Added estimathon

Advanced/Estimathon/main.tex

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+% use [nosolutions] flag to hide solutions.
+% use [solutions] flag to show solutions.
+\documentclass[
+	solutions,
+	singlenumbering
+]{../../resources/ormc_handout}
+\usepackage{../../resources/macros}
+
+
+\uptitlel{Advanced 2}
+\uptitler{Winter 2023}
+\title{Estimathon}
+\subtitle{Prepared by \githref{Mark} on \today{}}
+
+
+\begin{document}
+
+
+	\maketitle
+
+	\section{Rules}
+
+	Your team will have 45 minutes to work on 20 estimation problems.
+	The answer to each problem is a positive real number. Your team will
+	submit intervals for each problem, which (ideally) contain the specified quantity.
+
+
+	\vspace{2mm}
+
+	An interval is \say{good} if it contains the true value. After the end of the game,
+	your team's score will be calculated as follows:
+
+	$$
+		\Biggl(10 +\sum_\text{good intervals}\biggl\lfloor\frac{\text{min}}{\text{max}}\biggr\rfloor\Biggr)
+		\times 2^{20 ~-~ \text{number of good intervals}}
+	$$
+
+	For every problem you miss or leave blank, your score doubles. \par
+	Your job is to \textbf{minimize} your score.
+
+
+	\vspace{8mm}
+
+	Every team will get 25 answer sheets. You may use one of these sheets to submit an interval at any time.
+	Make sure you write your team name, problem number, and interval (min and max) every time you submit.
+
+	\vspace{2mm}
+
+	There are 20 problems, but you are given 25 answer sheets. You may re-submit your solution to any problem
+	(as long as you have sheets remaining). Your latest answer will be kept.
+
+	\vspace{2mm}
+
+	Your interval may not use any mathematical operations except for scientific notation \par
+	(for example, $[2 \times 10^2, 3 \times 10^2]$ or $[2\text{e}2, 3\text{e}2]$)
+
+
+
+	\vfill
+	\pagebreak
+
+	\section{Problems}
+
+	\problem{}
+	What is the highest posted speed limit in the United States?
+
+	\begin{solution}
+		$85$ mi/hr
+	\end{solution}
+
+	\problem{}
+	What is the melting point of gold?
+
+	\begin{solution}
+		$1064.18$ C
+	\end{solution}
+
+	\problem{}
+	How many ways are there to tile a square with $2 \times 1$ and $1 \times 2$ dominos?
+
+	\problem{}
+	How many words are in Isaac Asimov's \textit{Foundation} trilogy?
+
+	\begin{solution}
+		About 250,000
+	\end{solution}
+
+
+	\problem{}
+	How much HP can the average horse produce (disregarding fatigue)?
+
+	\begin{solution}
+		About 15HP, as measured in 1925.
+	\end{solution}
+
+
+	\problem{}
+	What is the approximate speed of the magnetic north pole's drift? (in km/year)
+	\begin{solution}
+		60km/yr
+	\end{solution}
+
+	\problem{}
+	How many creatures are there in \textit{Dwarf Fortress}?
+
+	\begin{solution}
+		500 (estimate, no way I'm counting them all)
+	\end{solution}
+
+	\problem{}
+	What was the stock price of Apple on $2023-01-10$?
+	\begin{solution}
+		$\$186.19$
+	\end{solution}
+
+	\problem{}
+	How many undergraduates were enrolled at UCLA in the Fall of 2021?
+
+	\begin{solution}
+		32,121
+	\end{solution}
+
+	\problem{}
+	How many distinct groups are there on $60$ elements?
+
+	\begin{solution}
+		13
+	\end{solution}
+
+
+	\problem{}
+	For how many positive integers $n$ less than $10,000$ is $2^n -n^2$ divisible by $7$?
+
+	\begin{solution}
+		2858
+	\end{solution}
+
+	\problem{}
+	How many Serbian dinars can you exchange for $\$32.53$?
+	\begin{solution}
+		3,473.02
+	\end{solution}
+
+	\problem{}
+	How many lines of code were in the Linux repository in 2022?
+
+	\begin{solution}
+		About 27.8 million
+	\end{solution}
+
+	\problem{}
+	How many hours of podcasts has Mark listened to in 3.5 years of driving to UCLA?
+
+	\begin{solution}
+		809.4 hours
+	\end{solution}
+
+	\problem{}
+	Five boxes are filled with pastries. We know that box C contains a third of the pastries in E, and that
+	B contains two times more than C and E combined. Box A contains half the number of pastries in E, and
+	a tenth of those in D. Box B contains four times more pastries than D. \par
+	What is the minimal possible positive number of pastries in all the boxes put together?
+
+	\begin{solution}
+		310
+	\end{solution}
+
+
+	\problem{}
+	How many officially-recognized time zones are there?
+
+	\begin{solution}
+		Oddly enough, 38
+	\end{solution}
+
+
+	\problem{}
+	What is the smallest number ending in 34, divisible by 34, with a sum of digits equal to 34?
+	\begin{solution}
+		198934
+	\end{solution}
+
+
+	\problem{}
+	How many distinct typewriter models were produced by \textit{Smith Corona} since 1886?
+
+	\begin{solution}
+		106
+	\end{solution}
+
+	\problem{}
+	About how many people live on Antarctica during the winter?
+
+	\begin{solution}
+		About 1100; rises to about 5000 in Summer.
+	\end{solution}
+
+
+	\problem{}
+	What is the standard deviation of the above solutions?
+
+	\begin{solution}
+		7,2318.7
+	\end{solution}
+
+\end{document}