Convert "Mario Kart" to typst
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| \documentclass[ | ||||
| 	solutions, | ||||
| 	hidewarning, | ||||
| 	singlenumbering, | ||||
| 	nopagenumber | ||||
| ]{../../../lib/tex/ormc_handout} | ||||
| \usepackage{../../../lib/tex/macros} | ||||
|  | ||||
|  | ||||
| \title{Warm-Up: Mario Kart} | ||||
| \uptitler{\smallurl{}} | ||||
| \subtitle{Prepared by Mark on \today} | ||||
|  | ||||
|  | ||||
| \begin{document} | ||||
|  | ||||
| 	\maketitle | ||||
|  | ||||
| 	\problem{} | ||||
| 	A standard Mario Kart cup consists of 12 players and four races. \par | ||||
| 	Each race is scored as follows: | ||||
| 	\begin{itemize} | ||||
| 		\item 15 points are awarded for first place; | ||||
| 		\item 12 for second; | ||||
| 		\item and $(13 - \text{place})$ otherwise. | ||||
| 	\end{itemize} | ||||
| 	In any one race, no players may tie. | ||||
| 	A player's score at the end of a cup is the sum of their scores for each of the four races. | ||||
|  | ||||
| 	\vspace{2mm} | ||||
|  | ||||
| 	An $n$-way tie occurs when the top $n$ players have the same score at the end of a round. \par | ||||
| 	What is the largest possible $n$, and how is it achieved? | ||||
|  | ||||
| 	\begin{solution} | ||||
| 		A 12-way tie is impossible, since the total number of point is not divisible by 12. | ||||
|  | ||||
| 		\vspace{2mm} | ||||
|  | ||||
| 		A 11-way tie is possible, with a top score of 28: | ||||
| 		\begin{itemize} | ||||
| 			\item Four players finish $1^\text{st}$, $3^\text{ed}$, $11^\text{th}$, and $12^\text{th}$; | ||||
|  | ||||
| 			% spell:off | ||||
| 			\item Four players finish $2^\text{nd}$, $4^\text{th}$, $9^\text{th}$, and $10^\text{th}$; | ||||
| 			% spell:on | ||||
|  | ||||
| 			\item Two players finish fifth twice and seventh twice, | ||||
| 			\item One player finishes sixth in each race. | ||||
| 		\end{itemize} | ||||
| 		The final player always finishes eighth, with a non-tie score of 20. | ||||
| 	\end{solution} | ||||
|  | ||||
| \end{document} | ||||
							
								
								
									
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| #import "@local/handout:0.1.0": * | ||||
|  | ||||
| #show: handout.with( | ||||
|   title: [Warm-Up: Mario Kart], | ||||
|   by: "Mark", | ||||
| ) | ||||
|  | ||||
| #problem() | ||||
| A standard Mario Kart cup consists of 12 players and four races. \ | ||||
| Each race is scored as follows: | ||||
| - 15 points are awarded for first place; | ||||
| - 12 for second; | ||||
| - and $(13 - #text("place"))$ otherwise. | ||||
|  | ||||
| In any one race, no players may tie. \ | ||||
| A player's score at the end of a cup is the sum of their scores for each of the four races. | ||||
|  | ||||
| #v(2mm) | ||||
|  | ||||
| An $n$-way tie occurs when the top $n$ players have the same score at the end of a round. \ | ||||
| What is the largest possible $n$, and how is it achieved? | ||||
|  | ||||
| #solution([ | ||||
|   A 12-way tie is impossible, since the total number of point is not divisible by 12. | ||||
|  | ||||
|   #v(2mm) | ||||
|  | ||||
|   A 11-way tie is possible, with a top score of 28: | ||||
|   - Four players finish $1^#text("st")$, $3^#text("ed")$, $11^#text("th")$, and $12^#text("th")$; | ||||
|   - Four players finish $2^#text("nd")$, $4^#text("th")$, $9^#text("th")$, and $10^#text("th")$; // spell:disable-line | ||||
|   - Two players finish fifth twice and seventh twice, | ||||
|   - One player finishes sixth in each race. | ||||
|   The final player always finishes eighth, with a non-tie score of 20. | ||||
|  | ||||
| ]) | ||||
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