Untitled

class Integer
  def pentagonal?
    ((Math.sqrt(24 * self + 1) + 1) / 6) % 1 == 0
  end
end

def pentagonal_number(n)
  n * (3 * n - 1) / 2
end

max = 10000
pentagonal_numbers = (1..max).to_a.map {|i| pentagonal_number(i) }

pentagonal_numbers.each do |sum|
  pentagonal_numbers.select {|v| v < sum / 2 }.each do |p1|
    p2 = sum - p1
    d = p2 - p1
    if p2.pentagonal? && d.pentagonal?
      p "sum:#{sum} p1:#{p1} p2:#{p2} d:#{d}"
      exit
    end
  end
end