gistfile1.txt

[5, ["1 x 5"]]
[7, ["1 x 7", "5 x 1 + 1 x 2"]]
[10, ["1 x 10", "2 x 5"]]
[13, ["1 x 13", "5 x 2 + 1 x 3", "10 x 1 + 1 x 3"]]
[15, ["1 x 15", "3 x 5", "10 x 1 + 1 x 5"]]
[18, ["1 x 18", "5 x 3 + 1 x 3", "10 x 1 + 1 x 8"]]
[20, ["1 x 20", "4 x 5", "10 x 2"]]
[25, ["1 x 25", "5 x 5", "10 x 2 + 1 x 5"]]

split_license_keys.rb

def convert_to_factors(seat_count,data)
  data.map do |c,rem,div|
    if c*div == seat_count
        "#{c} x #{div}".split(/ x /).sort.join(" x ")
    elsif c*div < seat_count and rem != 0 and div != 0
        "#{c} x #{div} + 1 x #{rem}"
    end
  end.compact.uniq
end

def split_license_keys(seat_count)
  convert_to_factors seat_count,
  ([1, 5, 10, 25].map do |c|
    [ c, seat_count % c.to_f, seat_count / c.to_f ]
  end.map do |c,rem,div|
    [ c, rem.floor, div.floor ]
  end)
end

p [5,  split_license_keys(5)]
p [7,  split_license_keys(7)]
p [10, split_license_keys(10)]
p [13, split_license_keys(13)]
p [15, split_license_keys(15)]
p [18, split_license_keys(18)]
p [20, split_license_keys(20)]
p [25, split_license_keys(25)]