day-6.livemd

Day 6: Wait For It

Part one

I didn't parse the input, since it was so simple. Just smashed it into the code here... 🤷🏼‍♂️

input_part_one = [[46, 214], [80, 1177], [78, 1402], [66, 1024]]

defmodule WaitForIt do
  def number_of_ways_to_beat_multiplied(races) do
    races
    |> Stream.map(fn [time, distance] -> number_of_ways_to_beat(time, distance) end)
    |> Enum.reduce(1, &Kernel.*/2)
  end

  def number_of_ways_to_beat(time, distance) do
    0..time
    |> Stream.map(&(&1 * (time - &1)))
    |> Stream.filter(&(&1 > distance))
    |> Enum.count()
  end
end

WaitForIt.number_of_ways_to_beat_multiplied(input_part_one)
# 512_295

Part two

input_part_two = [[46_807_866, 214_117_714_021_024]]

WaitForIt.number_of_ways_to_beat_multiplied(input_part_two)
# 36_530_883

... or solve the quadratic equation:

d = x * (t - x) => -x^2 + tx - d = 0

this equation has two roots, for d = 46_807_866 and t = 214_117_714_021_024:

• 5_138_491.2
• 41_669_374.8

considering all points in-between need to be integers, this gives this amount of possibilities to beat the target distance:

41_669_375 - 5_138_492 = 36_530_883