Convert "Passing Balls" to typst
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This commit is contained in:
Mark 2025-01-23 13:34:46 -08:00
parent 7bc3520855
commit 358a289da2
Signed by: Mark
GPG Key ID: C6D63995FE72FD80
2 changed files with 38 additions and 47 deletions

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\documentclass[
solutions,
singlenumbering,
nopagenumber
]{../../../lib/tex/ormc_handout}
\usepackage{../../../lib/tex/macros}
\usepackage{graphicx}
\title{Warm-Up: Passing Balls}
\uptitler{\smallurl{}}
\subtitle{Prepared by Mark on \today}
\begin{document}
\maketitle
\problem{}
Twelve people are standing in a circle. Each is assigned a number between 1 and 12. \par
Participants numbered 1, 2, 3, and 4 hold red, green, yellow, and black balls, respectively. \par
Everyone else is empty-handed.
\vspace{2mm}
Each participant can pass their ball to any student that is exactly 5 positions away. \par
Balls cannot be passed to someone who has one in hand.
\vspace{2mm}
After a number of passes, the first four participants again hold all the balls. \par
Participant 1 has a black ball. Which balls are held by participants 2, 3, and 4?
\begin{solution}
\begin{itemize}
\item the graph of possible moves is isomorphic to a circle (since 5 and 12 are coprime),
\item but the balls get passed around, so swapping the place of any two balls is not allowed. \\
Therefore, the balls will stay in their initial (cyclic) order:
\end{itemize}
\begin{center}
\includegraphics[width=\textwidth]{pass-sol.png}
\end{center}
\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: Passing Balls],
by: "Mark",
)
#problem()
Twelve people are standing in a circle. Each is assigned a number between 1 and 12. \
Participants numbered 1, 2, 3, and 4 hold red, green, yellow, and black balls, respectively. \
Everyone else is empty-handed.
#v(2mm)
Each participant can pass their ball to any student that is exactly 5 positions away. \
Balls cannot be passed to someone who has one in hand.
#v(2mm)
After a number of passes, the first four participants again hold all the balls. \
Participant 1 has a black ball. Which balls are held by participants 2, 3, and 4?
#solution([
The graph of possible moves is isomorphic to a circle (since 5 and 12 are coprime), \
but the balls get passed around, so swapping the place of any two balls is not allowed.
#v(3mm)
Therefore, the balls will stay in their initial (cyclic) order:
// TODO: do this in CeTZ
#figure(image("pass-sol.png", width: 90%))
])