diff --git a/app/src/main/res/values/strings.xml b/app/src/main/res/values/strings.xml
index fc2605c..8ce9a44 100644
--- a/app/src/main/res/values/strings.xml
+++ b/app/src/main/res/values/strings.xml
@@ -620,7 +620,7 @@
         <item>This one is very similar to the fox problem: the answer is simple if you use linearity of expectation. If you focus on the women, for example, the answer is 8*E[X_1], where X_1 is the number of men sitting next to woman number one, i.e. X_1 is either 0, 1 or 2.</item>
         <item>Try solving the previous puzzle first (read its hint if you are stuck). The only difference here is accounting for the probability of sitting at the ends of the table, in which case you have only one neighbor. Intuitively, this should lead to a smaller number than in the previous puzzle. See https://stats.stackexchange.com/a/509919/9330 for a detailed solution.</item>
         <item>The definition of correlation is Corr[X, Y] = Cov[X, Y] / (Var[X]*Var[Y])^0.5, and you can reach the answer by following the definitions and integrating. A trick is to think of a regression of writing ability on math ability conditional on attending college &#8212; the slope of that regression line will give the correlation. Make sure you understand why that works!</item>
-        <item>Use the inclusion-exclusion principle. The two-event version is Pr[A or B] = Pr[A] + Pr[B] - Pr[A and B]; you need to use the n-event version where n is the number of people (and also the number of hats).</item>
+        <item>Use the inclusion-exclusion principle. The two-event version is Pr[A or B] = Pr[A] + Pr[B] - Pr[A and B]; you need to use the n-event version where n is the number of people (and also the number of hats). See https://stats.stackexchange.com/questions/464727/unexpected-result-from-very-simple-statistics-problem for a solution to a very similar problem.</item>
         <item>Starting at any positive initial wealth x, think about the probability of ever reaching state (x - 1). The answer you\'re looking for is just the square of that probability: to go broke you have to at some point reach a wealth of $1, and then, having gotten there, at some point reach a wealth of $0.</item>
         <item>Suppose I were asking about a resample of size five from a collection of five objects. Picture five dots and four bars laid out in a line, like this: oo|o||oo|. That particular sequence represents a resample in which the first object is sampled twice, the second once, the third never, the fourth twice, and the fifth never. How many distinct sequences can be generated using the same number of circles and bars?</item>
         <item>Start by calculating the expected number of total visits to the origin. What is the connection between that number and the probability of ever returning?</item>
diff --git a/scripts/create_res_drawable.R b/scripts/create_res_drawable.R
new file mode 100644
index 0000000..bbbd33c
--- /dev/null
+++ b/scripts/create_res_drawable.R
@@ -0,0 +1,479 @@
+## From the Android docs
+## https://developer.android.com/guide/topics/resources/drawable-resource
+## "A drawable resource is a general concept for a graphic that can be drawn to the screen"
+## This script creates the graphics that are shown underneath certain puzzle descriptions
+## For example, app/src/main/res/drawable-hdpi/backgammon_small.png
+## is shown in a puzzle about the probability of certain jumps in the game of backgammon
+
+library(ggplot2)
+library(grid)
+library(optparse)
+
+source("utils.R")
+
+opt_list <- list(make_option("--filename_suffix", default="", type="character"),
+                 make_option("--voter_x_label", default="voter 4", type="character"),
+                 make_option("--voter_y_label", default="voter 3", type="character"))
+opt <- parse_args(OptionParser(option_list=opt_list))
+
+message("command line options: ", paste(sprintf("%s=%s", names(opt), opt), collapse=", "))
+
+set_ggplot_theme()
+theme_update(panel.grid.major=element_blank())
+theme_update(panel.grid.minor=element_blank())
+theme_update(axis.text=element_text(size=rel(1.6)))
+theme_update(axis.text.x=element_text(size=rel(1.6)))
+theme_update(axis.text.y=element_text(size=rel(1.6)))
+df <- data.frame(x=c(0, 0, 1, 1),
+                 y=c(0, -1, 0, -1),
+                 label=c("?", "?", "?", "0.6*2/3"))
+colors <- c("#a6611a", "#018571")
+jitter <- 0.05
+p <- (ggplot(df, aes(x=x, y=y, label=label)) +
+      geom_rect(xmin=-0.5+jitter, xmax=1.5+jitter, ymin=-1.5+jitter, ymax=-0.5+jitter,
+                fill="white", color=colors[1], size=3.0, alpha=0) +  # Horizontal
+      annotate("text", x=1.8, y=-1+jitter, color=colors[1], label="0.6", size=11) +
+      geom_rect(xmin=0.5, xmax=1.5, ymin=-1.5, ymax=0.5, fill="white", color=colors[2], size=3.0, alpha=0) +  # Vertical
+      annotate("text", x=1, y=0.65, color=colors[2], label="0.6", size=11) +
+      geom_text(size=8) +
+      scale_y_continuous(opt$voter_y_label, breaks=c(-1, 0), labels=c("C", "T"), lim=c(-2, 1)) +
+      scale_x_continuous(opt$voter_x_label, breaks=c(0, 1), labels=c("T", "C"), lim=c(-1, 2)))
+p
+ggsave(sprintf("CT_vote_table%s.png", opt$filename_suffix), p, width=8, height=8)
+
+set_ggplot_theme()
+df <- data.frame(number_bets=seq(0, 11), fortune=c(seq(1, 6), seq(5, 0)))
+df$fortune_alternate <- cumsum(c(1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1))
+p <- (ggplot(df, aes(x=number_bets, y=fortune)) +
+      geom_segment(aes(x=0, y=0, xend=max(df$number_bets), yend=0), size=1.5, color="grey", linetype=2) +
+      geom_point(aes(x=0, y=1), color="black", size=4) +
+      geom_line(size=3, color="black") +
+      geom_line(aes(x=number_bets, y=fortune_alternate), size=3, color="black") +
+      geom_point(aes(x=max(df$number_bets), y=0), color="#E69F00", size=6) +
+      scale_x_continuous("number of bets completed", breaks=c(0, 5, 10)) +
+      ylab("gambler's fortune"))
+p
+ggsave("gambler_broke_11_bets.png", p, width=8, height=6)
+
+color_left <- "#386cb0"
+color_right <- "#7fc97f"
+breakpoint <- 0.4
+p <- (ggplot(data.frame(x=c(0, 1), y=c(0, 0)), aes(x=x, y=y)) +
+      geom_segment(x=0, y=0, xend=breakpoint, yend=0, size=3, color=color_left) +
+      geom_segment(x=breakpoint, y=0, xend=1.0, yend=0, size=3, color=color_right) +
+      annotate("text", x=breakpoint/2, y=0.01, label="left piece", color=color_left, size=10) +
+      annotate("text", x=(breakpoint + 1)/2, y=0.01, label="right piece", color=color_right, size=10) +
+      scale_x_continuous("", breaks=c(0, breakpoint, 1), labels=c("0", "uniform random breakpoint", "1"),
+                         lim=c(0, 1)) +
+      scale_y_continuous("", breaks=NULL, lim=c(-0.02, 0.05)))
+p
+ggsave("random_breakpoint.png", p, width=8, height=4)
+
+votes_C <- 70
+votes_T <- 30
+df <- data.frame(counted=seq(0, votes_C + votes_T))
+df$lower_bound <- cumsum(c(0, rep(-1, votes_T), rep(1, votes_C)))
+df$upper_bound <- cumsum(c(0, rep(1, votes_C), rep(-1, votes_T)))
+df$path1 <- c(0, cumsum(c(rep(1, 8),
+                          sample(c(rep(1, votes_C-8), rep(-1, votes_T)), size=votes_C + votes_T - 8, replace=FALSE))))
+df$path2 <- c(0, cumsum(c(rep(1, 5),
+                          rep(-1, 5),
+                          sample(c(rep(1, votes_C-5), rep(-1, votes_T-5)), size=votes_C + votes_T - 10, replace=FALSE))))
+df$path2_color <- ifelse(df$counted <= 10, "before", "after")
+scale_color <- c("before"="#E69F00", "after"="black")
+
+p <- (ggplot(df, aes(x=counted, y=upper_bound)) +
+      geom_segment(aes(x=0, y=0, xend=2*votes_T, yend=0), size=1.5, color="grey", linetype=2) +
+      geom_point(aes(x=0, y=0), color="black", size=4) +
+      geom_point(aes(x=max(df$counted), y=votes_C - votes_T), color="black", size=4) +
+      geom_line(size=3.0, color="black") +
+      geom_line(aes(x=counted, y=lower_bound), size=3.0, color="black") +
+      geom_line(aes(x=counted, y=path1), size=2.0, color="black") +
+      geom_line(aes(x=counted, y=path2), size=2.0, color="black") +
+      geom_point(aes(x=10, y=0), color="#E69F00", size=8, shape="O") +  # No longer strictly in the lead
+      scale_color_manual("", values=scale_color, guide=FALSE) +
+      xlab("number of votes counted") + ylab("net votes for C"))
+p
+ggsave("vote_counting.png", p, width=8, height=6)
+
+votes_C <- 7
+votes_T <- 3
+df <- data.frame(counted=seq(0, votes_C + votes_T))
+df$lower_bound <- cumsum(c(0, rep(-1, votes_T), rep(1, votes_C)))
+df$upper_bound <- cumsum(c(0, rep(1, votes_C), rep(-1, votes_T)))
+df$path1 <- c(0, cumsum(c(rep(1, 2),
+                          sample(c(rep(1, votes_C-2), rep(-1, votes_T)), size=votes_C + votes_T - 2, replace=FALSE))))
+df$path2 <- c(0, cumsum(c(rep(1, 2),
+                          rep(-1, 2),
+                          sample(c(rep(1, votes_C-2), rep(-1, votes_T-2)), size=votes_C + votes_T - 4, replace=FALSE))))
+p <- (ggplot(df, aes(x=counted, y=upper_bound)) +
+      geom_segment(aes(x=0, y=0, xend=2*votes_T, yend=0), size=1.5, color="grey", linetype=2) +
+      geom_point(aes(x=0, y=0), color="black", size=4) +
+      geom_point(aes(x=max(df$counted), y=votes_C - votes_T), color="black", size=4) +
+      geom_line(size=3.0, color="black") +
+      geom_line(aes(x=counted, y=lower_bound), size=3.0, color="black") +
+      geom_line(aes(x=counted, y=path1), size=2.0, color="black") +
+      geom_line(aes(x=counted, y=path2), size=2.0, color="black") +
+      geom_point(aes(x=4, y=0), color="#E69F00", size=8, shape="O") +  # No longer strictly in the lead
+      scale_color_manual("", values=scale_color, guide=FALSE) +
+      scale_x_continuous("number of votes counted", breaks=seq(0, 10, 2)) +
+      scale_y_continuous("net votes for C", breaks=seq(-2, 6, 2)))
+p
+ggsave("vote_counting_easy.png", p, width=8, height=6)
+
+df <- data.frame(x=c(0, 100), y=c(20, 80))
+p <- (ggplot(df, aes(x=x, y=y)) +
+      geom_abline(intercept=0, slope=1, color="grey", linetype=2, size=2) +
+      geom_line(size=3, color="#009E73") +
+      scale_y_continuous("child's income percentile", limits=c(0, 100),
+                         breaks=c(0, 20, 100)) +
+      scale_x_continuous("parents' income percentile", breaks=c(0, 100)))
+p
+ggsave("income.png", p, width=8, height=6)
+
+draw_curve1 <- curveGrob(0, 1, 1, 0,  # Top left to bottom right
+                         default.units="npc",
+                         curvature=-0.3, angle=90, ncp=20, shape=1,
+                         square=FALSE, squareShape=1,
+                         inflect=FALSE, arrow=arrow(), open=TRUE,
+                         debug=FALSE, name=NULL, gp=gpar(lwd=3), vp=NULL)
+draw_curve2 <- curveGrob(0, 1, 1, 0,  # Top left to bottom right, used for 0 to 6 jump in backgammon
+                         default.units="npc",
+                         curvature=-0.5, angle=90, ncp=20, shape=1,
+                         square=FALSE, squareShape=1,
+                         inflect=FALSE, arrow=arrow(), open=TRUE,
+                         debug=FALSE, name=NULL, gp=gpar(lwd=3), vp=NULL)
+draw_curve3 <- curveGrob(0, 0, 1, 1,  # Bottom left to top right
+                         default.units="npc",
+                         curvature=-0.4, angle=90, ncp=20, shape=1,
+                         square=FALSE, squareShape=1,
+                         inflect=FALSE, arrow=arrow(), open=TRUE,
+                         debug=FALSE, name=NULL, gp=gpar(lwd=3), vp=NULL)
+draw_curve4 <- curveGrob(1, 1, 0, 0,  # Top right to bottom left
+                         default.units="npc",
+                         curvature=0.5, angle=90, ncp=20, shape=1,
+                         square=FALSE, squareShape=1,
+                         inflect=FALSE, arrow=arrow(), open=TRUE,
+                         debug=FALSE, name=NULL, gp=gpar(lwd=3), vp=NULL)
+draw_curve5 <- curveGrob(1, 0, 0, 1,  # Bottom right to top left
+                         default.units="npc",
+                         curvature=-0.3, angle=90, ncp=20, shape=1,
+                         square=FALSE, squareShape=1,
+                         inflect=FALSE, arrow=arrow(), open=TRUE,
+                         debug=FALSE, name=NULL, gp=gpar(lwd=3), vp=NULL)
+
+set_ggplot_theme()
+df <- data.frame(x=seq(0, 6), y=0)
+p <- (ggplot(df, aes(x=x, y=y)) +
+      scale_x_continuous("", breaks=seq(0, 6), limits=c(-0.75, 6.75)) +
+      scale_y_continuous("", breaks=c(), limits=c(-0.01, 0.10)) +
+      geom_hline(yintercept=0, size=1.25) +
+      geom_rect(xmin=-0.4, xmax=0.4, ymin=0.005, ymax=0.02, color="black", fill="black") +
+      geom_rect(xmin=-0.4, xmax=0.4, ymin=0.025, ymax=0.04, color="black", fill="black") +
+      geom_rect(xmin=5.6, xmax=6.4, ymin=0.005, ymax=0.02, color="grey", fill="grey") +
+      annotation_custom(grob=draw_curve1, 0, 3.95, 0.005, 0.045) +  # Little jump
+      annotation_custom(grob=draw_curve2, 0, 6, 0.026, 0.045) +  # Big jump from 0 to 6
+      annotation_custom(grob=draw_curve3, 4.05, 5.8, 0.005, 0.023) +  # Second little jump
+      geom_blank())
+p
+ggsave("backgammon.png", p, width=10, height=6)
+
+set_ggplot_theme(map=TRUE)
+n <- 4
+x <- seq(0, n)
+df <- data.frame(p=dbinom(x, n, prob=0.35), x=x)
+stopifnot(sum(df$p) == 1)
+p <- (ggplot(df, aes(x=x, y=p)) +
+      geom_bar(stat="identity", color="black", fill="white", size=5) +
+      xlab("") + ylab(""))
+p
+ggsave("probility_mass.png", p, width=10, height=8)  # Unused
+
+set_ggplot_theme()
+theme_update(panel.grid.major=element_line(size=0.6, color="grey90"))
+theme_update(panel.grid.minor=element_blank())
+range <- 1
+df <- expand.grid(x=seq(-range, range), y=seq(-range, range))
+df <- subset(df, (x != 0 & y != 0) | (y == 0 & x == 0))
+my_arrow <- arrow(length=unit(1, "cm"))
+end <- 0.85
+line_color <-"#999999"
+p <- (ggplot(df, aes(x=x, y=y)) +
+      xlim((range + 0.5)*c(-1, 1)) + ylim((range + 0.5)*c(-1, 1)) +
+      xlab("") + ylab("") +
+      geom_segment(aes(x=0, y=0, xend=end, yend=end), arrow=my_arrow, size=2,
+                   color=line_color) +
+      geom_segment(aes(x=-0, y=0, xend=-end, yend=end), arrow=my_arrow, size=2,
+                   color=line_color) +
+      geom_segment(aes(x=0, y=-0, xend=end, yend=-end), arrow=my_arrow, size=2,
+                   color=line_color) +
+      geom_segment(aes(x=-0, y=-0, xend=-end, yend=-end), arrow=my_arrow, size=2,
+                   color=line_color) +
+      geom_point(size=12, color="black"))
+p
+ggsave("particle_large.png", p, width=10, height=8)
+ggsave("particle_small.png", p, width=5, height=4)
+
+set_ggplot_theme(map=TRUE)
+n_guests <- 9
+theta <- head(seq(0, 2*pi, length.out=n_guests + 2), n_guests + 1)
+df <- data.frame(theta=theta)
+df$is_host <- FALSE
+df$is_host[3] <- TRUE
+df$x <- cos(theta)
+df$y <- sin(theta)
+p <- (ggplot(df, aes(x=x, y=y, color=is_host)) +
+      scale_color_manual("", guide=F, values=c("black", "#E69F00")) +
+      xlim(c(-1.1, 1.1)) + ylim(c(-1.1, 1.1)) +
+      annotate("text", x=df$x[2] + 0.12, y=df$y[2] + 0.15, label="A", color="black", size=10) +
+      annotate("text", x=df$x[1] - 0.2, y=df$y[1] + 0.05, label="B", color="black", size=10) +
+      annotate("text", x=df$x[10] + 0.12, y=df$y[10] - 0.1, label="C", color="black", size=10) +
+      annotate("text", x=df$x[3] - 0.25, y=df$y[3] + 0.12, label="host",
+               color="#E69F00", size=10) +
+      annotate("text", x=df$x[4] - 0.25, y=df$y[4] + 0.1, label="you",
+               color="black", size=10) +
+      annotation_custom(grob=draw_curve2,
+                        df$x[3], df$x[2] - 0.01,
+                        df$y[3], df$y[2] + 0.1) +  # From host to A
+      annotation_custom(grob=draw_curve2,
+                        df$x[2], df$x[1] + 0.05,
+                        df$y[2], df$y[1] + 0.1) +  # From A to B
+      annotation_custom(grob=draw_curve5,
+                        df$x[1], df$x[2] + 0,
+                        df$y[1], df$y[2] - 0.1) +  # From B back to A
+      annotation_custom(grob=draw_curve4,
+                        df$x[1], df$x[10] - 0,
+                        df$y[1], df$y[10] + 0.1) +  # From B to C
+      geom_point(shape=20, size=14) +  # Draw points after arrows
+      xlab("") + ylab(""))
+p
+ggsave("table.png", p, width=6, height=6)
+
+## Sum equals 12
+set_ggplot_theme()
+df <- expand.grid(first=seq(1, 6), second=seq(1, 6))
+df$condition <- (df$first + df$second) == 12
+p <- (ggplot(df, aes(x=first, y=second, color=condition, shape=condition)) +
+      scale_color_manual("", guide=F, values=c("#0072B2", "#D55E00")) +
+      scale_shape_manual("", guide=F, values=c(1, 19)) +
+      xlab("first roll") + ylab("second roll") +
+      scale_x_continuous(breaks=seq(1, 6)) +
+      scale_y_continuous(breaks=seq(1, 6)) +
+      geom_point(size=10))
+p
+ggsave("roll_12.png", p, width=6, height=5)  # Unused
+
+## Sum equals 7
+set_ggplot_theme()
+df <- expand.grid(first=seq(1, 6), second=seq(1, 6))
+df$condition <- (df$first + df$second) == 7
+df$sum <- df$first + df$second
+p <- (ggplot(df, aes(x=first, y=second, color=condition, shape=condition)) +
+      scale_color_manual("", guide=F, values=c("#0072B2", "#D55E00")) +
+      scale_shape_manual("", guide=F, values=c(1, 19)) +
+      xlab("first roll") + ylab("second roll") +
+      scale_x_continuous(breaks=seq(1, 6)) +
+      scale_y_continuous(breaks=seq(1, 6)) +
+      geom_point(size=10))
+p
+ggsave("roll_7.png", p, width=6, height=5)  # Unused
+
+p <- (ggplot(df, aes(x=first, y=second, color=sum)) +
+      xlab("first roll") + ylab("second roll") +
+      scale_color_gradient2("", guide=FALSE, midpoint=7,
+                            low="#f0f0f0", mid="#1c9099", high="#f0f0f0") +
+      scale_x_continuous(breaks=seq(1, 6)) +
+      scale_y_continuous(breaks=seq(1, 6)) +
+      geom_point(size=10))
+p
+ggsave("roll_7.png", p, width=6, height=5)
+
+## Two girls out of two children
+set_ggplot_theme()
+theme_update(axis.text=element_text(size=rel(1.6)))
+theme_update(axis.text.x=element_text(size=rel(1.6)))
+theme_update(axis.text.y=element_text(size=rel(1.6)))
+n_children <- 2
+n_girls <- seq(0, n_children)
+df <- data.frame(girls=n_girls, prob=dbinom(x=n_girls, size=n_children, prob=0.49))
+df$condition <- df$girls == 2
+p <- (ggplot(df, aes(x=girls, y=prob, color=condition)) +
+      geom_bar(fill="white", size=4, stat="identity") +
+      scale_color_manual("", guide=F, values=c("#999999", "#009E73")) +
+      xlab("number of girls") + ylab("probability"))
+p
+ggsave(filename="two_girls.png", p, width=6, height=4)  # Unused
+
+n_children <- 2
+n_girls <- seq(0, n_children)
+df <- data.frame(girls=n_girls, prob=dbinom(x=n_girls, size=n_children, prob=0.49))
+p <- (ggplot(df, aes(x=girls, y=prob)) +
+      geom_segment(aes(x=girls, xend=girls, yend=prob), y=0, size=2, color="grey") +
+      geom_point(size=10, shape=16) +
+      ylab("probability") + ylim(0, 0.55) +
+      scale_x_continuous("number of girls", breaks=df$girls))
+p
+ggsave(filename="two_girls_v2.png", p, width=6, height=4)
+
+n_children <- 2
+n_girls <- seq(0, n_children)
+df <- data.frame(girls=n_girls, prob=dbinom(x=n_girls, size=n_children, prob=0.49))
+p <- (ggplot(df, aes(x=girls, y=prob)) +
+      geom_segment(aes(x=girls, xend=girls, yend=prob), y=0, size=12, color="grey") +
+      ylab("probability") + ylim(0, 0.55) +
+      scale_x_continuous("number of girls", breaks=df$girls, limits=c(-0.1, n_children + 0.1)))
+p
+ggsave(filename="two_girls_v3.png", p, width=6, height=4)
+
+## One girl out of three children
+n_children <- 3
+n_girls <- seq(0, n_children)
+df <- data.frame(girls=n_girls, prob=dbinom(x=n_girls, size=n_children, prob=0.49))
+df$condition <- df$girls == 1
+p <- (ggplot(df, aes(x=girls, y=prob, color=condition)) +
+      geom_bar(fill="white", size=4, stat="identity") +
+      scale_color_manual("", guide=F, values=c("#999999", "#009E73")) +
+      xlab("number of girls") + ylab("probability"))
+p
+ggsave(filename="one_girl_out_of_three.png", p, width=6, height=4)  # Unused
+
+set_ggplot_theme()
+n_children <- 3
+n_girls <- seq(0, n_children)
+df <- data.frame(girls=n_girls, prob=dbinom(x=n_girls, size=n_children, prob=0.49))
+p <- (ggplot(df, aes(x=girls, y=prob)) +
+      geom_segment(aes(x=girls, xend=girls, yend=prob), y=0, size=2, color="grey") +
+      geom_point(size=10, shape=16) +
+      ylab("probability") + ylim(0, 0.45) +
+      scale_x_continuous("number of girls", breaks=df$girls))
+p
+ggsave(filename="one_girl_out_of_three_v2.png", p, width=6, height=4)
+
+n_children <- 3
+n_girls <- seq(0, n_children)
+df <- data.frame(girls=n_girls, prob=dbinom(x=n_girls, size=n_children, prob=0.49))
+p <- (ggplot(df, aes(x=girls, y=prob)) +
+      geom_segment(aes(x=girls, xend=girls, yend=prob), y=0, size=12, color="grey") +
+      ylab("probability") + ylim(0, 0.45) +
+      scale_x_continuous("number of girls", breaks=df$girls, limits=c(-0.1, n_children + 0.1)))
+p
+ggsave(filename="one_girl_out_of_three_v3.png", p, width=6, height=4)
+
+## Eight children
+n_children <- 8
+n_girls <- seq(0, n_children)
+df <- data.frame(girls=n_girls, prob=dbinom(x=n_girls, size=n_children, prob=0.49))
+df$condition <- df$girls %in% c(0, 8)
+p <- (ggplot(df, aes(x=girls, y=prob, color=condition)) +
+      geom_bar(fill="white", size=4, stat="identity") +
+      scale_color_manual("", guide=F, values=c("#999999", "#009E73")) +
+      scale_x_continuous("number of girls", breaks=df$girls) +
+      ylab("probability"))
+p
+ggsave(filename="eight_children.png", p, width=8, height=4)  # Unused
+
+n_children <- 8
+n_girls <- seq(0, n_children)
+df <- data.frame(girls=n_girls, prob=dbinom(x=n_girls, size=n_children, prob=0.49))
+p <- (ggplot(df, aes(x=girls, y=prob)) +
+      geom_segment(aes(x=girls, xend=girls, yend=prob), y=0, size=2, color="grey") +
+      geom_point(size=10, shape=16) +
+      ylab("probability") + ylim(0, 0.30) +
+      scale_x_continuous("number of girls", breaks=df$girls))
+p
+ggsave(filename="eight_children_v2.png", p, width=8, height=4)
+
+n_children <- 8
+n_girls <- seq(0, n_children)
+df <- data.frame(girls=n_girls, prob=dbinom(x=n_girls, size=n_children, prob=0.49))
+p <- (ggplot(df, aes(x=girls, y=prob)) +
+      geom_segment(aes(x=girls, xend=girls, yend=prob), y=0, size=12, color="grey") +
+      ylab("probability") + ylim(0, 0.30) +
+      scale_x_continuous("number of girls", breaks=df$girls, limits=c(-0.1, n_children + 0.1)))
+p
+ggsave(filename="eight_children_v3.png", p, width=8, height=4)
+
+## Probability of joining team, four shots or six
+set_ggplot_theme()
+four <- function(skill) {
+    return(1 - pbinom(q=1, size=4, prob=skill))
+}
+six <- function(skill) {
+    return(1 - pbinom(q=2, size=6, prob=skill))
+}
+color_4 <- "#0072B2"
+color_6 <- "#D55E00"
+p <- (ggplot(data.frame(x=c(0, 1)), aes(x=x)) +
+      stat_function(fun=four, color=color_4, size=2) +
+      stat_function(fun=six, color=color_6, size=2) +
+      scale_y_continuous("probability of joining", breaks=c(0, 0.5, 1)) +
+      annotate("text", x=0.3, y=0.68, label="four shots", color=color_4, size=8) +
+      annotate("text", x=0.52, y=0.35, label="six shots", color=color_6, size=8) +
+      scale_x_continuous("skill", breaks=c(0, 1)))
+p
+ggsave("proba_join.png", p, width=6, height=5)
+
+## Random walk
+get_df <- function(rounds=61) {
+    wealth <- rep(NA, rounds)
+    goes_broke <- FALSE
+    wealth[1] <- 2
+    last_round <- rounds-1
+    for(t in seq(2, length(wealth))) {
+        wealth[t] <- wealth[t-1] + sample(c(1, -1), size=1, prob=c(3/4, 1/4))
+        if(wealth[t] <= 0) {
+            goes_broke <- TRUE
+            last_round <- t-1
+            break
+        }
+    }
+    return(data.frame(t=seq(0, rounds-1), wealth=wealth, last_round=last_round,
+                      group=round(runif(1, 0, 10^6)), goes_broke=goes_broke))
+}
+
+df <- do.call(rbind, replicate(30, get_df(), simplify=F))
+df$broke <- df$wealth == 0
+set_ggplot_theme()
+p <- (ggplot(df, aes(x=t, y=wealth, group=group, color=goes_broke)) +
+      geom_line(size=2) +
+      geom_line(data=subset(df, goes_broke), size=2) +
+      geom_point(data=subset(df, goes_broke & t == last_round), size=5) +
+      scale_color_manual("", guide=FALSE, values=c("black", "#D55E00")) +
+      ## geom_hline(color="#D55E00", yintercept=0, linetype=2, size=1.5) +
+      xlab("rounds played") + ylab("dollars"))
+p
+ggsave("gambling.png", p, width=6, height=5)
+
+f <- function(x) {
+    df <- data.frame(a=c(0, 2, 10, 30, 70), b=c(2, 10, 30, 70, 90))
+    stopifnot(all(df$b[1:(nrow(df)-1)] == df$a[2:nrow(df)]))
+    stopifnot(all(df$a < df$b))
+    conditional <- rep(0, nrow(df))
+    proba <- rep(0, nrow(df))
+    for(i in seq_len(nrow(df))) {
+        if(x > df$b[i]) next
+        conditional[i] <- 0.5 * (max(x, df$a[i]) + df$b[i])
+        if(x < df$a[i]) {
+            proba[i] <- 0.2
+        } else {
+            proba[i] <- 0.2 * (df$b[i] - x) / (df$b[i] - df$a[i])
+        }
+    }
+    stopifnot(length(conditional) == length(proba))
+    stopifnot(length(conditional) == nrow(df))
+    proba <- proba / sum(proba)
+    return(sum(proba * conditional))
+}
+f_vec <- Vectorize(f)
+curve(f_vec, from=0, to=90)
+curve(f_vec(x) - x, from=0, to=90)
+f_vec(30)  # 65
+
+set_ggplot_theme()
+p <- (ggplot(data.frame(x=c(0, 90)), aes(x=x)) +
+      stat_function(fun=f_vec, color="#0072B2", size=2) +
+      geom_abline(intercept=0, slope=1, color="grey", size=2, linetype=2) +
+      scale_y_continuous("life expectancy", breaks=c(0, 31.4, 90), limits=c(0, 90)) +
+      scale_x_continuous("age", breaks=seq(0, 90, 30)))
+p
+ggsave("life_expectancy.png", p, width=6, height=5)
diff --git a/scripts/utils.R b/scripts/utils.R
new file mode 100644
index 0000000..73d1247
--- /dev/null
+++ b/scripts/utils.R
@@ -0,0 +1,36 @@
+set_ggplot_theme <- function(map=FALSE) {
+    require(ggplot2)
+    require(grid)  # For unit
+    theme_set(theme_bw())
+    ## For axis titles: margin instead of vjust
+    ## See https://stackoverflow.com/questions/14487188/increase-distance-between-text-and-title-on-the-y-axis
+    theme_update(axis.title.x=element_text(size=rel(1.4), margin=margin(10, 0, 0, 0)))
+    theme_update(axis.title.y=element_text(angle=90, size=rel(1.4),
+                                           margin=margin(0, 20, 0, 0)))
+    theme_update(axis.text.x=element_text(size=rel(1.2)))
+    theme_update(axis.text.y=element_text(size=rel(1.2)))
+    theme_update(plot.margin=unit(c(1, 1, 2, 2), "lines"))
+    theme_update(plot.title=element_text(size=rel(1.4), vjust=1.25))
+    theme_update(strip.background=element_rect(colour="white"))
+    theme_update(legend.key=element_blank())
+    theme_update(panel.border=element_blank())
+    theme_update(panel.grid.minor=element_blank())
+    if (map) {
+        theme_update(axis.text=element_blank())
+        theme_update(axis.ticks=element_blank())
+        theme_update(legend.background=element_blank())
+        theme_update(legend.margin=unit(0, "lines"))
+        theme_update(legend.position="bottom")
+        theme_update(panel.border=element_blank())
+        theme_update(panel.grid.major=element_blank())
+        theme_update(panel.grid.minor=element_blank())
+    }
+    return(invisible())
+}
+legend_guide <- guide_legend(direction="horizontal",
+                             title.position="top",
+                             label.position="bottom",
+                             label.hjust=0.5, label.vjust=2,
+                             title.hjust=0.5,
+                             label.theme=element_text(angle=0),
+                             keywidth=3.5, keyheight=1)