prob012.rb

#!/usr/bin/env ruby1.9

# Project Euler, Problem 12
#
# The sequence of triangle numbers is generated by adding the natural
# numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 =
# 28. The first ten terms would be:
#
#       1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
#
# Let us list the factors of the first seven triangle numbers:
#
#        1: 1
#        3: 1,3
#        6: 1,2,3,6
#       10: 1,2,5,10
#       15: 1,3,5,15
#       21: 1,3,7,21
#       28: 1,2,4,7,14,28
#
# We can see that 28 is the first triangle number to have over five divisors.
#
# What is the value of the first triangle number to have over five hundred
# divisors?
#
# Lawrence Velazquez
# 10 March 2012

class Integer
  def divisors
    divs = [1, self]
    2.upto(Math.sqrt(self)) {|i| divs.concat [i, self / i] if self % i == 0}
    divs
  end
end

i = 1
ans = while true
  tri_n = i * (i + 1) / 2
  break tri_n if tri_n.divisors.count > 500
  i += 1
end
puts ans