diff --git a/src/Warm-Ups/Mario Kart/main.tex b/src/Warm-Ups/Mario Kart/main.tex deleted file mode 100755 index f5af8a0..0000000 --- a/src/Warm-Ups/Mario Kart/main.tex +++ /dev/null @@ -1,54 +0,0 @@ -\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} \ No newline at end of file diff --git a/src/Warm-Ups/Mario Kart/main.typ b/src/Warm-Ups/Mario Kart/main.typ new file mode 100644 index 0000000..4c594b9 --- /dev/null +++ b/src/Warm-Ups/Mario Kart/main.typ @@ -0,0 +1,41 @@ +#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. + +])