Fermi Questions C

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Re: Fermi Questions C

Postby talkingturtle101 » June 30th, 2017, 10:14 pm

Consider the partial sum of a harmonic series; that is, . What is the minimum such that the partial sum will be above 12?
My Answer
Dang, that was a good question. I have no idea how to do this mathematically, but the higher n gets, the smaller the fraction is. So to get to 12, you'd probably have to go to a million, Fermi Answer of 6.
Actual Answer
Guessing and checking on Wolfram by powers of 10 says that when n equals 100,000, the sum is 12.09, so Fermi Answer of 5
If you cut down all the trees in the world please don't try this at home, then how many Major League-size baseball bats could you make?
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Re: Fermi Questions C

Postby Adi1008 » July 1st, 2017, 10:20 am

If you cut down all the trees in the world please don't try this at home, then how many Major League-size baseball bats could you make?
My attempt
I believe there's on the order of [math]10^{12}[/math] trees on Earth. I'll assume that about E2 can be made from each tree. Fermi answer of 14.
Actual answer
-There are about [math]3 \times 10^{12}[/math] trees on Earth -There isn't a definitive answer, but it looks like 50-100 bats can be made from the average tree. -Using either 50 or 100 gives a Fermi Answer of 14.
How many textbooks do you need to equal the weight of all the water in the Pacific Ocean?
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Re: Fermi Questions C

Postby NeilMehta » July 2nd, 2017, 10:17 am

If you cut down all the trees in the world please don't try this at home, then how many Major League-size baseball bats could you make?
My attempt
I believe there's on the order of [math]10^{12}[/math] trees on Earth. I'll assume that about E2 can be made from each tree. Fermi answer of 14.
Actual answer
-There are about [math]3 \times 10^{12}[/math] trees on Earth -There isn't a definitive answer, but it looks like 50-100 bats can be made from the average tree. -Using either 50 or 100 gives a Fermi Answer of 14.
How many textbooks do you need to equal the weight of all the water in the Pacific Ocean?
Attempt
Density of water = 1 gram per mL one textbook is about 5ish kg I remember from a previous fermi test that there are E20 gallons of water in the pacific. A gallon is equal to 16 cups which is about 5000 mL = 5000 g = 5 kg Answer: E20
Solution
Average weight of textbook = 4.8 pounds Weight of a gallon of water = 8.34 lbs Water in pacific = about 3E20 gallons Final answer: 5.21E20 = E21 (so close :cry: )
How many letters are in George Orwell's Animal Farm?
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Re: Fermi Questions C

Postby Justin72835 » July 2nd, 2017, 2:20 pm

Attempt
I think there were around 200 pages in Animal Farm, and also about 200 words per page. The average word should contain about 5 letters. Using dimensional analysis: 5*200*200 = 200,000, or 2e5 Fermi Answer: 5
Solution
So I downloaded a .pdf version of Animal Farm and converted it to a Word file. So now according to the counter, it says that there are 138,159 characters in the whole book (not including spaces) or 1.4e5 letters. Final answer: 5
Determine the volume of water the average American will use for bathing throughout their whole life divided by the volume of the ocean.
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Re: Fermi Questions C

Postby Adi1008 » July 2nd, 2017, 2:35 pm

Determine the volume of water the average American will use for bathing throughout their whole life divided by the volume of the ocean.
Which ocean?
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Re: Fermi Questions C

Postby Justin72835 » July 2nd, 2017, 3:19 pm

Determine the volume of water the average American will use for bathing throughout their whole life divided by the volume of the ocean.
Which ocean?
My bad, I meant all of Earth's oceans combined.
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Re: Fermi Questions C

Postby Adi1008 » July 2nd, 2017, 3:43 pm

Determine the volume of water the average American will use for bathing throughout their whole life divided by the volume of the ocean.
Which ocean?
My bad, I meant all of Earth's oceans combined.
Coolbeans ty
My attempt
-Doing some sketchy math I estimate the volume of all the oceans on Earth to be about e18 L -I know from hydrogeology that the average bathtub holds about 140 L -I'll assume that people take a bath (as opposed to showers) once a week(?) -People live about 80 years which is about 4200 weeks. -140*4200; x = 140, 4200 = 30x; 30x^2; 30*19600; 600000 L in one's lifetime; estimate is e6 for water usage in lifetime in liters [b]Fermi Answer: -12[/b]
Actual answer
-The actual volume of all the oceans is 1.347e21 L. rip -The average volume of a bathtub is 36 gallons, which is about 136 L -Average life expectancy for an American is 78.94 years. -I wasn't able to find out how often Americans bathe as opposed to taking showers. I'll go with my assumption that people take a bath (as opposed to a shower) once a week -Therefore, the total water usage is about 5.6e5 => e6 L [b]Fermi Answer: -15[/b]
How many burgers were sold in America since the Model T was invented?
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Re: Fermi Questions C

Postby Justin72835 » July 3rd, 2017, 2:19 pm

Attempt
-The Model T was introduced a little more than a century ago, so I'm going to round to 100 years. -I'm going to assume that burgers were around at the time of the Model T too. -I'm guessing that the average American eats at least one burger a week? -The average population of America throughout the last 100 years is probably around 300 million people (I think the population growth has stagnated in the last few decades). 3e8 people * 1 burger/week * 52 weeks/year * 100 years = 1.56e12 [b]Fermi Answer: 12[/b]
Answer
-The average American consumes 3 burgers each week according to PBS. However, I don't think this value accounts for statistics from over a couple decades ago. Also, I don't think that Americans consumed as many burgers back then as they do now. Because of that, I'm going to adjust by using 2 burgers each week. -It turns out that the average population of America throughout the last 100 years is about 180 million. -The Model T was invented in 1908, so 109 years ago 1.8e8 people * 2 burger/week * 52 weeks/year * 109 years = 2e12 [b]Fermi Answer: 12[/b]
How many text messages have been sent since the release of the first iPhone?
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Re: Fermi Questions C

Postby NeilMehta » July 4th, 2017, 3:02 pm

Attempt
-The Model T was introduced a little more than a century ago, so I'm going to round to 100 years. -I'm going to assume that burgers were around at the time of the Model T too. -I'm guessing that the average American eats at least one burger a week? -The average population of America throughout the last 100 years is probably around 300 million people (I think the population growth has stagnated in the last few decades). 3e8 people * 1 burger/week * 52 weeks/year * 100 years = 1.56e12 [b]Fermi Answer: 12[/b]
Answer
-The average American consumes 3 burgers each week according to PBS. However, I don't think this value accounts for statistics from over a couple decades ago. Also, I don't think that Americans consumed as many burgers back then as they do now. Because of that, I'm going to adjust by using 2 burgers each week. -It turns out that the average population of America throughout the last 100 years is about 180 million. -The Model T was invented in 1908, so 109 years ago 1.8e8 people * 2 burger/week * 52 weeks/year * 109 years = 2e12 [b]Fermi Answer: 12[/b]
How many text messages have been sent since the release of the first iPhone?
Attempt
I read at one point that E9 messages are sent daily or something along the lines of that iPhone was released E1 years ago E2 days in a year Final answer: E12
solution
I can't find an answer online, but from other information it looks like it's along the lines of e13-e14
What is the collective volume of all of the sci-o medals ever awarded (not including ribbons)?
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Re: Fermi Questions C

Postby Unome » July 5th, 2017, 9:55 am

What is the collective volume of all of the sci-o medals ever awarded (not including ribbons)?
Attempt
- There are roughly 5E2 tournaments a year (accounting for multiple divisions). Each tournament probably medals to an average of four, so that's around 2E2 medals. E5 medals per year. - Obviously there were less tournaments the farther back one goes, so going back 1.5E1 years with this number of tournaments should suffice - there were likely less than 30 invitationals nationwide at 15 years back. This gives 1.5E6. - Medal volume varies, but I'd estimate 0.5 cm x 6 cm x 6 cm on average (since regional and invitational medals would be the most common), which makes 1.8E1 mL (btw you didn't specify units). Fermi Answer: 7
Actual Answer
There's so much data I'd have to collect here, this would be very difficult to estimate (though I think I could manage with enough research). The most important things to know, however, is the data on old-style medals - the years they were around, as well as their volume (I believe they are somewhat thinner). The number of tournaments and the medals awarded in each year can be reasonably estimated without too much uncertainty. If anyone has this info, I can update this post with a calculation of the actual answer.
Continuing the scioly theme: how many total Fermi Questions tests have been written for Science Olympiad tournaments in the 21st century?
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Re: Fermi Questions C

Postby NeilMehta » July 5th, 2017, 10:03 am

What is the collective volume of all of the sci-o medals ever awarded (not including ribbons)?
Attempt
- There are roughly 5E2 tournaments a year (accounting for multiple divisions). Each tournament probably medals to an average of four, so that's around 2E2 medals. E5 medals per year. - Obviously there were less tournaments the farther back one goes, so going back 1.5E1 years with this number of tournaments should suffice - there were likely less than 30 invitationals nationwide at 15 years back. This gives 1.5E6. - Medal volume varies, but I'd estimate 0.5 cm x 6 cm x 6 cm on average (since regional and invitational medals would be the most common), which makes 1.8E1 mL (btw you didn't specify units). Fermi Answer: 7
Actual Answer
There's so much data I'd have to collect here, this would be very difficult to estimate (though I think I could manage with enough research). The most important things to know, however, is the data on old-style medals - the years they were around, as well as their volume (I believe they are somewhat thinner). The number of tournaments and the medals awarded in each year can be reasonably estimated without too much uncertainty. If anyone has this info, I can update this post with a calculation of the actual answer.
Continuing the scioly theme: how many total Fermi Questions tests have been written for Science Olympiad tournaments in the 21st century?
Based on your estimate, I'd say there's E3 tests, considering the event was run for two years again, there isn't really a clear solution

Next question: what is the total number of posts on the Scioly.org forums?
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Re: Fermi Questions C

Postby Adi1008 » July 5th, 2017, 1:21 pm

Next question: what is the total number of posts on the Scioly.org forums?
My attempt
Every year there's about e4 posts (excluding general chat). scioly.org has been a thing for about 20 years, so that's about 2e5 posts total. I know general chat has around 1.5e5 total posts. My estimate is about 3.5e5 total posts. Fermi Answer of [b]5[/b]
Actual answer
Adding stuff up: 2017: 11531 2016: 9496 2015: 9682 2014: 10301 2013: 14041 2012: 14952 2011: 22429 2010: 16273 2009: 21894 2001-2008: The [url=https://scioly.org/wiki/index.php/Scioly.org_History]Scioly.org history wiki[/url] says 36163 General Chat: 136330 Administrative: 2046 [b]Total: 305,138 posts Fermi Answer: 5[/b]
How many Planck lengths would New Horizons travel in the time it takes for our Solar System to make one orbit around the center of the Milky Way?
Last edited by Adi1008 on July 5th, 2017, 2:15 pm, edited 1 time in total.
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Re: Fermi Questions C

Postby NeilMehta » July 5th, 2017, 2:10 pm

Next question: what is the total number of posts on the Scioly.org forums?
My attempt
Every year there's about e4 posts (excluding general chat). scioly.org has been a thing for about 20 years, so that's about 2e5 posts total. I know general chat has around 1.5e5 total posts. My estimate is about 3.5e5 total posts. Fermi Answer of [b]5[/b]
Actual answer
Adding stuff up: 2017: 11531 2016: 9496 2015: 9682 2014: 10301 2013: 14041 2012: 14952 2011: 22429 2010: 16273 2009: 21894 2001-2008: The [url=https://scioly.org/wiki/index.php/Scioly.org_History]Scioly.org history wiki[/url] says 36163 General Chat: 136330 Administrative: 2046 [b]Total: 305,138 posts Fermi Answer: 5[/b]
How far, in Planck lengths, would New Horizons travel in the time it takes for our Solar System to make one orbit around the center of the Milky Way?
There's a post count at the bottom of the main page :P
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Re: Fermi Questions C

Postby Unome » July 5th, 2017, 2:26 pm

Next question: what is the total number of posts on the Scioly.org forums?
My attempt
Every year there's about e4 posts (excluding general chat). scioly.org has been a thing for about 20 years, so that's about 2e5 posts total. I know general chat has around 1.5e5 total posts. My estimate is about 3.5e5 total posts. Fermi Answer of [b]5[/b]
Actual answer
Adding stuff up: 2017: 11531 2016: 9496 2015: 9682 2014: 10301 2013: 14041 2012: 14952 2011: 22429 2010: 16273 2009: 21894 2001-2008: The [url=https://scioly.org/wiki/index.php/Scioly.org_History]Scioly.org history wiki[/url] says 36163 General Chat: 136330 Administrative: 2046 [b]Total: 305,138 posts Fermi Answer: 5[/b]
How far, in Planck lengths, would New Horizons travel in the time it takes for our Solar System to make one orbit around the center of the Milky Way?
There's a post count at the bottom of the main page :P
By the way, the OBB archive has 177,009 posts, according to the Internet Archive (the Scioly.org History wiki page definitely has some incorrect information). You also forgot to include the posts from here, though I doubt those would change the answer.
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Re: Fermi Questions C

Postby Unome » July 10th, 2017, 12:32 pm

Current question, since we need some activity:
How far, in Planck lengths, would New Horizons travel in the time it takes for our Solar System to make one orbit around the center of the Milky Way?
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