Commit 13559f9

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+require 'spec_helper'
+require 'prime'
+=begin
+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?
+
+help:
+* http://www.wikihow.com/Determine-the-Number-of-Divisors-of-an-Integer
+* https://www.khanacademy.org/math/pre-algebra/factors-multiples/prime_factorization/v/prime-factorization
+=end
+
+class TriangleNumbers
+  include Enumerable
+
+  def each(&block)
+    n = 1
+    loop do
+      block.call(sum_of(n))
+      n += 1
+    end
+  end
+
+  private
+
+  def sum_of(n)
+    n.downto(0).inject(0) { |total, m| total += m }
+  end
+
+end
+
+describe 'problem 12' do
+  describe TriangleNumbers do
+    it 'produces the first 7 triangle numbers' do
+      expect(subject.take(7)).to eql([1, 3, 6, 10, 15, 21, 28])
+    end
+
+    it 'produces the first 10 triangle numbers' do
+      expect(subject.take(10)).to eql([1, 3, 6, 10, 15, 21, 28, 36, 45, 55])
+    end
+  end
+
+  class Divisors
+    def divisors_for(n)
+      1.upto(n).find_all do |x|
+        (n % x).zero?
+      end
+    end
+
+    def number_of_divisors_for(n)
+      prime_factors = n.prime_division
+      powers_plus_one = prime_factors.map do |(prime, exponent)|
+        exponent + 1
+      end
+      powers_plus_one.inject(1) { |total, power| total *= power }
+    end
+  end
+
+  describe Divisors do
+    it 'returns each factor for a number' do
+      {
+        1 => [1],
+        2 => [1, 2],
+        3 => [1,3],
+        4 => [1,2,4],
+        5 => [1, 5],
+        6 => [1,2,3,6],
+        7 => [1, 7],
+        8 => [1, 2, 4, 8],
+        9 => [1, 3, 9],
+        10 => [1,2,5,10],
+        11 => [1, 11],
+        12 => [1, 2, 3, 4, 6, 12],
+        13 => [1, 13],
+        14 => [1, 2, 7, 14],
+        15 => [1,3,5,15],
+        16 => [1, 2, 4, 8, 16],
+        21 => [1,3,7,21],
+        24 => [1, 2, 3, 4, 6, 8, 12, 24],
+        28 => [1, 2, 4, 7, 14, 28],
+      }.each do |key, values|
+        expect(subject.divisors_for(key)).to eql(values)
+      end
+    end
+
+    it 'brute forces the answer' do
+      subject = TriangleNumbers.new
+      divisors = Divisors.new
+      result = subject.find do |n|
+        divisors.number_of_divisors_for(n) >= 500
+      end
+      expect(result).to eql(76576500)
+    end
+  end
+end