18.rb

s = [[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]]

v = s.dup
s.each_index do |x|
  s[x].each_index do |y|
    if x == 0
      v[x][y] = s[x][y]
    elsif y == 0
      v[x][y] = s[x - 1][0] + s[x][y]
    elsif y == s[x].length - 1
      v[x][y] = s[x - 1][-1] + s[x][y]
    else
      v[x][y] = s[x][y] + (s[x - 1][y - 1] > s[x - 1][y] ? s[x - 1][y - 1] : s[x - 1][y] )
    end
  end
end

#p v
p v[-1].sort[-1]