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1a486e2d98
WIP ODD DICE
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2025-01-23 10:33:32 -08:00

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@ -1,6 +1,4 @@
#import "@local/handout:0.1.0": *
#import "@preview/cetz:0.3.1"
#show: doc => handout(
doc,
@ -29,7 +27,7 @@ Create a set of nontransitive six-sided dice. \
- Die $B$: $1, 1, 6, 6, 8, 8$
- Die $C$: $3, 3, 5, 5, 7, 7$
#v(2mm)
#v(4mm)
Another solution is below:
- Die $A$: $3, 3, 3, 3, 3, 6$
@ -49,66 +47,38 @@ Now, consider the set of six-sided dice below:
- 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: *
#solution([
/*
\begin{tikzpicture}[scale = 0.5]
\begin{scope}[layer = nodes]
\node[main] (a) at (-2, 0.2) {$a$};
\node[main] (b) at (0, 2) {$b$};
\node[main] (c) at (2, 0.2) {$c$};
\node[main] (d) at (1, -2) {$d$};
\node[main] (e) at (-1, -2) {$e$};
\end{scope}
let s = 0.8 // Scale
let t = 13pt * s // text size
let radius = 0.3 * s
\draw[->]
(a) edge (b)
(b) edge (c)
(c) edge (d)
(d) edge (e)
(e) edge (a)
// 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*]))
}),
),
)
(a) edge (c)
(b) edge (d)
(c) edge (e)
(d) edge (a)
(e) edge (b)
;
\end{tikzpicture}
*/
])
#v(1fr)
#problem()
Now, say we roll each die twice. What happens to the graph from the previous problem?
Now, say we roll each die twice. What happens to the graph fromE the previous problem?
#solution([
The direction of each edge is reversed!