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Message: [QUOTE="Ken Bloom, post: 4525656"] Since the order of digits in the number doesn't matter, here's code to generate digits whose numbers are in nondecreasing order. This makes the "happiest number" test finish almost instantly when the numbers are generated this way: #generates all numbers in the given range whose digits are in #nondecreasing order. the order in which the numbers are generated is #undefined, so it's possible for 123 to appear before 23, for #example. def nondec_digits(range,&b) yield 0 if range.first<=0 (1..9).each { |x| noninc_digits_internal(x,x,range,&b) } end def nondec_digits_internal(last,accum,range,&b) (last..9).each do |x| iaccum=accum*10+x b.call(iaccum) if range.include?(iaccum) noninc_digits_internal(x,iaccum,range,&b) if iaccum<=range.last end end [/QUOTE]