[Notes] - Guestimathon

Notes for Guestimathon by Lawrence Weinstein

Chapter 1

1. Take a problem, break into smaller steps s.t. for these steps you can estimate the upperbound and lowerbound immediately. Estimate the smaller steps and multiply it to get an estimate for the eventual answer.

2. Take the geometric mean of the upperbound and lowerbound. An estimate of the geometric mean is the average of the coefficients and exponents.

Estimate of Geometric mean of and :

If the sum of exponents is odd, round down and * 3.

Useful Numbers

Common Numbers in Life

1. # seconds in a year:

2. # people in the world: , in developed countries

3. Average computer runs about 3GHz, which is instructions per second

4. Area of the united states: .

5. Weights of a Car:

6. Liquid to Gas: Density expand by 1000.

7. U.S. per capita gross domestic
   product: $85.8k

8. A person drives per year

Energy

1. Heat capacity of water is (among the highest of any material in the world)
   , Note that 1 cal = 1 J

2. Cost of 1kWh is about $

3. Typical energy of a strong chemical bond is . We know this because common batteries, which convert chemical energy into electrical energy, operate at . It takes one chemical reaction to move one electron through a potential difference of , changing its energy by .

4. Energy Density of Carbon Energy Density of Gasoline:

6. Density of water:

7. Cars on average drives on gasoline

8. Flushing toilet cost 5L water, 15L/min when showering