Embed.ly challenge http://apply.embed.ly/

Challenge 1.rb

$cache = []

def fib(n)
  return $cache[n] unless $cache[n].nil?
  return 1 if n == 0
  res = n * fib(n-1)
  $cache << res
  return $cache[n-1]
end

sum = 0
i = 0

while sum != 8001
  i += 1
  num = fib(i)
  digits = num.to_s.split('')
  sum = digits.reduce(0) do |tsum, value|
    tsum + value.to_i
  end
end

puts i-1

Challenge 2.rb

require 'open-uri'
require 'nokogiri'

module Enumerable
  def sum
    self.inject(0){|accum, i| accum + i }
  end
  
  def mean
    self.sum/self.length.to_f
  end
  
  def sample_variance
    m = self.mean
    sum = self.inject(0){|accum, i| accum +(i-m)**2 }
    sum/(self.length - 1).to_f
  end
  
  def standard_deviation
    return Math.sqrt(self.sample_variance)
  end
end

doc = Nokogiri::HTML(open("http://apply.embed.ly/static/data/2.html"))
depths = []
doc.css('p').each do |node|
  depths << node.ancestors.count
end

puts depths.standard_deviation

Challenge 3.rb

$cache = []

def fib(n)
  return $cache[n] unless $cache[n].nil?
  return 1 if n == 0
  res = n * fib(n-1)
  $cache << res
  return $cache[n-1]
end

total_words = fib(900)
sum_words = 0

for i in 1..900
  sum_words += total_words/i
end

sum = 0
i = 0
while sum <= sum_words/2
  i += 1
  sum += total_words/i
end

puts i