src/Warm-Ups/Passing Balls/main.tex

@@ -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}

src/Warm-Ups/Passing Balls/main.typ

@@ -0,0 +1,192 @@
+#import "@local/handout:0.1.0": *
+#import "@preview/cetz:0.3.1"
+
+#show: handout.with(
+  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), \
+  so the order of the balls cannot be changed as they are passed around.
+
+  #v(2mm)
+
+  Therefore, the balls will stay in their initial (cyclic) order:
+
+  #v(2mm)
+
+  #{
+    let s = 0.7 // scale
+    let t = 12pt * s // text size
+    let radius = 0.35
+
+    let pts = (
+      (0 * s, 3 * s),
+      (1 * s, 2 * s),
+      (2 * s, 1 * s),
+      (3 * s, 0 * s),
+      (2 * s, -1 * s),
+      (1 * s, -2 * s),
+      (0 * s, -3 * s),
+      (-1 * s, -2 * s),
+      (-2 * s, -1 * s),
+      (-3 * s, 0 * s),
+      (-2 * s, 1 * s),
+      (-1 * s, 2 * s),
+    )
+
+    let pts_shuf = (
+      (0 * s, 3 * s), // 1
+      (1 * s, -2 * s), // 6
+      (-2 * s, 1 * s), // 11
+      (3 * s, 0 * s), // 4
+      (-2 * s, -1 * s), // 9
+      (1 * s, 2 * s), // 2
+      (0 * s, -3 * s), // 7
+      (-1 * s, 2 * s), // 12
+      (2 * s, -1 * s), // 5
+      (-3 * s, 0 * s), // 10
+      (2 * s, 1 * s), // 3
+      (-1 * s, -2 * s), // 8
+    )
+
+    table(
+      stroke: none,
+      align: center,
+      columns: (1fr, 1fr, 1fr),
+      cetz.canvas({
+        import cetz.draw: *
+
+        set-style(stroke: (thickness: 0.4mm, paint: black))
+        line(..pts_shuf, close: true)
+
+        let i = 1
+        for p in pts {
+          circle(
+            p,
+            radius: radius * s,
+            fill: if i == 1 {
+              ored
+            } else if i == 2 {
+              ogreen
+            } else if i == 3 {
+              oorange
+            } else if i == 4 {
+              oblue
+            } else { white },
+          )
+
+          content(
+            p,
+            text(
+              fill: if i <= 4 {
+                white
+              } else {
+                black
+              },
+              size: t,
+              [*#i*],
+            ),
+          )
+          i = i + 1
+        }
+      }),
+      cetz.canvas({
+        import cetz.draw: *
+
+        set-style(stroke: (thickness: 0.4mm, paint: black))
+        line(..pts, close: true)
+
+        let i = 1
+        for p in pts {
+          let l = calc.rem(((i - 1) * 5), 12) + 1
+
+
+          circle(
+            p,
+            radius: radius * s,
+            fill: if l == 1 {
+              ored
+            } else if l == 2 {
+              ogreen
+            } else if l == 3 {
+              oorange
+            } else if l == 4 {
+              oblue
+            } else { white },
+          )
+
+          content(
+            p,
+            text(
+              fill: if l <= 4 {
+                white
+              } else {
+                black
+              },
+              size: t,
+              [*#l*],
+            ),
+          )
+          i = i + 1
+        }
+      }),
+      cetz.canvas({
+        import cetz.draw: *
+
+        set-style(stroke: (thickness: 0.4mm, paint: black))
+        line(..pts, close: true)
+
+        let i = 1
+        for p in pts {
+          let l = calc.rem(((i - 1) * 5), 12) + 1
+
+
+          circle(
+            p,
+            radius: radius * s,
+            fill: if l == 1 {
+              oblue
+            } else if l == 2 {
+              oorange
+            } else if l == 3 {
+              ored
+            } else if l == 4 {
+              ogreen
+            } else { white },
+          )
+
+          content(
+            p,
+            text(
+              fill: if l <= 4 {
+                white
+              } else {
+                black
+              },
+              size: t,
+              [*#l*],
+            ),
+          )
+          i = i + 1
+        }
+      }),
+    )
+  }
+])