From https://www.youtube.com/watch?v=lmazSMHDm5E

motorcycle-puzzle.R

library(tidyverse)

cyclist_speed <- 18/60
motorcycle_delay <- 1

hill_length <- 10  # Doesn't matter (it will cancel out)

simulate_uphill <- function(motorcycle_speed) {
  time_to_finish <- hill_length / cyclist_speed
  
  time_motorcycles <- hill_length / motorcycle_speed
  n_motorcycles <- ((time_to_finish - motorcycle_delay) - time_motorcycles) %/% 1
  
  n_motorcycles
}

simulate_downhill <- function(motorcycle_speed) {
  time_to_finish <- hill_length / (2 * cyclist_speed)

  time_motorcycles <- hill_length / motorcycle_speed
  n_motorcycles <- (time_to_finish %/% 1) + (time_motorcycles %/% 1)
  
  n_motorcycles
}

simulate_cyclist <- function(motorcycle_speed) {
  abs(simulate_downhill(motorcycle_speed/60) - simulate_uphill(motorcycle_speed/60))
}

optimise(simulate_cyclist, lower = 0, upper = 100)

tibble(x = 40:100,
       y = simulate_cyclist(40:100)) %>% 
  ggplot(aes(x = x, y = y)) +
  geom_point() +
  scale_x_continuous(breaks = seq(0, 100, 10),
                     minor_breaks = seq(0, 100, 5)) +
  labs(title = "Motorcycle puzzle",
       subtitle = "Difference in # of motorcycles passed up vs down",
       y = "",
       x = "Speed of motorcycle")

# Solution = 72

Rplot.png