```I have a solution for the "effectively useless" basket. It's a naive
algorithm, and I haven't yet received a number above 70 from it.

The advantages are that it's straightforward idiomatic Ruby, and core of the
algorithm is expressed about as tersely as Martin's definition. And I like
my ArraySubsetList class.

class Fixnum
def divisors
(1..self).select {|i| self % i == 0 }
end
end
module Enumerable
def sum
inject(0) {|m, o| m + o }
end
end
class Array
def subsets
ArraySubsetList.new(self)
end
end
class ArraySubsetList
def initialize(array)
@array = array
end
def [](index)
return nil unless (0...size) === index
ret = []
@array.size.times {|i| ret << @array[i] if index[i] == 1 }
ret
end
def each
size.times {|bits| yield self[bits] }
end
include Enumerable
def size
1 << @array.size
end
alias length size
end
def wierd_numbers_up_to(max)
ret = []
for n in 1..max
# A weird number is defined as a number, n, such that the sum of all
its divisors
# (excluding n itself) is greater than n, but no subset of its
divisors sums up to
# exactly n.
divs = n.divisors
divs.delete i
if divs.sum > i &&
divs.subsets.select {|subset| subset.sum == i }.empty?
ret << i
yield i if block_given?
end
end
ret
end
if \$0 == __FILE__
if ARGV.size == 1 && (ARGV[0].to_i rescue 0) > 0
wierd_numbers_up_to(ARGV[0].to_i) {|n| puts n }
else
puts "usage: #\$0 n\n  Find all weird numbers less than n"
end
end

Cheers,
Dave

```