Wednesday, January 30, 2013

Interview: How many quarters would you need to reach the height of the Empire State building?

How many quarters would you need to reach the height of the Empire State building?

Below are 4 different ways that I could answer the question. The third one is the standard answer you'll hear from most people. The others are just my way of being different... although they may have already been thought by other people but I didn't find any (not that I spent a lot of time trying).

1. Assuming you start at the base of the Empire State building and knowing that the tallest building is around half a mile in height, the cheapest way to reach the height of the building would be to hike up a mountain. I don't know where the closest mountain is, flights are rather cheap. All flights will reach the needed height, thus the cheapest flight will do. Flight can be as low as $79, so $100 would be a safe guarantee for a flight. Thus it would take 429 quarters, including $5 for the airtrain to JFK and subway ($2.25).
2. If you had to return back to the base, then a helicopter tour would be cheaper at $150. Thus 600, maybe 618 if you take the subway.
3. If assuming stacking quarters as most people would assume it is asking, then you'll need the height of the building and the thickness of quarters to determine the "minimum" number of quarters you will need. Empire is not the tallest so I'd take a wild guess that it is about a third of a mile, thus around 1500 feet. Thickness of a quarter is maybe a sixteenth of an inch. 4 quarters is about a quarter inch, so seems reasonable. Since we're estimating let's use 15 (because it seems like it would be a nice round number for 1500). 1500 feet = 18000 inches. 18k * 15 quarters / inch = 270,000 quarters.
4. Given that I cannot even stack quarters beyond a foot, you'll probably need a pyramid worth of quarters. Equation for a cone is (pi) * r ^ 2 *h / 3. 45 degrees is a safe angle to stack quarters without them shifting, so r will the same as h. (3.14159 * 18k ^ 3) / 3 ~ (20k ^ 3) = 8 * 10 ^ 12 in^3. Volume of a quarter is a (pi) r^2 * h. Quarter is about an inch wide, (3 * 1^2 * 1/16) = 3/16 ~ 1/4 in^3. So it would take apprximately 32 * 10^12 quarters to reach the height of the empire state building.
5. Add the cost of all the labor to complete #4.

One answer provided online is 263,000 quarters. My third number is not far from that value. I still think the fourth one is most reasonable, although I think the first and second are funnier.

Other notes: Elevator available to the public doesn't take you all the way to the top. There is an argument whether antennas should be included in the height of a build. Asking what/which quarter implies you can ask the height of the empire state building, thus that would not be a good question (but it may not hurt to ask).

~ - approximately for easier calcuations
Question -
Anwer -
  Height of Empire State Building (roof) = 1250 feet = 381.0 meters = 102 floors
  Height of the tip of ESB = 1454 feet = 443.2 meters

1 comment:

  1. In the olden days of the Empire State Bldg, decades before any security measures one could park outside late at night and if people knew you where a broadcast engineer you could go up to the top free. Now to reach the very top you would have to coordinate with radio and TV stations to switch to alternate antennas to protect you from excessive RFR radio frequency radiation and probably be certified to climb and bring appropriate climbing gear. there you could do it with no quarters directly involved.