Convert "Odd Dice" to typst

2025-01-23 12:11:59 -08:00
parent de44590e49
commit 9ab33f47b3
2 changed files with 111 additions and 132 deletions
--- a/src/Warm-Ups/Odd
+++ b/src/Warm-Ups/Odd
@ -0,0 +1,111 @@
+#import "@local/handout:0.1.0": *
+#import "@preview/cetz:0.3.1"
+
+
+#show: handout.with(
+  title: [Warm-Up: Odd Dice],
+  by: "Mark",
+)
+
+#problem()
+We say a set of dice ${A, B, C}$ is _nontransitive_
+if, on average, $A$ beats $B$, $B$ beats $C$, and $C$ beats $A$.
+In other words, we get a counterintuitive "rock - paper - scissors" effect.
+
+#v(2mm)
+
+Create a set of nontransitive six-sided dice. \
+#hint([All sides should be numbered with positive integers less than 10.])
+
+#solution([
+  One possible set can be numbered as follows:
+  - Die $A$: $2, 2, 4, 4, 9, 9$
+  - Die $B$: $1, 1, 6, 6, 8, 8$
+  - Die $C$: $3, 3, 5, 5, 7, 7$
+
+  #v(2mm)
+
+  Another solution is below:
+  - Die $A$: $3, 3, 3, 3, 3, 6$
+  - Die $B$: $2, 2, 2, 5, 5, 5$
+  - Die $C$: $1, 4, 4, 4, 4, 4$
+
+])
+
+#v(1fr)
+
+#problem()
+Now, consider the set of six-sided dice below:
+- Die $A$: $4, 4, 4, 4, 4, 9$
+- Die $B$: $3, 3, 3, 3, 8, 8$
+- Die $C$: $2, 2, 2, 7, 7, 7$
+- Die $D$: $1, 1, 6, 6, 6, 6$
+- Die $E$: $0, 5, 5, 5, 5, 5$
+On average, which die beats each of the others? Draw a diagram.
+
+#solution(
+  align(
+    center,
+    cetz.canvas({
+      import cetz.draw: *
+
+      let s = 0.8 // Scale
+      let t = 13pt * s // text size
+      let radius = 0.3 * s
+
+      // Points
+      let a = (-2 * s, 0.2 * s)
+      let b = (0 * s, 2 * s)
+      let c = (2 * s, 0.2 * s)
+      let d = (1.2 * s, -2.1 * s)
+      let e = (-1.2 * s, -2.1 * s)
+
+      set-style(
+        stroke: (thickness: 0.6mm * s),
+        mark: (
+          end: (
+            symbol: ">",
+            fill: black,
+            offset: radius + (0.025 * s),
+            width: 1.2mm * s,
+            length: 1.2mm * s,
+          ),
+        ),
+      )
+
+      line(a, b)
+      line(b, c)
+      line(c, d)
+      line(d, e)
+      line(e, a)
+      line(a, c)
+      line(b, d)
+      line(c, e)
+      line(d, a)
+      line(e, b)
+
+      circle(a, radius: radius, fill: oblue, stroke: none)
+      circle(b, radius: radius, fill: oblue, stroke: none)
+      circle(c, radius: radius, fill: oblue, stroke: none)
+      circle(d, radius: radius, fill: oblue, stroke: none)
+      circle(e, radius: radius, fill: oblue, stroke: none)
+
+      content(a, text(fill: white, size: t, [*A*]))
+      content(b, text(fill: white, size: t, [*B*]))
+      content(c, text(fill: white, size: t, [*C*]))
+      content(d, text(fill: white, size: t, [*D*]))
+      content(e, text(fill: white, size: t, [*E*]))
+    }),
+  ),
+)
+
+#v(1fr)
+
+#problem()
+Now, say we roll each die twice. What happens to the graph from the previous problem?
+
+#solution([
+  The direction of each edge is reversed!
+])
+
+#v(1fr)