Solve a logic puzzle with Elixir

logic_puzzle.exs

defmodule LogicChallenge do
  @type combination :: String.t()
  
  @spec run :: combination | :error
  def run() do
    1..999
    |> Enum.map(&to_string/1)
    |> Enum.map(&String.pad_leading(&1, 3, "0"))
    |> Enum.map(&String.graphemes/1)
    |> Enum.filter(&check/1)
    |> case do
      [x] -> Enum.join(x)
      _ -> :error
    end
  end
  
  defp check([_, _, _] = n) do
    logic_1(n) and logic_2(n) and logic_3(n) and logic_4(n) and logic_5(n)
  end

  defp logic_1([a, b, c]) when a in ["4", "7"] do
    b not in ["1", "7"] and c not in ["1", 4]
  end
  defp logic_1([a, b, c]) when b in ["1", "7"] do
    a not in ["4", "7"] and c not in ["1", 4]
  end
  defp logic_1([a, b, c]) when c in ["1", "4"] do
    a not in ["4", "7"] and b not in ["1", "7"]
  end
  defp logic_1([_, _, _]), do: false

  defp logic_2(["1", a, b]) when a not in ["8", "9"] and b not in ["8", "9"], do: true
  defp logic_2([a, "8", b]) when a not in ["1", "9"] and b not in ["1", "9"], do: true
  defp logic_2([a, b, "9"]) when a not in ["1", "8"] and b not in ["1", "8"], do: true
  defp logic_2([_, _, _]), do: false

  defp logic_3(["6", "4", x]) when x != "9", do: true
  defp logic_3(["4", x, "6"]) when x != "9", do: true
  defp logic_3([x, "4", "6"]) when x != "9", do: true
  defp logic_3(["4", "9", x]) when x != "6", do: true
  defp logic_3(["4", x, "9"]) when x != "6", do: true
  defp logic_3([x, "4", "9"]) when x != "6", do: true
  defp logic_3(["6", "9", x]) when x != "4", do: true
  defp logic_3(["6", x, "9"]) when x != "4", do: true
  defp logic_3([x, "9", "6"]) when x != "4", do: true
  defp logic_3(_), do: false

  defp logic_4([a, b, c]) when a in ["5", "2", "3"] or b in ["5", "2", "3"] or c in ["5", "2", 3],
    do: false

  defp logic_4([_, _, _]), do: true

  defp logic_5([a, b, c]) when a in ["8", "6"] do
    b not in ["2", "6"] and c not in ["2", "8"]
  end

  defp logic_5([a, b, c]) when b in ["2", "6"] do
    a not in ["8", "6"] and c not in ["2", "8"]
  end

  defp logic_5([a, b, c]) when c in ["2", "8"] do
    a not in ["8", "6"] and b not in ["2", "6"]
  end

  defp logic_5([_, _, _]), do: false
end

IO.puts LogicChallenge.run()