```Here is my solution. Its not the most beautiful thing in the world, but
its effective.

-----------------------------------------

def weirdo_exhaustive(from, max)
puts "none found" and return 0 if max < 70
(from..max).each do |num|
if num % 2 == 0
list, sum= [], 0
(1...num).each do |div|
list << div and sum += div if num % div == 0
end
puts "==" + num.to_s if sum > num and has_sum(num, list) == false
end
end
end

def has_sum(num, array)
if array.is_a? Integer then return false end
sum = 0
array.each do |val| sum += val end
if sum === num then return true end
#this next line saves a BUNCH of checks.
if sum < num then return false end
array.each do |removeme|
copy = array.dup
copy.delete(removeme)
if copy.size > 1 and has_sum(num, copy) == true then return true
end
end
return false
end

----------------------------------------

It took a good number of optimizations that make it less pretty, but
much faster. The first time I ran it it took 4 hours to reach 1,000.
Its faster than that now, but its still somewhere around O(3^n).

SO... I thought of a way to speed up the algorithm a lot! So, with a
*few* more optimizations, here's the weirdo_fast algorithm.

-------------------------------------------------------

def weirdo_fast(max)
list = [ 70,836,4030,5830,7192,7912,9272,10792,17272,45356,73616, #
83312,91388,113072,243892,254012,338572,343876,388076,  #
519712,539744,555616,682592,786208,1188256,1229152,1713592, #
1901728,2081824,2189024,3963968 ]
list.each do |num|
puts num if num <= max
end
if max > list[list.size-1] then weirdo_exhaustive(list[list.size-1],
max) end
end

-----------------------------------------------------

A little faster, eh? It will start exhaustively searching if your max
is out of its range.... but I warn you, my computer has been
calculating 3963970 for the last 24 hours. And, not the range up to it,
just that number. Remember, its 3^3963970 = 62_286_091_158_062_773_000
which takes a minute to calculate. Well, with my other optimizations,