problem_18.rb

array = [[75],
         [95, 64],
         [17, 47, 82],
         [18, 35, 87, 10],
         [20,  4, 82, 47, 65],
         [19,  1, 23, 75,  3, 34],
         [88,  2, 77, 73,  7, 63, 67],
         [99, 65,  4, 28,  6, 16, 70, 92],
         [41, 41, 26, 56, 83, 40, 80, 70, 33],
         [41, 48, 72, 33, 47, 32, 37, 16, 94, 29],
         [53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14],
         [70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57],
         [91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48],
         [63, 66,  4, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31],
         [ 4, 62, 98, 27, 23,  9, 70, 98, 73, 93, 38, 53, 60,  4, 23]]

until array.size == 1 do
  array[-2].each_with_index do |n, i|
    first_num = n + array[-1][i]
    sec_num = n + array[-1][i + 1]
    if first_num > sec_num
      array[-2][i] = first_num
    else
      array[-2][i] = sec_num
    end
  end
  array.delete_at(-1)
end

p array