world’s hungriest man bought an M1 Abrams tank and filled it with slices of Gouda, how many official servings of dairy would that be?
22. How many points did Olympic judges give out in 2010?
23. How many times did a tennis ball hit the ground in the 2011 U.S. Open?
24. The world’s hungriest man uses a napkin every time he eats one barbecued pork rib. If he is about to sit down to a feast of three U-haul trucks of pork ribs, how much money will he need to spend on Walmart’s cheapest brand of napkins?
25. If you covered Interstate 90 from end to end in tortillas, how many tacos are you an idiot for not making instead?

So maybe I wrote this when I was kinda hungry myself.

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6 Comments

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6 responses to “Fermi Questions

  1. As a consultant, I did the first six out of obligation, since these are the kinds of questions you could expect in a consulting case interview. I did everything out of my head (no fact checking)!
    1. 8 million (1 cow for every two humans, 1 cubic foot a day)/(170 x 80 x 10 ft)
    2. 3000 (1 beat per second, 1 note per beat, album 50 minutes long)
    3. 125,000 (150 million car-filler-uppers, fill every two weeks, each person spills a tenth of an ounce per time)
    4. 35 years (ran for 3.5 years, criss-crossed the US six times, 4000 miles each way; moon is 240,000 miles away)
    5. 35,000 (inside of a cello fits 135—4x18x24inches inside, five stacks are a 4x4x4 cube)
    6. If there’s no one around to hear it, does it still make a sound? Jk…assuming it’s from low altitude, the sound of the pianos is minimal to the jet engines, which is 120 db; the pianos don’t splinter but sink into the grass, so while you might get a plank in your eye, no splinters or specks. As for cost, each grand piano is $10,000, each flight is $1000 (crew+gas), so let’s say $5,000,000

    …Maybe I’ll come back to the others later 😉

  2. Technically correct English Major answer to all questions: Quite a few.

  3. Andrew

    Starting from the bottom like a boss:
    25. 3 (1-10) billion give or take – 4-lane road, ~1000km, ~10cm.10cm for a tortilla
    24. $4k or so – pork chop is ~10cm.2,5cm.1cm so there are 10.4.100=4000/m^3, box truck is 4x3x2m, so 3 trucks is ~100m^3 = 4.10^5 pork chops, napkins are probably ~1c each so $4000
    23. 20,000 – assume single-elim tournament, 128 participants = 64+32+…=127~100 matches, 3 games per match, 10 sets per game, 6 rallies per set with one bounce per rally = 18000, round to 20000 so as to not appear to have precision.
    22. 30,000 points – assume 5 games with point-based scoring, 200 participants, average score of 6 with four judges.
    21. 3 million slices – cheese slice is about one serve of dairy if it’s good fatty cheese, and they’re ~10x10x0.3cm, so you can get 30000 per m^3, and an abrams tank is something like 10x5x3m probably half-full of steel at least which is 75~100m^3, giving ~3mil

  4. 25. An interstate lane is 12 feet wide, so a four-lane road is 48 feet, plus shoulders. Maybe 60 feet. Round up to 75, since the road will occasionally be wider than 4 lanes. I-90 is maybe 3,000 miles long. A tortilla is perhaps eight inches in diameter. There’ll be gaps between the tortillas, because they’re circular, so we’ll treat them as eight-inch squares.

    Computing the answer, we find that you’re an idiot for not making 2.7 * 10^9 tacos. That’s 2.7 billion tacos.

    http://www.wolframalpha.com/input/?i=75+feet+*+3000+miles+%2F+%28%288+inches%292%29

    That’s nearly a trillion calories. Awesome.

  5. Whoa…did you think anyone would actually try to answer any of these, Brian?

  6. Dennis Hermanson

    Let me count the Byways…

    I just stumbled into your blog searching for “Traveler’s Remorse.” “where is that?” It’s a travel question, perhaps deeply philosophical in a zennish way, “Did you mean to be here?” Or “which here are you in at the moment.” If you are a visitor, you might not know. You are in a traveler’s moment in a differnent place. When do you slip into that “real” or “actual” place, or it is just “another special moment place, for me” ?
    I wonder if, since I see from your blog that you are a cowboy… er, thinker, if you’ve heard of the concept of “Frame” as used in travel? I use the frame as a device of meaning, a signifier. Remember the story of Joshua Bell playing in the Washington DC subway, and those who didn’t recognize him, for the most part, passed him by as a regular street musician. Even though he was playing great music in a wonderful way.
    I wonder if travel affords the opposite effect, what I might call the “glow” effect, where one can be in a frame of appreciatlonal reference wherein most everything seems special, significant, wonderfully beautiful.
    Of course, beautiful views are beautiful, and each is its own singularity. I know that’s why we travel. But once we’ve left, is the view any different than say, one of your fine photographs of that view, in our mind’s eye memory?
    I know, this is a reponse to facts as meaning, quantification.
    Perhaps travel appeals to the other side of life.
    Not counting, not object, not routine, but impulse, adventure, and effect.
    So, the opposite of traveler’s remorse, “so many places, so little time, I can’t do them all …” (also, the lover’s remorse) … in travel becomes,
    “Why is the rest of the world so much more beautiful than where I go back to?”
    We go home to be, we travel to see, and perhaps become.

    Den NC USA

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