morning_brew_puzzle.ex

defmodule MorningBrewPuzzle do
  @moduledoc """
    Brain Teaser from Morning Brew newsletter
    Each letter stands for a unique digit that makes the arithmetic equation true. Can you solve it?
    
    (J+O+I+N+T)^3=JOINT
  """
  
  @doc """
    Build permutations of digits from 1 to 9 (exclude 0 for simplifying a bit), slice
    each element to 5 digits and unique it and then see which one solves the puzzle.
  """
  def solve_puzzle do
    build_list()
    |> Enum.find(fn x -> is_solution?(x) end)
  end

  def build_list do
    1..9
    |> Enum.to_list()
    |> permutations()
    |> Enum.map(fn x -> Enum.slice(x, 0, 5) end)
    |> Enum.uniq()
  end

  def permutations([]), do: [[]]

  def permutations(list),
    do: for(elem <- list, rest <- permutations(list -- [elem]), do: [elem | rest])

  def is_solution?(num_list) do
    val = build_number(num_list)
    add_val = num_list |> add_list() |> :math.pow(3)
    val == add_val
  end

  def add_list(num_list) do
    num_list
    |> Enum.reduce(0, fn x, acc -> acc + x end)
  end

  def build_number(num_list) do
    num_list
    |> Enum.join("")
    |> String.to_integer()
  end
end