```#!/usr/bin/env ruby
#
# Ruby Quiz Weird Numbers solution.
#
# I found only two significant optimizations:
# 1. Use continuations when generating the powerset of
#    divisors to sum. Evaluate each sum immediately
#    and break upon determining the number is semiperfect.
# 2. Sort the divisors in descending order so that
#    subsets involving the larger divisors are considered
#    first.
#
# On my machine, generating results for numbers up to 5000
# took less than a minute. Generating results up to 12000
# took almost twenty minutes.
#
# This powerset implementation was inspired by a post to
# Ruby-Talk by Robert Klemme on May 14, 2004:
#
http://blade.nagaokaut.ac.jp/cgi-bin/scat.rb/ruby/ruby-talk/100258?help-en
#
#

module Enumerable

def powerset
for element_map in 0...(1 << self.length) do
subset = []
each_with_index do |element, index|
subset << element if element_map[index] == 1
end
yield subset
end
end

end

class Array

def sum
return self.inject { |total,x| total += x }
end

end

class Integer

def weird?
divs = self.divisors.reverse
return false unless divs.sum > self
divs.powerset { |subset| return false if subset.sum == self }
return true
end

def divisors
list = []
(1..Math.sqrt(self).to_i).each do |x|
if (self / x) * x == self
list << x
list << (self / x) unless x == 1 or (self / x) == x
end
end
return list.sort
end

end

####################

(1..5000).each { |n| puts n if n.weird? }

--
Posted via http://www.ruby-forum.com/.

```