How many permutations of rows can make 51 stars, max of 25 per row, max of 10 rows, can alternate

brute_force_calculate_stars.exs

defmodule FlagStars do
  def calculate() do
    Enum.reduce(1..25, [], fn first, acc ->
      acc ++ Enum.reduce(1..25, [], fn second, acc ->
        acc ++ Enum.reduce(1..10, [], fn rows, acc ->
          acc ++ cond do
            (rows * first) == 51 -> [{first, rows}]
            ((div(rows, 2) + rem(rows, 2)) * first) + (div(rows, 2) * second) == 51 -> [{first, second, rows}]
            true -> []
          end
        end)
      end)
    end)
    |> Enum.uniq()
    |> Enum.each(&(print_stars(&1)))
  end

  def print_stars({first, rows}) do
    IO.puts "#{rows} rows with #{first} each"
    Enum.each(1..rows, fn _ ->
      IO.puts String.duplicate("*", first)
    end)
    IO.puts "\n"
  end

  def print_stars({first, second, rows}) do
    IO.puts "#{rows} rows alternating #{first} and #{second}"
    Enum.each(1..rows, fn row ->
      case rem(row, 2) do
        1 -> IO.puts String.duplicate("*", first)
        0 -> IO.puts String.duplicate("*", second)
      end
    end)
    IO.puts "\n"
  end
end

FlagStars.calculate()

flag_stars.txt

6 rows alternating 1 and 17
*
****************
*
****************
*
****************


5 rows alternating 1 and 24
*
************************
*
************************
*


6 rows alternating 2 and 15
**
***************
**
***************
**
***************


9 rows alternating 3 and 9
***
*********
***
*********
***
*********
***
*********
***


7 rows alternating 3 and 13
***
*************
***
*************
***
*************
***


6 rows alternating 3 and 14
***
**************
***
**************
***
**************


5 rows alternating 3 and 21
***
*********************
***
*********************
***


6 rows alternating 4 and 13
****
*************
****
*************
****
*************


6 rows alternating 5 and 12
*****
************
*****
************
*****
************


5 rows alternating 5 and 18
*****
******************
*****
******************
*****


7 rows alternating 6 and 9
******
*********
******
*********
******
*********
******


6 rows alternating 6 and 11
******
***********
******
***********
******
***********


9 rows alternating 7 and 4
*******
****
*******
****
*******
****
*******
****
*******


6 rows alternating 7 and 10
*******
**********
*******
**********
*******
**********


5 rows alternating 7 and 15
*******
***************
*******
***************
*******


6 rows alternating 8 and 9
********
*********
********
*********
********
*********


7 rows alternating 9 and 5
*********
*****
*********
*****
*********
*****
*********


6 rows alternating 9 and 8
*********
********
*********
********
*********
********


5 rows alternating 9 and 12
*********
************
*********
************
*********


6 rows alternating 10 and 7
**********
*******
**********
*******
**********
*******


6 rows alternating 11 and 6
***********
******
***********
******
***********
******


5 rows alternating 11 and 9
***********
*********
***********
*********
***********


7 rows alternating 12 and 1
************
*
************
*
************
*
************


6 rows alternating 12 and 5
************
*****
************
*****
************
*****


6 rows alternating 13 and 4
*************
****
*************
****
*************
****


5 rows alternating 13 and 6
*************
******
*************
******
*************


3 rows alternating 13 and 25
*************
*************************
*************


6 rows alternating 14 and 3
**************
***
**************
***
**************
***


3 rows alternating 14 and 23
**************
***********************
**************


6 rows alternating 15 and 2
***************
**
***************
**
***************
**


5 rows alternating 15 and 3
***************
***
***************
***
***************


3 rows alternating 15 and 21
***************
*********************
***************


6 rows alternating 16 and 1
****************
*
****************
*
****************
*


3 rows alternating 16 and 19
****************
*******************
****************


3 rows with 17 each
*****************
*****************
*****************


3 rows alternating 18 and 15
******************
***************
******************


3 rows alternating 19 and 13
*******************
*************
*******************


3 rows alternating 20 and 11
********************
***********
********************


3 rows alternating 21 and 9
*********************
*********
*********************


3 rows alternating 22 and 7
**********************
*******
**********************


3 rows alternating 23 and 5
***********************
*****
***********************


3 rows alternating 24 and 3
************************
***
************************


3 rows alternating 25 and 1
*************************
*
*************************