diff --git a/src/Warm-Ups/Passing Balls/main.tex b/src/Warm-Ups/Passing Balls/main.tex deleted file mode 100755 index 4a57dc1..0000000 --- a/src/Warm-Ups/Passing Balls/main.tex +++ /dev/null @@ -1,47 +0,0 @@ -\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} \ No newline at end of file diff --git a/src/Warm-Ups/Passing Balls/main.typ b/src/Warm-Ups/Passing Balls/main.typ new file mode 100644 index 0000000..27e9e4f --- /dev/null +++ b/src/Warm-Ups/Passing Balls/main.typ @@ -0,0 +1,38 @@ +#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%)) +])