MathDB

Description
The Estimation Round is a 60-minute team competition with a set of 8 short answer questions. In these questions, students must approximate a diverse set of real-world quantities as accurately as possible using their mathematical skills and worldly knowledge.
Answer Format and Scoring
Each problem’s answer is a positive integer as close to the true answer as our staff can produce. Teams will submit a positive integer answer for each problem in either fully simplified form (for example,

123456789

) or scientific notation (for example,

1.23456789\times10^8

). For problem

k

, let the staff answer be

z_k

. If a team leaves the answer space for problem

k

blank, their score on that problem will be

S_k=0

. Otherwise, let the team’s submission be

x_k

. Then their score on problem

k

S_k=\max\left(0,1-\left|\frac{\log_{10}|x_k/z_k|}{5}\right|\right)

This is constructed such that the score is in the interval

[0,1]

, and so that an estimate that is at most an order of magnitude from the staff answer earns a high score (at least

0.8

). A team's total score

S

on the exam, which will be used for rankings, is the sum of the scores for each problem:

S=\sum_{k=1}^8S_k

Verification
A team may ask, up to three times during the duration of the exam, whether, for a problem

k

, a closed interval of integers contains the staff answer

z_k

. (This does not mean three times per problem, but rather three attempts for the entire exam.) ——-- Problems
1. How many pet cats were there in the United States in

2012

?
2. How many passengers passed through Beijing Capital International Airport in

2015

?
3. What was the total worldwide revenue of all films in

2015

, in US dollars?
4. How many candies are in the container displayed in the front of the room?
5. If you stacked them from head to toe, how many male giraffes, on average, would it take to reach from the surface of the Earth to that of the moon, when the Earth and the moon are closest to each other?
6. How many total millimeters of rain does Singapore receive in an average year?
7. What is the mass of the Empire State Building in kilograms?
8. How many minutes before the scheduled start of this tournament’s opening ceremony was this problem written?
Appendix
Here are some facts that may or may not be useful for these problems.
[*] Population of the United States on December

31

2012

315219776

[/*] [*] Aircraft movements at Beijing Capital International Airport in

2015

590169

[/*] [*] Exchange rate for US dollars to CNY (Chinese Yuan/Renminbi) on December

31

2015

1\text{ USD}=6.5138\text{ CNY}

[/*] [*] Total sales for the

10

th highest selling film in

2015

(The Martian):

630161890\text{ USD}

[/*] [*] Average height of the International Space Station from Earth:

400\text{ km}

[/*] [*] Land area of Singapore at the end of

2016

719.7\text{ km}^2

[/*] [*] Density of iron:

7.874\text{ g/cm}^3

[/*] [*] The Empire State Building is a skyscraper in New York City and is

443.2\text{ m}

high. Refer to the projector screen for a picture of the building; it’s the largest building in the middle with the antenna. [/*]

Problem Statement