Convert "Mario Kart" to typst

This commit is contained in:
Mark 2025-01-22 21:18:40 -08:00
parent 285ccaad01
commit a7d869cc68
Signed by: Mark
GPG Key ID: C6D63995FE72FD80
2 changed files with 41 additions and 54 deletions

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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: doc => handout(
doc,
quarter: link(
"https://betalupi.com/handouts",
"betalupi.com/handouts",
),
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 $10^#text("th")$;
- 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.
])